Hans Andersen

All Publications

• Dynamic force matching: Construction of dynamic coarse-grained models with realistic short time dynamics and accurate long time dynamics JOURNAL OF CHEMICAL PHYSICS Davtyan, A., Voth, G. A., Andersen, H. C. 2016; 145 (22)

  Abstract

  We recently developed a dynamic force matching technique for converting a coarse-grained (CG) model of a molecular system, with a CG potential energy function, into a dynamic CG model with realistic dynamics [A. Davtyan et al., J. Chem. Phys. 142, 154104 (2015)]. This is done by supplementing the model with additional degrees of freedom, called "fictitious particles." In that paper, we tested the method on CG models in which each molecule is coarse-grained into one CG point particle, with very satisfactory results. When the method was applied to a CG model of methanol that has two CG point particles per molecule, the results were encouraging but clearly required improvement. In this paper, we introduce a new type (called type-3) of fictitious particle that exerts forces on the center of mass of two CG sites. A CG model constructed using type-3 fictitious particles (as well as type-2 particles previously used) gives a much more satisfactory dynamic model for liquid methanol. In particular, we were able to construct a CG model that has the same self-diffusion coefficient and the same rotational relaxation time as an all-atom model of liquid methanol. Type-3 particles and generalizations of it are likely to be useful in converting more complicated CG models into dynamic CG models.

  View details for DOI 10.1063/1.4971430

  View details for Web of Science ID 000391582700010

  View details for PubMedID 27984910

• Critical Slowing of Density Fluctuations Approaching the Isotropic-Nematic Transition in Liquid Crystals: 2D IR Measurements and Mode Coupling Theory. journal of physical chemistry. B Sokolowsky, K. P., Bailey, H. E., Hoffman, D. J., Andersen, H. C., Fayer, M. D. 2016; 120 (28): 7003-7015

  Abstract

  Two-dimensional infrared (2D IR) data are presented for a vibrational probe in three nematogens: 4-cyano-4'-pentylbiphenyl, 4-cyano-4'-octylbiphenyl, and 4-(trans-4-amylcyclohexyl)-benzonitrile. The spectral diffusion time constants in all three liquids in the isotropic phase are proportional to [T*/(T - T*)](1/2), where T* is 0.5-1 K below the isotropic-nematic phase transition temperature (TNI). Rescaling to a reduced temperature shows that the decays of the frequency-frequency correlation function (FFCF) for all three nematogens fall on the same curve, suggesting a universal dynamic behavior of nematogens above TNI. Spectral diffusion is complete before significant orientational relaxation in the liquid, as measured by optically heterodyne detected-optical Kerr effect (OHD-OKE) spectroscopy, and before any significant orientational randomization of the probe measured by polarization selective IR pump-probe experiments. To interpret the OHD-OKE and FFCF data, we constructed a mode coupling theory (MCT) schematic model for the relationships among three correlation functions: ϕ1, a correlator for large wave vector density fluctuations; ϕ2, the orientational correlation function whose time derivative is the observable in the OHD-OKE experiment; and ϕ3, the FFCF for the 2D IR experiment. The equations for ϕ1 and ϕ2 match those in the previous MCT schematic model for nematogens, and ϕ3 is coupled to the first two correlators in a straightforward manner. Resulting models fit the data very well. Across liquid crystals, the temperature dependences of the coupling constants show consistent, nonmonotonic behavior. A remarkable change in coupling occurs at ∼5 K above TNI, precisely where the rate of spectral diffusion in 5CB was observed to deviate from that of a similar nonmesogenic liquid.

  View details for DOI 10.1021/acs.jpcb.6b04997

  View details for PubMedID 27363680

• Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence JOURNAL OF CHEMICAL PHYSICS Davtyan, A., Dama, J. F., Voth, G. A., Andersen, H. C. 2015; 142 (15)

  Abstract

  Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

  View details for DOI 10.1063/1.4917454

  View details for Web of Science ID 000353307700005

  View details for PubMedID 25903863

• A diagrammatic kinetic theory of density fluctuations in simple liquids in the overdamped limit. I. A long time scale theory for high density JOURNAL OF CHEMICAL PHYSICS Pilkiewicz, K. R., Andersen, H. C. 2014; 140 (15)

  View details for DOI 10.1063/1.4871111

  View details for Web of Science ID 000336045800027

• A diagrammatic kinetic theory of density fluctuations in simple liquids in the overdamped limit. II. The one-loop approximation JOURNAL OF CHEMICAL PHYSICS Pilkiewicz, K. R., Andersen, H. C. 2014; 140 (15)

  View details for DOI 10.1063/1.4871112

  View details for Web of Science ID 000336045800028

• Modified scaling principle for rotational relaxation in a model for suspensions of rigid rods JOURNAL OF CHEMICAL PHYSICS Tse, Y. S., Andersen, H. C. 2013; 139 (4)

  Abstract

  We have performed simulations of the model of infinitely thin rigid rods undergoing rotational and translational diffusion, subject to the restriction that no two rods can cross one another, for various concentrations well into the semidilute regime. We used a modification of the algorithm of Doi et al. [J. Phys. Soc. Jpn. 53, 3000 (1984)] that simulates diffusive dynamics using a Monte Carlo method and a nonzero time step. In the limit of zero time step, this algorithm is an exact description of diffusive dynamics subject to the noncrossing restriction. For a wide range of concentrations in the semidilute regime, we report values of the long time rotational diffusion constant of the rods, extrapolated to the limit of zero time step, for various sets of values of the infinite dilution (bare) diffusion constants. These results are compared with the results of a previous simulation of the model by Doi et al. and of previous simulations of rods with finite aspect ratio by Fixman and by Cobb and Butler that had been extrapolated to the limit of infinitely thin rods. The predictions of the Doi-Edwards (DE) scaling law do not hold for this model for the concentrations studied. The simulation data for the model display two deviations from the predictions of the DE theory that have been observed in experimental systems in the semidilute regime, namely, the very slow approach toward DE scaling behavior as the concentration is increased and the large value of the prefactor in the DE scaling law. We present a modified scaling principle for this model that is consistent with the simulation results for a broad range of concentrations in the semidilute regime. The modified scaling principle takes into account two physical effects, which we call "leakage" and "drift," that were found to be important for the transport properties of a simpler model of nonrotating rods on a lattice [Y.-L. S. Tse and H. C. Andersen, J. Chem. Phys. 136, 024904 (2012)].

  View details for DOI 10.1063/1.4816001

  View details for Web of Science ID 000322949300067

  View details for PubMedID 23902017

• The multiscale coarse-graining method. IX. A general method for construction of three body coarse-grained force fields JOURNAL OF CHEMICAL PHYSICS Das, A., Andersen, H. C. 2012; 136 (19)

  Abstract

  The multiscale coarse-graining (MS-CG) method is a method for constructing a coarse-grained (CG) model of a system using data obtained from molecular dynamics simulations of the corresponding atomically detailed model. The formal statistical mechanical derivation of the method shows that the potential energy function extracted from an MS-CG calculation is a variational approximation for the true potential of mean force of the CG sites, one that becomes exact in the limit that a complete basis set is used in the variational calculation if enough data are obtained from the atomistic simulations. Most applications of the MS-CG method have employed a representation for the nonbonded part of the CG potential that is a sum of all possible pair interactions. This approach, despite being quite successful for some CG models, is inadequate for some others. Here we propose a systematic method for including three body terms as well as two body terms in the nonbonded part of the CG potential energy. The current method is more general than a previous version presented in a recent paper of this series [L. Larini, L. Lu, and G. A. Voth, J. Chem. Phys. 132, 164107 (2010)], in the sense that it does not make any restrictive choices for the functional form of the three body potential. We use hierarchical multiresolution functions that are similar to wavelets to develop very flexible basis function expansions with both two and three body basis functions. The variational problem is solved by a numerical technique that is capable of automatically selecting an appropriate subset of basis functions from a large initial set. We apply the method to two very different coarse-grained models: a solvent free model of a two component solution made of identical Lennard-Jones particles and a one site model of SPC/E water where a site is placed at the center of mass of each water molecule. These calculations show that the inclusion of three body terms in the nonbonded CG potential can lead to significant improvement in the accuracy of CG potentials and hence of CG simulations.

  View details for DOI 10.1063/1.4705417

  View details for Web of Science ID 000304303500015

  View details for PubMedID 22612087

• The multiscale coarse-graining method. X. Improved algorithms for constructing coarse-grained potentials for molecular systems JOURNAL OF CHEMICAL PHYSICS Das, A., Lu, L., Andersen, H. C., Voth, G. A. 2012; 136 (19)

  Abstract

  The multiscale coarse-graining (MS-CG) method uses simulation data for an atomistic model of a system to construct a coarse-grained (CG) potential for a coarse-grained model of the system. The CG potential is a variational approximation for the true potential of mean force of the degrees of freedom retained in the CG model. The variational calculation uses information about the atomistic positions and forces in the simulation data. In principle, the resulting MS-CG potential will be an accurate representation of the true CG potential if the basis set for the variational calculation is complete enough and the canonical distribution of atomistic states is well sampled by the data set. In practice, atomistic configurations that have very high potential energy are not sampled. As a result there usually is a region of CG configuration space that is not sampled and about which the data set contains no information regarding the gradient of the true potential. The MS-CG potential obtained from a variational calculation will not necessarily be accurate in this unsampled region. A priori considerations make it clear that the true CG potential of mean force must be very large and positive in that region. To obtain an MS-CG potential whose behavior in the sampled region is determined by the atomistic data set, and whose behavior in the unsampled region is large and positive, it is necessary to intervene in the variational calculation in some way. In this paper, we discuss and compare two such methods of intervention, which have been used in previous MS-CG calculations for dealing with nonbonded interactions. For the test systems studied, the two methods give similar results and yield MS-CG potentials that are limited in accuracy only by the incompleteness of the basis set and the statistical error of associated with the set of atomistic configurations used. The use of such methods is important for obtaining accurate CG potentials.

  View details for DOI 10.1063/1.4705420

  View details for Web of Science ID 000304303500016

  View details for PubMedID 22612088

• The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis functions and basis function selection in the construction of coarse-grained force fields JOURNAL OF CHEMICAL PHYSICS Das, A., Andersen, H. C. 2012; 136 (19)

  Abstract

  The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a molecular system using data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The coarse-grained potential obtained using the MS-CG method is a variational approximation for the exact many-body potential of mean force for the coarse-grained sites. Here we propose a new numerical algorithm with noise suppression capabilities and enhanced numerical stability for the solution of the MS-CG variational problem. The new method, which is a variant of the elastic net method [Friedman et al., Ann. Appl. Stat. 1, 302 (2007)], allows us to construct a large basis set, and for each value of a so-called "penalty parameter" the method automatically chooses a subset of the basis that is most important for representing the MS-CG potential. The size of the subset increases as the penalty parameter is decreased. The appropriate value to choose for the penalty parameter is the one that gives a basis set that is large enough to fit the data in the simulation data set without fitting the noise. This procedure provides regularization to mitigate potential numerical problems in the associated linear least squares calculation, and it provides a way to avoid fitting statistical error. We also develop new basis functions that are similar to multiresolution Haar functions and that have the differentiability properties that are appropriate for representing CG potentials. We demonstrate the feasibility of the combined use of the elastic net method and the multiresolution basis functions by performing a variational calculation of the CG potential for a relatively simple system. We develop a method to choose the appropriate value of the penalty parameter to give the optimal basis set. The combined effect of the new basis functions and the regularization provided by the elastic net method opens the possibility of using very large basis sets for complicated CG systems with many interaction potentials without encountering numerical problems in the variational calculation.

  View details for DOI 10.1063/1.4705384

  View details for Web of Science ID 000304303500014

  View details for PubMedID 22612086

• A lattice model of the translational dynamics of nonrotating rigid rods JOURNAL OF CHEMICAL PHYSICS Tse, Y. S., Andersen, H. C. 2012; 136 (2)

  Abstract

  We present a lattice model of oriented, nonrotating, rigid rods in three dimensions with random walk dynamics, computer simulation results for the model, and a theory for the translational diffusion constant of the rods in the perpendicular direction, D(⊥), in the semidilute regime. The theory is based on the "tube model" of Doi-Edwards (DE) theory for the rotational diffusion constant of rods that can both translate and rotate in continuous space. The theory predicts that D(⊥) is proportional to (νL(3))(-2), where ν is the concentration of rods and L is the length of the rods, which is analogous to the Doi-Edwards scaling law for rotational diffusion. The simulations find that, as νL(3) is increased, the approach to the limit of DE scaling is slow, and the -2 power in the DE scaling law is never quite achieved even at the highest concentration (νL(3) = 200) simulated. We formulate a quantitative theory for the prefactor in the scaling relationship using only DE ideas, but it predicts a proportionality constant that is much too small. To explain this discrepancy, we modify the DE approach to obtain a more accurate estimate of the average tube radius and take into account effects of perpendicular motion of rods that are not included in the original DE theory. With these changes, the theory predicts values of D(⊥) that are in much better agreement with the simulations. We propose a new scaling relationship that fits the data very well. This relationship suggests that the DE scaling law is the correct description of the scaling for infinitely thin rods only in the limit of infinite concentration, and that corrections to the DE scaling law because of finite concentration are significant even at concentrations that are well inside the semidilute regime. The implications of these results for the DE theory of rotating rods are discussed.

  View details for DOI 10.1063/1.3673791

  View details for Web of Science ID 000299126400058

  View details for PubMedID 22260613

• A Bayesian method for construction of Markov models to describe dynamics on various time-scales JOURNAL OF CHEMICAL PHYSICS Rains, E. K., Andersen, H. C. 2010; 133 (14)

  Abstract

  The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time-scales.

  View details for DOI 10.1063/1.3496438

  View details for Web of Science ID 000283200400016

  View details for PubMedID 20949993

• Statistical mechanical basis of coarse graining Das, A., Andersen, H. C. AMER CHEMICAL SOC. 2010

  View details for Web of Science ID 000208164702360

• The multiscale coarse-graining method. V. Isothermal-isobaric ensemble JOURNAL OF CHEMICAL PHYSICS Das, A., Andersen, H. C. 2010; 132 (16)

  Abstract

  The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a system using the data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The MS-CG method, as originally formulated for systems at constant volume, has previously been given a rigorous statistical mechanical basis for the canonical ensemble. Here, we propose and test a version of the MS-CG method suitable for the isothermal-isobaric ensemble. The method shows how to construct an effective potential energy function for a CG system that generates the correct volume fluctuations as well as correct distribution functions in the configuration space of the CG sites. The formulation of the method requires introduction of an explicitly volume dependent term in the potential energy function of the CG system. The theory is applicable to simulations with isotropic volume fluctuations and cases where both the atomistic and CG models do not have any intramolecular constraints, but it is straightforward to extend the theory to more general cases. The present theory deals with systems that have short ranged interactions. (The extension to Coulombic forces using Ewald methods requires additional considerations.) We test the theory for constant pressure MS-CG simulations of a simple model of a solution. We show that both the volume dependent and the coordinate dependent parts of the potential are transferable to larger systems than the one used to obtain these potentials.

  View details for DOI 10.1063/1.3394862

  View details for Web of Science ID 000277241500010

  View details for PubMedID 20441257

• Efficient, Regularized, and Scalable Algorithms for Multiscale Coarse-Graining JOURNAL OF CHEMICAL THEORY AND COMPUTATION Lu, L., Izvekov, S., Das, A., Andersen, H. C., Voth, G. A. 2010; 6 (3): 954-965

  View details for DOI 10.1021/ct900643r

  View details for Web of Science ID 000275189400032

• Kinetic theories of dynamics and persistent caging in a one-dimensional lattice gas PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Abel, S. M., Tse, Y. S., Andersen, H. C. 2009; 106 (36): 15142-15147

  Abstract

  The one-dimensional, single-occupancy lattice gas exhibits highly cooperative particle motion and provides an interesting challenge for theoretical methods designed to describe caging in liquids. We employ this model in an effort to gain insight into caging phenomena in more realistic models of liquids, using a diagrammatic kinetic theory of density fluctuations to develop a series of approximations to the kinetic equations for the van Hove self-correlation function. The approximations are formulated in terms of the irreducible memory function, and we assess their efficacy by comparing their solutions with computer simulation results and the well-known subdiffusive behavior of a tagged particle at long times. The first approximation, a mode coupling theory, factorizes the 4-point propagators that contribute to the irreducible memory function into products of independent single-particle propagators. This approximation fails to capture the subdiffusive behavior of a tagged particle at long times. Analysis of the mode coupling approximation in terms of the diagrammatic kinetic theory leads to the development of two additional approximations that can be viewed as diagrammatic extensions or modifications of mode coupling theory. The first, denoted MC1, captures the long-time subdiffusive behavior of a tagged particle. The second, denoted MC2, captures the subdiffusive behavior of a tagged particle and also yields the correct amplitude of its mean square displacement at long times. Numerical and asymptotic solutions of the approximate kinetic equations share many qualitative and quantitative features with simulation results at all timescales.

  View details for DOI 10.1073/pnas.0901693106

  View details for Web of Science ID 000269632400012

  View details for PubMedID 19564606

• The multiscale coarse-graining method. III. A test of pairwise additivity of the coarse-grained potential and of new basis functions for the variational calculation JOURNAL OF CHEMICAL PHYSICS Das, A., Andersen, H. C. 2009; 131 (3)

  Abstract

  The multiscale coarse-graining (MS-CG) method, proposed by Izvekov and Voth [J. Phys. Chem. B 109, 2469 (2005); Izvekov and VothJ. Chem. Phys. 123, 134105 (2005)], is a method for determining the effective potential energy function for a coarse-grained model of a fluid using data obtained from molecular dynamics (MD) simulation of the corresponding atomically detailed model. The method has been given a rigorous statistical mechanical basis [Noid et al. J. Chem. Phys. 128, 244114 (2008); Noid et al., J. Chem. Phys. 128, 244115 (2008)]. The coarse-grained (CG) potentials obtained using the MS-CG method are an approximate variational solution for the exact many-body potential of mean force for the coarse-grained sites. In this paper we apply this method to study the many-body potential of mean force among solutes in a simple model of a solution of Lennard-Jones particles. We use a new set of basis functions for the variational calculation that is useful when the coarse-grained potential is approximately equal to an arbitrarily complicated pairwise additive, central interaction among the sites of the coarse-grained model. For this model, pairwise additivity of the many-body potential of mean force is a very good approximation when the solute concentration is low, and it becomes less accurate for high concentrations, indicating the importance of many-body contributions to the coarse-grained potential. The best possible pairwise additive CG potential of the solute particles is found to be quite long ranged for all concentrations except those for which the mole fraction of solute is very close to unity. We discuss strategies for construction of short-ranged potentials for efficient but accurate CG MD simulation. We also discuss how the choice of basis functions for the variational calculation can be used to provide smoothing of the calculated CG potential function to overcome statistical sampling error in the atomistic simulation data used for the generation of the potential.

  View details for DOI 10.1063/1.3173812

  View details for Web of Science ID 000268206800008

  View details for PubMedID 19624176

• Scaling Analysis of Dynamic Heterogeneity in a Supercooled Lennard-Jones Liquid PHYSICAL REVIEW LETTERS Stein, R. S., Andersen, H. C. 2008; 101 (26)

  Abstract

  We have performed molecular dynamics computer simulations of a dense Lennard-Jones liquid mixture to study dynamic heterogeneity from normal liquid temperatures down to a supercooled temperature 15% above the previously identified mode-coupling temperature Tc of the model. A temperature-dependent correlation length associated with the correlation function of mobility fluctuations is calculated. The results are used to test two sets of scaling hypotheses for the dynamic heterogeneity. The results are in close agreement with the inhomogeneous mode-coupling theory of Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)] for both the alpha and beta relaxation regimes. Comparison with results for kinetically constrained models suggest that the Lennard-Jones mixture studied is more similar to models of fragile liquids than models of very strong liquids.

  View details for DOI 10.1103/PhysRevLett.101.267802

  View details for Web of Science ID 000262247100081

  View details for PubMedID 19437674

• The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models JOURNAL OF CHEMICAL PHYSICS Noid, W. G., Liu, P., Wang, Y., Chu, J., Ayton, G. S., Izvekov, S., Andersen, H. C., Voth, G. A. 2008; 128 (24)

  Abstract

  The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM(+)NO(3) (-) ionic liquid are provided to illustrate the method.

  View details for DOI 10.1063/1.2938857

  View details for Web of Science ID 000257284000018

  View details for PubMedID 18601325

• The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models JOURNAL OF CHEMICAL PHYSICS Noid, W. G., Chu, J., Ayton, G. S., Krishna, V., Izvekov, S., Voth, G. A., Das, A., Andersen, H. C. 2008; 128 (24)

  Abstract

  Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.

  View details for DOI 10.1063/1.2938860

  View details for Web of Science ID 000257284000017

  View details for PubMedID 18601324

• A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. VI. Binary collision approximations for the memory function for self-correlation functions JOURNAL OF CHEMICAL PHYSICS Noah-Vanhoucke, J. E., Andersen, H. C. 2007; 127 (6)

  Abstract

  We use computer simulation results for a dense Lennard-Jones fluid for a range of temperatures to test the accuracy of various binary collision approximations for the memory function for density fluctuations in liquids. The approximations tested include the moderate density approximation of the generalized Boltzmann-Enskog memory function (MGBE) of Mazenko and Yip [Statistical Mechanics. Part B. Time-Dependent Processes, edited by B. J. Berne (Plenum, New York, 1977)], the binary collision approximation (BCA) and the short time approximation (STA) of Ranganathan and Andersen [J. Chem. Phys. 121, 1243 (2004); J. Phys. Chem. 109, 21437 (2005)] and various other approximations we derived by using diagrammatic methods. The tests are of two types. The first is a comparison of the correlation functions predicted by each approximate memory function with the simulation results, especially for the self-longitudinal current correlation (SLCC) function. The second is a direct comparison of each approximate memory function with a memory function numerically extracted from the correlation function data. The MGBE memory function is accurate at short times but decays to zero too slowly and gives a poor description of the correlation function at intermediate times. The BCA is exact at zero time, but it predicts a correlation function that diverges at long times. The STA gives a reasonable description of the SLCC but does not predict the correct temperature dependence of the negative dip in the function that is associated with caging at low temperatures. None of the other binary collision approximations is a systematic improvement on the STA. The extracted memory functions have a rapidly decaying short time part, much like the STA, and a much smaller, more slowly decaying part of the type predicted by a mode coupling theory. Theories that use mode coupling commonly include a binary collision term in the memory function but do not discuss in detail the nature of that term. It is clear from the present work that the short time part of the memory function has a behavior associated with brief binary repulsive collisions, such as those described by the STA. Collisions that include attractive as well as repulsive interactions, such as those of the MGBE, have a much longer duration, and theories that include them have memory functions that decay to zero much too slowly to provide a good first approximation of the correlation function. This leads us to speculate that the memory function for density fluctuations can be usefully regarded as a sum of at least three parts: a contribution from repulsive binary collisions (the STA or something similar to it), another short time part that is related to all the other interactions (but whose nature is not understood), and a longer time slowly decaying part that describes caging (of the type predicted by the mode coupling theory).

  View details for DOI 10.1063/1.2752153

  View details for Web of Science ID 000248760300026

  View details for PubMedID 17705607

• A mode coupling theory description of the short- and long-time dynamics of nematogens in the isotropic phase JOURNAL OF CHEMICAL PHYSICS Li, J., Cang, H., ANDERSEN, H. C., Fayer, M. D. 2006; 124 (1)

  Abstract

  Optical heterodyne-detected optical Kerr effect (OHD-OKE) experimental data are pre-sented on nematogens 4-(trans-4-n-octylcyclohexyl)isothiocyanatobenzene (8-CHBT), and 4-(4-pentyl-cyclohexyl)-benzonitrile (5-PCH) in the isotropic phase. The 8-CHBT and 5-PCH data and previously published data on 4-pentyl-4-biphenylcarbonitrile (5-CB) are analyzed using a modification of a schematic mode coupling theory (MCT) that has been successful in describing the dynamics of supercooled liquids. At long time, the OHD-OKE data (orientational relaxation) are well described with the standard Landau-de Gennes (LdG) theory. The data decay as a single exponential. The decay time diverges as the isotropic to nematic phase transition is approached from above. Previously there has been no theory that can describe the complex dynamics that occur at times short compared to the LdG exponential decay. Earlier, it has been noted that the short-time nematogen dynamics, which consist of several power laws, have a functional form identical to that observed for the short time behavior of the orientational relaxation of supercooled liquids. The temperature-dependent orientational dynamics of supercooled liquids have recently been successfully described using a schematic mode coupling theory. The schematic MCT theory that fits the supercooled liquid data does not reproduce the nematogen data within experimental error. The similarities of the nematogen data to the supercooled liquid data are the motivation for applying a modification of the successful MCT theory to nematogen dynamics in the isotropic phase. The results presented below show that the new schematic MCT theory does an excellent job of reproducing the nematogen isotropic phase OHD-OKE data on all time scales and at all temperatures.

  View details for DOI 10.1063/1.2145679

  View details for Web of Science ID 000234428900043

  View details for PubMedID 16409058

• Diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. V. The short time approximation for the memory function JOURNAL OF PHYSICAL CHEMISTRY B Ranganathan, M., ANDERSEN, H. C. 2005; 109 (45): 21437-21444

  Abstract

  The correlation function for density fluctuations in a monatomic fluid obeys a formally exact kinetic equation containing a memory function. A previously derived short time approximation (STA) for this memory function is tested by comparing its predictions with the results of molecular dynamic simulations of a dense Lennard-Jones fluid at a variety of temperatures. This approximation takes into account the contribution to the correlation function of uncorrelated repulsive binary collisions. The qualitative changes of predicted correlation functions with temperature and wave vector are generally correct. The major exception to this is the transverse current correlation function for small wave vector. The quantitative accuracy is better at short times than long times and better at high temperatures than low temperatures. The major failing of the STA is its underestimation of the amplitudes of the negative dips in the current autocorrelation functions and of the temperature dependence of the amplitudes of the dips. Despite its deficiencies in predicting the time dependence of current correlation functions, the STA gives accurate results for the self-diffusion coefficient and the shear viscosity coefficient at the highest temperatures studied.

  View details for DOI 10.1021/jp0523017

  View details for Web of Science ID 000233280600029

  View details for PubMedID 16853781

• Boson peak in supercooled liquids: Time domain observations and mode coupling theory JOURNAL OF CHEMICAL PHYSICS Cang, H., Li, J., ANDERSEN, H. C., Fayer, M. D. 2005; 123 (6)

  Abstract

  Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments are presented for the supercooled liquid acetylsalicylic acid (aspirin - ASP). The ASP data and previously published OHD-OKE data on supercooled dibutylphthalate (DBP) display highly damped oscillations with a periods of approximately 2 ps as the temperature is reduced to and below the mode coupling theory (MCT) temperature T(C). The oscillations become more pronounced below T(C). The oscillations can be interpreted as the time domain signature of the boson peak. Recently a schematic MCT model, the Sjogren model, was used to describe the OHD-OKE data for a number of supercooled liquids by Gotze and Sperl [W. Gotze and M. Sperl, Phys. Rev. E 92, 105701 (2004)] , but the short-time and low-temperature behaviors were not addressed. Franosch et al. [T. Franosch, W. Gotze, M. R. Mayr, and A. P. Singh, Phys. Rev. E 55, 3183 (1997)] found that the Sjogren model could describe the boson peak observed by depolarized light-scattering (DLS) experiments on glycerol. The OHD-OKE experiment measures a susceptibility that is a time domain equivalent of the spectrum measured in DLS. Here we present a detailed analysis of the ASP and DBP data over a broad range of times and temperatures using the Sjogren model. The MCT schematic model is able to describe the data very well at all temperatures and relevant time scales. The trajectory of MCT parameters that fit the high-temperature data (no short-time oscillations) when continued below T(C) results in calculations that reproduce the oscillations seen in the data. The results indicate that increasing translational-rotational coupling is responsible for the appearance of the boson peak as the temperature approaches and drops below T(C).

  View details for DOI 10.1063/1.2000235

  View details for Web of Science ID 000231310500043

  View details for PubMedID 16122327

• Molecular dynamics studies of heterogeneous dynamics and dynamic crossover in supercooled atomic liquids PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Andersen, H. C. 2005; 102 (19): 6686-6691

  Abstract

  Supercooled liquids near the glass transition exhibit the phenomenon of heterogeneous relaxation; at any specific time, a nominally homogeneous equilibrium fluid undergoes dynamic fluctuations in its structure on a molecular distance scale with rates that are very different in different regions of the sample. Several theoretical and simulation studies have suggested a change in the nature of the dynamics of fluids as they are supercooled, leading to the concept of a dynamic crossover that is often associated with mode coupling theory. Here, we will review the use of molecular dynamics computer simulation methods to investigate heterogeneous dynamics and dynamic crossovers in models of atomic liquids.

  View details for DOI 10.1073/pnas.05009464102

  View details for Web of Science ID 000229048500010

  View details for PubMedID 15870201

  View details for PubMedCentralID PMC1100779

• Tests of an approximate scaling principle for dynamics of classical fluids JOURNAL OF PHYSICAL CHEMISTRY B Young, T., Andersen, H. C. 2005; 109 (7): 2985-2994

  Abstract

  We used molecular dynamics computer simulations to test an approximate scaling principle that conjectures that two equilibrium atomic liquids have very similar dynamical properties if they have the same density and similar static pair correlation functions when the length scales of the two liquids are adjusted appropriately, even if they have different interatomic potentials and different temperatures. The simulations were performed on two types of model atomic liquids at various temperatures at the same density. In the first type, the interatomic potential is the Lennard-Jones potential (LJ). In the second type, the interatomic potential is the repulsive part of the Lennard-Jones potential (RLJ). We identified pairs of systems that have very similar pair correlation functions despite the fact that they had different potentials. Each pair consisted of an LJ liquid at a specific temperature and a corresponding RLJ liquid at a lower temperature. We compared various time correlation functions and transport coefficients of the two systems in each pair. Many dynamical properties are very similar in each pair, in accordance with the approximate scaling principle, whereas others are significantly different. The results indicate that certain dynamical properties are very insensitive to large changes in the interatomic potential that leave the pair correlation function largely unchanged, whereas other dynamical properties are much more sensitive to such changes in the potential. The transport coefficients for diffusion and viscosity are among the dynamical properties that are insensitive to such changes in the potential, and this may be part of the reason transport properties of many fluids have been calculated or rationalized in terms of a simple hard sphere model of liquids.

  View details for DOI 10.1021/jp0454927

  View details for Web of Science ID 000227108800071

  View details for PubMedID 16851313

• A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. IV. The short time behavior of the memory function JOURNAL OF CHEMICAL PHYSICS Ranganathan, M., Andersen, H. C. 2004; 121 (3): 1243-1257

  Abstract

  Using a recently developed diagrammatic formulation of the kinetic theory of fluctuations in liquids, we investigate the short time behavior of the memory function for density fluctuations in a classical atomic fluid. At short times, the memory function has a large contribution that is generated by the repulsive part of the interatomic potential. We introduce a small parameter that is a measure of the softness of the repulsive part of the potential. The diagrams in the memory function that contribute to lowest order in that small parameter are identified and summed to give an explicit expression for the dominant contribution to the memory function at short times. The result leads to a theory for fluids with continuous potentials that is similar to the Enskog theory for hard sphere fluids.

  View details for DOI 10.1063/1.1764492

  View details for Web of Science ID 000222663300009

  View details for PubMedID 15260665

• Diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. III. Cluster analysis of the renormalized interactions and a second diagrammatic representation of the correlation functions JOURNAL OF PHYSICAL CHEMISTRY B ANDERSEN, H. C. 2003; 107 (37): 10234-10242

  View details for DOI 10.1021/jp034754m

  View details for Web of Science ID 000185345400044

• A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. II. Equations of motion of the fluctuation fields and their diagrammatic solution JOURNAL OF PHYSICAL CHEMISTRY B Andersen, H. C. 2003; 107 (37): 10226-10233

  View details for DOI 10.1021/jp034753u

  View details for Web of Science ID 000185345400043

• Dynamical corrections to quantum transition state theory JOURNAL OF CHEMICAL PHYSICS Cheney, B. G., Andersen, H. C. 2003; 118 (21): 9542-9551

  View details for DOI 10.1063/1.1570404

  View details for Web of Science ID 000182890000011

• A scaling principle for the dynamics of density fluctuations in atomic liquids JOURNAL OF CHEMICAL PHYSICS Young, T., ANDERSEN, H. C. 2003; 118 (8): 3447-3450

  View details for DOI 10.1063/1.1553757

  View details for Web of Science ID 000180803800001

• A diagrammatic theory of time correlation functions of facilitated kinetic Ising models JOURNAL OF CHEMICAL PHYSICS Pitts, S. J., ANDERSEN, H. C. 2001; 114 (3): 1101-1114

  View details for Web of Science ID 000166213100006

• Facilitated spin models, mode coupling theory, and ergodic-nonergodic transitions JOURNAL OF CHEMICAL PHYSICS Pitts, S. J., Young, T., ANDERSEN, H. C. 2000; 113 (19): 8671-8679

  View details for Web of Science ID 000165083500031

• The meaning of the irreducible memory function in stochastic theories of dynamics with detailed balance JOURNAL OF CHEMICAL PHYSICS Pitts, S. J., ANDERSEN, H. C. 2000; 113 (10): 3945-3950

  View details for Web of Science ID 000089034900003

• Functional and graphical methods for classical statistical dynamics. I. A formulation of the Martin-Siggia-Rose method JOURNAL OF MATHEMATICAL PHYSICS ANDERSEN, H. C. 2000; 41 (4): 1979-2020

  View details for Web of Science ID 000086056600025

• Local parabolic reference approximation of thermal Feynman path integrals in quantum Monte Carlo simulations JOURNAL OF CHEMICAL PHYSICS Chao, C. E., ANDERSEN, H. C. 1997; 107 (23): 10121-10130

  View details for Web of Science ID A1997YK98200047

• Dynamics of a supercooled Lennard-Jones system: Qualitative and quantitative tests of mode-coupling theory PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT Kob, W., Nauroth, M., ANDERSEN, H. C. 1997: 35-42

  View details for Web of Science ID A1997XK52400008

• Observation of a two-stage melting transition in two dimensions PHYSICAL REVIEW E Bagchi, K., ANDERSEN, H. C., Swope, W. 1996; 53 (4): 3794-3803

  View details for Web of Science ID A1996UH48200022

• Properties of quantum transition state theory and its corrections JOURNAL OF PHYSICAL CHEMISTRY Hansen, N. F., ANDERSEN, H. C. 1996; 100 (4): 1137-1143

  View details for Web of Science ID A1996TR60600007

• Computer simulation study of the melting transition in two dimensions PHYSICAL REVIEW LETTERS Bagchi, K., ANDERSEN, H. C., Swope, W. 1996; 76 (2): 255-258

  View details for Web of Science ID A1996TN76100025

• TESTING MODE-COUPLING THEORY FOR A SUPERCOOLED BINARY LENNARD-JONES MIXTURE .2. INTERMEDIATE SCATTERING FUNCTION AND DYNAMIC SUSCEPTIBILITY PHYSICAL REVIEW E Kob, W., ANDERSEN, H. C. 1995; 52 (4): 4134-4153

  View details for Web of Science ID A1995TA52500023

• TESTING MODE-COUPLING THEORY FOR A SUPERCOOLED BINARY LENNARD-JONES MIXTURE - THE VAN HOVE CORRELATION-FUNCTION PHYSICAL REVIEW E Kob, W., ANDERSEN, H. C. 1995; 51 (5): 4626-4641

  View details for Web of Science ID A1995QZ15500014

• A COMPUTER-SIMULATION METHOD FOR THE CALCULATION OF CHEMICAL-POTENTIALS OF LIQUIDS AND SOLIDS USING THE BICANONICAL ENSEMBLE JOURNAL OF CHEMICAL PHYSICS Swope, W. C., ANDERSEN, H. C. 1995; 102 (7): 2851-2863

  View details for Web of Science ID A1995QF82100021

• A NEW FORMULATION OF QUANTUM TRANSITION-STATE THEORY FOR ADIABATIC RATE CONSTANTS JOURNAL OF CHEMICAL PHYSICS Hansen, N. F., ANDERSEN, H. C. 1994; 101 (7): 6032-6037

  View details for Web of Science ID A1994PH98700061

• SCALING BEHAVIOR IN THE BETA-RELAXATION REGIME OF A SUPERCOOLED LENNARD-JONES MIXTURE PHYSICAL REVIEW LETTERS Kob, W., ANDERSEN, H. C. 1994; 73 (10): 1376-1379

  View details for Web of Science ID A1994PE72700017

• SCALING BEHAVIOR IN THE DYNAMICS OF A SUPERCOOLED LENNARD-JONES MIXTURE NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA D-CONDENSED MATTER ATOMIC MOLECULAR AND CHEMICAL PHYSICS FLUIDS PLASMAS BIOPHYSICS Kob, W., ANDERSEN, H. C. 1994; 16 (8): 1291-1295

  View details for Web of Science ID A1994RE31700036

• A NEW FORMULATION OF THE HARTREE-FOCK-ROOTHAAN METHOD FOR ELECTRONIC-STRUCTURE CALCULATIONS ON CRYSTALS JOURNAL OF CHEMICAL PHYSICS Hammes-Schiffer, S., ANDERSEN, H. C. 1994; 101 (1): 375-393

  View details for Web of Science ID A1994NT52100041

• KINETIC LATTICE-GAS MODEL OF CAGE EFFECTS IN HIGH-DENSITY LIQUIDS AND A TEST OF MODE-COUPLING THEORY OF THE IDEAL-GLASS TRANSITION PHYSICAL REVIEW E Kob, W., ANDERSEN, H. C. 1993; 48 (6): 4364-4377

  View details for Web of Science ID A1993MQ16400034

• THE ADVANTAGES OF THE GENERAL HARTREE-FOCK METHOD FOR FUTURE COMPUTER-SIMULATION OF MATERIALS JOURNAL OF CHEMICAL PHYSICS Hammes-Schiffer, S., ANDERSEN, H. C. 1993; 99 (3): 1901-1913

  View details for Web of Science ID A1993LN78200048

• ABINITIO AND SEMIEMPIRICAL METHODS FOR MOLECULAR-DYNAMICS SIMULATIONS BASED ON GENERAL HARTREE-FOCK THEORY JOURNAL OF CHEMICAL PHYSICS Hammes-Schiffer, S., ANDERSEN, H. C. 1993; 99 (1): 523-532

  View details for Web of Science ID A1993LJ30800055

• RELAXATION DYNAMICS IN A LATTICE-GAS - A TEST OF THE MODE-COUPLING THEORY OF THE IDEAL GLASS-TRANSITION PHYSICAL REVIEW E Kob, W., ANDERSEN, H. C. 1993; 47 (5): 3281-3302

  View details for Web of Science ID A1993LF06700037

• INTERATOMIC POTENTIALS AND THE PHASE-DIAGRAM OF XE/PT(111) JOURNAL OF CHEMICAL PHYSICS Rejto, P. A., ANDERSEN, H. C. 1993; 98 (9): 7636-7647

  View details for Web of Science ID A1993LA76300113

• THERMODYNAMICS, STATISTICAL THERMODYNAMICS, AND COMPUTER-SIMULATION OF CRYSTALS WITH VACANCIES AND INTERSTITIALS PHYSICAL REVIEW A Swope, W. C., ANDERSEN, H. C. 1992; 46 (8): 4539-4548

  View details for Web of Science ID A1992JW97400020

• MOLECULAR-DYNAMICS SIMULATION OF SILICA LIQUID AND GLASS JOURNAL OF CHEMICAL PHYSICS DELLAVALLE, R. G., ANDERSEN, H. C. 1992; 97 (4): 2682-2689

  View details for Web of Science ID A1992JJ41100055

• TEST OF A PAIRWISE ADDITIVE IONIC POTENTIAL MODEL FOR SILICA JOURNAL OF CHEMICAL PHYSICS DELLAVALLE, R. G., ANDERSEN, H. C. 1991; 94 (7): 5056-5060

  View details for Web of Science ID A1991FF82000038

• INTERATOMIC POTENTIAL FOR SILICON CLUSTERS, CRYSTALS, AND SURFACES PHYSICAL REVIEW B BOLDING, B. C., ANDERSEN, H. C. 1990; 41 (15): 10568-10585

  View details for Web of Science ID A1990DF14100028

• A REACTIVE-FLUX THEORY OF CHEMICAL SURFACE-DIFFUSION JOURNAL OF CHEMICAL PHYSICS Rejto, P. A., ANDERSEN, H. C. 1990; 92 (10): 6217-6224

  View details for Web of Science ID A1990DD72500055

• 10(6)-PARTICLE MOLECULAR-DYNAMICS STUDY OF HOMOGENEOUS NUCLEATION OF CRYSTALS IN A SUPERCOOLED ATOMIC LIQUID PHYSICAL REVIEW B Swope, W. C., ANDERSEN, H. C. 1990; 41 (10): 7042-7054

  View details for Web of Science ID A1990CY12400038

• LOW-TEMPERATURE APPROXIMATIONS FOR FEYNMAN PATH-INTEGRALS AND THEIR APPLICATIONS IN QUANTUM EQUILIBRIUM AND DYNAMIC PROBLEMS JOURNAL OF CHEMICAL PHYSICS Mak, C. H., ANDERSEN, H. C. 1990; 92 (5): 2953-2965

  View details for Web of Science ID A1990CQ90700031

• ICOSAHEDRAL ORDERING IN THE LENNARD-JONES LIQUID AND GLASS PHYSICAL REVIEW LETTERS Jonsson, H., ANDERSEN, H. C. 1988; 60 (22): 2295-2298

  View details for Web of Science ID A1988N594300019

• MONTE-CARLO STUDIES OF DIFFUSION ON INHOMOGENEOUS SURFACES JOURNAL OF CHEMICAL PHYSICS Mak, C. H., ANDERSEN, H. C., George, S. M. 1988; 88 (6): 4052-4061

  View details for Web of Science ID A1988M666800080

• MOLECULAR-DYNAMICS STUDY OF MELTING AND FREEZING OF SMALL LENNARD-JONES CLUSTERS JOURNAL OF PHYSICAL CHEMISTRY Honeycutt, J. D., ANDERSEN, H. C. 1987; 91 (19): 4950-4963

  View details for Web of Science ID A1987K065400015

• MOLECULAR-DYNAMICS COMPUTER-SIMULATION OF AMORPHOUS MOLYBDENUM-GERMANIUM ALLOYS PHYSICAL REVIEW B Ding, K., ANDERSEN, H. C. 1987; 36 (5): 2675-2686

  View details for Web of Science ID A1987J819600018

• THEORETICAL-STUDY OF THE LOCALIZATION-DELOCALIZATION TRANSITION IN AMORPHOUS MOLYBDENUM-GERMANIUM ALLOYS PHYSICAL REVIEW B Ding, K., ANDERSEN, H. C. 1987; 36 (5): 2687-2694

  View details for Web of Science ID A1987J819600019

• MOLECULAR-DYNAMICS SIMULATION OF AMORPHOUS-GERMANIUM PHYSICAL REVIEW B Ding, K. J., ANDERSEN, H. C. 1986; 34 (10): 6987-6991

  View details for Web of Science ID A1986E842800053

• TRUNCATION OF COULOMBIC INTERACTIONS IN COMPUTER-SIMULATIONS OF LIQUIDS JOURNAL OF CHEMICAL PHYSICS Linse, P., ANDERSEN, H. C. 1986; 85 (5): 3027-3041

  View details for Web of Science ID A1986D739900084

• SMALL SYSTEM SIZE ARTIFACTS IN THE MOLECULAR-DYNAMICS SIMULATION OF HOMOGENEOUS CRYSTAL NUCLEATION IN SUPERCOOLED ATOMIC LIQUIDS JOURNAL OF PHYSICAL CHEMISTRY Honeycutt, J. D., ANDERSEN, H. C. 1986; 90 (8): 1585-1589

  View details for Web of Science ID A1986A860900026

• MOLECULAR-DYNAMICS STUDY OF THE HYDROPHOBIC INTERACTION IN AN AQUEOUS-SOLUTION OF KRYPTON JOURNAL OF PHYSICAL CHEMISTRY Watanabe, K., ANDERSEN, H. C. 1986; 90 (5): 795-802

  View details for Web of Science ID A1986A255400020

• A COMPARISON OF THE MOLECULAR-DYNAMICS METHOD AND ENERGY MINIMIZATION METHODS FOR MODELING THE STRUCTURE OF AMORPHOUS METALS JOURNAL OF NON-CRYSTALLINE SOLIDS GRABOW, M. H., ANDERSEN, H. C. 1985; 75 (1-3): 225-236

  View details for Web of Science ID A1985ATE3500031

• EFFECTS OF 3-BODY INTERACTIONS ON THE STRUCTURE OF CLUSTERS SURFACE SCIENCE BLAISTENBAROJAS, E., ANDERSEN, H. C. 1985; 156 (JUN): 548-555

  View details for Web of Science ID A1985AMF8200066

• FACILITATED KINETIC ISING-MODELS AND THE GLASS-TRANSITION JOURNAL OF CHEMICAL PHYSICS FREDRICKSON, G. H., ANDERSEN, H. C. 1985; 83 (11): 5822-5831

  View details for Web of Science ID A1985AUR0400063

• MACROMOLECULAR PAIR CORRELATION-FUNCTIONS FROM FLUORESCENCE DEPOLARIZATION EXPERIMENTS JOURNAL OF POLYMER SCIENCE PART B-POLYMER PHYSICS FREDRICKSON, G. H., ANDERSEN, H. C., Frank, C. W. 1985; 23 (3): 591-599

  View details for Web of Science ID A1985ADN6900014

• HOPPING TRANSPORT ON A RANDOMLY SUBSTITUTED LATTICE FOR LONG-RANGE AND NEAREST NEIGHBOR INTERACTIONS JOURNAL OF CHEMICAL PHYSICS Loring, R. F., ANDERSEN, H. C., Fayer, M. D. 1984; 80 (11): 5731-5744

  View details for Web of Science ID A1984SV51900052

• MOLECULAR-DYNAMICS SIMULATIONS OF A SUPERCOOLED MONATOMIC LIQUID AND GLASS JOURNAL OF PHYSICAL CHEMISTRY Fox, J. R., ANDERSEN, H. C. 1984; 88 (18): 4019-4027

  View details for Web of Science ID A1984TH00500032

• THE EFFECT OF PERIODIC BOUNDARY-CONDITIONS ON HOMOGENEOUS NUCLEATION OBSERVED IN COMPUTER-SIMULATIONS CHEMICAL PHYSICS LETTERS Honeycutt, J. D., ANDERSEN, H. C. 1984; 108 (6): 535-538

  View details for Web of Science ID A1984TE30400003

• HOPPING TRANSPORT ON A RANDOMLY SUBSTITUTED LATTICE IN THE PRESENCE OF DILUTE DEEP TRAPS CHEMICAL PHYSICS Loring, R. F., ANDERSEN, H. C., Fayer, M. D. 1984; 85 (1): 149-164

  View details for Web of Science ID A1984SH34000014

• KINETIC ISING-MODEL OF THE GLASS-TRANSITION PHYSICAL REVIEW LETTERS FREDRICKSON, G. H., ANDERSEN, H. C. 1984; 53 (13): 1244-1247

  View details for Web of Science ID A1984TJ67300011

• A MOLECULAR-DYNAMICS METHOD FOR CALCULATING THE SOLUBILITY OF GASES IN LIQUIDS AND THE HYDROPHOBIC HYDRATION OF INERT-GAS ATOMS IN AQUEOUS-SOLUTION JOURNAL OF PHYSICAL CHEMISTRY Swope, W. C., ANDERSEN, H. C. 1984; 88 (26): 6548-6556

  View details for Web of Science ID A1984TZ31000015

• ELECTRONIC EXCITED-STATE TRANSPORT AND TRAPPING ON POLYMER-CHAINS MACROMOLECULES FREDRICKSON, G. H., ANDERSEN, H. C., Frank, C. W. 1984; 17 (1): 54-59

  View details for Web of Science ID A1984SB10300010

• ELECTRONIC EXCITATION TRANSPORT AS A PROBE OF CHAIN FLEXIBILITY MACROMOLECULES FREDRICKSON, G. H., ANDERSEN, H. C., Frank, C. W. 1984; 17 (8): 1496-1499

  View details for Web of Science ID A1984TF17900013

• RATTLE - A VELOCITY VERSION OF THE SHAKE ALGORITHM FOR MOLECULAR-DYNAMICS CALCULATIONS JOURNAL OF COMPUTATIONAL PHYSICS ANDERSEN, H. C. 1983; 52 (1): 24-34

  View details for Web of Science ID A1983RQ23800002

• VANDERWAALS PICTURE OF LIQUIDS, SOLIDS, AND PHASE-TRANSFORMATIONS SCIENCE CHANDLER, D., WEEKS, J. D., ANDERSEN, H. C. 1983; 220 (4599): 787-794

  Abstract

  The van der Waals picture focuses on the differing roles of the strong short-ranged repulsive intermolecular forces and the longer ranged attractions in determining the structure and dynamics of dense fluids and solids. According to this physical picture, the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces. This very useful approach, its limitations, and its successful application to a wide variety of static and dynamic phenomena in condensed matter systems are reviewed.

  View details for Web of Science ID A1983QP69600006

  View details for PubMedID 17834156

• A THEORY OF THE ANOMALOUS THERMODYNAMIC PROPERTIES OF LIQUID WATER JOURNAL OF CHEMICAL PHYSICS DAHL, L. W., ANDERSEN, H. C. 1983; 78 (4): 1980-1993

  View details for Web of Science ID A1983QD40400044

• THE ROLE OF LONG RANGED FORCES IN DETERMINING THE STRUCTURE AND PROPERTIES OF LIQUID WATER JOURNAL OF CHEMICAL PHYSICS ANDREA, T. A., Swope, W. C., ANDERSEN, H. C. 1983; 79 (9): 4576-4584

  View details for Web of Science ID A1983RN51200063

• CLUSTER EXPANSIONS FOR HYDROGEN-BONDED FLUIDS .3. WATER JOURNAL OF CHEMICAL PHYSICS DAHL, L. W., ANDERSEN, H. C. 1983; 78 (4): 1962-1979

  View details for Web of Science ID A1983QD40400043

• ELECTRONIC EXCITED-STATE TRANSPORT ON ISOLATED POLYMER-CHAINS MACROMOLECULES FREDRICKSON, G. H., ANDERSEN, H. C., Frank, C. W. 1983; 16 (9): 1456-1464

  View details for Web of Science ID A1983RG93400009

• EXCITATION TRANSPORT ON SUBSTITUTIONALLY DISORDERED LATTICES Loring, R. F., ANDERSEN, H. C., Fayer, M. D. AMER INST PHYSICS. 1983: 1389–89

  View details for Web of Science ID A1983RL10600060

• ELECTRONIC EXCITED-STATE TRANSPORT AND TRAPPING AS A PROBE OF INTRAMOLECULAR POLYMER STRUCTURE JOURNAL OF CHEMICAL PHYSICS FREDRICKSON, G. H., ANDERSEN, H. C., Frank, C. W. 1983; 79 (7): 3572-3580

  View details for Web of Science ID A1983RJ50400051

• EXCITATION TRANSPORT ON SUBSTITUTIONALLY DISORDERED LATTICES PHYSICAL REVIEW LETTERS Loring, R. F., ANDERSEN, H. C., Fayer, M. D. 1983; 50 (17): 1324-1327

  View details for Web of Science ID A1983QL86700027

• ELECTRONIC EXCITED-STATE TRANSPORT AND TRAPPING IN SOLUTION JOURNAL OF CHEMICAL PHYSICS Loring, R. F., ANDERSEN, H. C., Fayer, M. D. 1982; 76 (4): 2015-2027

  View details for Web of Science ID A1982NB26300051

• A THEORY OF EFFECTS OF PROTONS AND DIVALENT-CATIONS ON PHASE-EQUILIBRIA IN CHARGED BILAYER-MEMBRANES - COMPARISON WITH EXPERIMENT BIOCHEMISTRY Copeland, B. R., ANDERSEN, H. C. 1982; 21 (12): 2811-2820

  Abstract

  We summarize the concepts in the recently developed statistical mechanical theory of the effects of proton binding and divalent cation binding on phase equilibria in bilayer membrane composed of acidic phospholipids. The theory is used to calculate membrane phase transition temperatures for different aqueous concentrations of protons, divalent cations and monovalent salt. We discuss methods for calculating transition temperatures even for systems in which there is not an excess of protons or divalent cations relative to lipids. The results are compared with existing experimental data for a number of lipids. There is good agreement between calculated transition temperature vs. pH curves and experimental data for dimyristoylmethylphosphatidic acid, dimyristoylphosphatidylglycerol, dipalmitoylphosphatidylglycerol, dipalmitoylphosphatidylserine, and dimyristoylphosphatidic acid. General thermodynamic considerations are used to derive in Clapeyron-like equation for the rate of variation in membrane transition temperature with divalent cation concentration. This equation and some available experimental data are used to argue that the large increase in solid to fluid phase transition temperature that is observed experimentally as the divalent cation concentration is increased is the result of the metastable solid phase that exists at low but not high divalent cation concentration. A calculated coexistence diagram is compared with existing experimental data for transition temperatures of dimyristoylphosphatidylglycerol membranes at different total calcium concentrations. Good agreement is obtained when the existence of a metastable solid phase is assumed.

  View details for Web of Science ID A1982NS33900001

  View details for PubMedID 6285955

• A COMPUTER-SIMULATION METHOD FOR THE CALCULATION OF EQUILIBRIUM-CONSTANTS FOR THE FORMATION OF PHYSICAL CLUSTERS OF MOLECULES - APPLICATION TO SMALL WATER CLUSTERS JOURNAL OF CHEMICAL PHYSICS Swope, W. C., ANDERSEN, H. C., BERENS, P. H., Wilson, K. R. 1982; 76 (1): 637-649

  View details for Web of Science ID A1982MW46500084

• MOLECULAR-DYNAMICS SIMULATION OF THE GLASS-TRANSITION ANNALS OF THE NEW YORK ACADEMY OF SCIENCES Fox, J. R., ANDERSEN, H. C. 1981; 371 (OCT): 123-135

  View details for Web of Science ID A1981MS72500009

• A THEORY FOR ION BINDING AND PHASE-EQUILIBRIA IN CHARGED LIPID-MEMBRANES .2. COMPETITIVE AND COOPERATIVE BINDING JOURNAL OF CHEMICAL PHYSICS Copeland, B. R., ANDERSEN, H. C. 1981; 74 (4): 2548-2558

  View details for Web of Science ID A1981LE27100065

• THEORY OF PHOTON-ECHOES FROM A PAIR OF COUPLED 2 LEVEL SYSTEMS - IMPURITY DIMERS AND ENERGY-TRANSFER IN MOLECULAR-CRYSTALS JOURNAL OF CHEMICAL PHYSICS Skinner, J. L., ANDERSEN, H. C., Fayer, M. D. 1981; 75 (7): 3195-3202

  View details for Web of Science ID A1981MF63600004

• CORRELATION-FUNCTION ANALYSIS OF COHERENT OPTICAL TRANSIENTS AND FLUORESCENCE FROM A QUASI-2-LEVEL SYSTEM PHYSICAL REVIEW A Skinner, J. L., ANDERSEN, H. C., Fayer, M. D. 1981; 24 (4): 1994-2008

  View details for Web of Science ID A1981ML75100038

• A THEORY OF ION BINDING AND PHASE-EQUILIBRIA IN CHARGED LIPID-MEMBRANES .1. PROTON BINDING JOURNAL OF CHEMICAL PHYSICS Copeland, B. R., ANDERSEN, H. C. 1981; 74 (4): 2536-2547

  View details for Web of Science ID A1981LE27100064

• QUANTUM-THEORY OF COHERENT HYPER-RAMAN SCATTERING FROM ISOTROPIC MATERIALS JOURNAL OF CHEMICAL PHYSICS Bjarnason, J. O., ANDERSEN, H. C., Hudson, B. S. 1980; 73 (4): 1827-1835

  View details for Web of Science ID A1980KG73000042

• A THEORY OF THE EFFECTS OF HEADGROUP STRUCTURE AND CHAIN UNSATURATION ON THE CHAIN MELTING TRANSITION OF PHOSPHOLIPID DISPERSIONS BIOCHEMISTRY Berde, C. B., ANDERSEN, H. C., Hudson, B. S. 1980; 19 (18): 4279-4293

  Abstract

  We have developed statistical mechanical descriptions of the effects of head-group structure and acyl chain unsaturation on the chain melting phase transition of aqueous dispersions of bilayers containing glycerophosphocholines and glycerophosphoethanolamines. The theoretical framework is an extension of the model of Jacobs et al. [Jacobs, R. E., Hudson, B. S., & Andersen, H. C. (1975) Proc. Natl. Acad. Sci. U.S.A. 72, 3993]. There are several systematic trends in the experimental transition data for various types of phospholipids. Assumptions about the physical origins of these trends were incorporated into statistical mechanical models, which were used to calculate transition temperatures and enthalpies. The extent to which the calculated results of a model reproduce the experimental trends is taken as a measure of the validity of the assumptions on which the model is based. We found that the gross differences among the transition temperatures of phospholipids with two saturated chains, two trans-unsaturated chains, two cis-unsaturated chains, and one cis-unsaturated and one saturated chain can all be explained in terms of the effect of the double bonds on molecular shape and the subsequent effect of shape on the ability of molecules to pack together into a low-energy state at high density. The dependence of transition temperature on the location of the double bond in cis-unsaturated molecules can be understood on the same basis. The differences between the transition temperatures of glycerophosphocholines and glycerophosphoethanolamines with the same hydrocarbon chains can be explained in terms of a larger intermolecular attraction (or smaller repulsion) for the latter than for the former. These differences depend on the presence or absence of unsaturation in the hydrocarbon chains in a way that is consistent with the postulate that hydrogen bonding between glycerophosphoethanolamines is responsible for the differences.

  View details for Web of Science ID A1980KG31600021

  View details for PubMedID 7417405

• QUANTUM-THEORY OF COHERENT RAMAN-SCATTERING BY OPTICALLY-ACTIVE ISOTROPIC MATERIALS JOURNAL OF CHEMICAL PHYSICS Bjarnason, J. O., ANDERSEN, H. C., Hudson, B. S. 1980; 72 (7): 4132-4140

  View details for Web of Science ID A1980JP80900038

• MOLECULAR-DYNAMICS SIMULATIONS AT CONSTANT PRESSURE AND-OR TEMPERATURE JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C. 1980; 72 (4): 2384-2393

  View details for Web of Science ID A1980JK06800026

• ELECTRONIC EXCITED-STATE TRANSPORT IN SOLUTION JOURNAL OF CHEMICAL PHYSICS Gochanour, C. R., ANDERSEN, H. C., Fayer, M. D. 1979; 70 (9): 4254-4271

  View details for Web of Science ID A1979GU87400035

• QUANTUM-THEORY OF LINE-SHAPES IN COHERENT RAMAN-SPECTROSCOPY OF GASES AND LIQUIDS JOURNAL OF CHEMICAL PHYSICS Bjarnason, J. O., Hudson, B. S., ANDERSEN, H. C. 1979; 70 (9): 4130-4148

  View details for Web of Science ID A1979GU87400019

• GLASS-TRANSITION OF ATOMIC GLASSES JOURNAL OF CHEMICAL PHYSICS Hudson, S., ANDERSEN, H. C. 1978; 69 (6): 2323-2331

  View details for Web of Science ID A1978FS43400007

• PROBES OF MEMBRANE STRUCTURE ANNUAL REVIEW OF BIOCHEMISTRY ANDERSEN, H. C. 1978; 47: 359-383

  View details for Web of Science ID A1978FH01600011

  View details for PubMedID 209727

• THEORY OF PHASE-TRANSITIONS AND PHASE-DIAGRAMS FOR ONE-COMPONENT AND 2-COMPONENT PHOSPHOLIPID BILAYERS BIOCHEMISTRY Jacobs, R. E., Hudson, B. S., ANDERSEN, H. C. 1977; 16 (20): 4349-4359

  Abstract

  A statistical mechanical partition function for phospholipid bilayers is constructed to obtain a theoretical description of the chain melting phase transition in lipid bilayer membranes and of the phase diagrams for two-component bilayers. In addition to providing an accurate representation of the transition temperatures and enthalpies of one-component bilayers composed of 1,2-diacylphosphatidylcholines, the theory can also account for the shapes of the phase diagrams observed for bilayers which are binary mixtures of these compounds with two different hydrocarbon chain lenghts.

  View details for Web of Science ID A1977DW50400004

  View details for PubMedID 911760

• CROSS-SECTIONS FOR PHOTODETACHMENT OF ELECTRONS FROM NEGATIVE-IONS NEAR THRESHOLD JOURNAL OF CHEMICAL PHYSICS Reed, K. J., Zimmerman, A. H., ANDERSEN, H. C., Brauman, J. I. 1976; 64 (4): 1368-1375

  View details for Web of Science ID A1976BH06300016

• INFRARED AND RAMAN STUDIES OF ROTATIONAL CORRELATION-FUNCTIONS IN LIQUIDS CHEMICAL PHYSICS Jones, D. R., ANDERSEN, H. C., Pecora, R. 1975; 9 (3): 339-358

  View details for Web of Science ID A1975AL80100008

• REPULSIVE PART OF EFFECTIVE INTERATOMIC POTENTIAL FOR LIQUID-METALS CHEMICAL PHYSICS Jacobs, R. E., ANDERSEN, H. C. 1975; 10 (1): 73-85

  View details for Web of Science ID A1975AP89800009

• THEORY OF CHAIN MELTING PHASE-TRANSITION OF AQUEOUS PHOSPHOLIPID DISPERSIONS PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Jacobs, R. E., Hudson, B., ANDERSEN, H. C. 1975; 72 (10): 3993-3997

  Abstract

  A model for the chain melting phase transition in dilute aqueous phospholipid bilayer dispersions is presented. This model includes interactions between head groups, between hydrocarbon chains, and within the chains. The head groups are modeled as hard disks which are constrained to lie on a two-dimensional surface separating the aqueous and hydrocarbon regions. The chain statistics problem is treated in an approximate manner using an approach motivated by scaled particle theory to describe the inter-chain steric repulsions in a mathematically tractable way. In this approach the whole system interacts with any given chain through an average lateral pressure which is proportional to the hard disk pressure. Following Nagle, we assume that the steric repulsions between chains and between head groups and the trans-gauche rotation energies are the dominant interactions in determining the transition and we describe the effect of the other interactions with a mean field approximation. Using the known transition temperature of a series of 1,2-diacyl phosphatidyl cholines to adjust two parameters in the theory, the model gives enthalpy and area changes that are in quite reasonable agreement with experiment. Moreover, the curvature observed in the plot of the transition temperature against acyl chain length is reproduced.

  View details for Web of Science ID A1975AW35900045

  View details for PubMedID 1060080

• THEORY OF TRANSPORT IN LIQUID-METALS .2. CALCULATION OF SHEAR VISCOSITY COEFFICIENTS CHEMICAL PHYSICS Protopapas, P., ANDERSEN, H. C., PARLEE, N. A. 1975; 8 (1-2): 17-26

  View details for Web of Science ID A1975AC13700002

• LIGHT-SCATTERING MEASUREMENT AND THEORETICAL INTERPRETATION OF MUTUAL DIFFUSION-COEFFICIENTS IN BINARY-LIQUID MIXTURES CHEMICAL PHYSICS CZWORNIAK, K. J., ANDERSEN, H. C., Pecora, R. 1975; 11 (3): 451-473

  View details for Web of Science ID A1975BA93300010

• STRUCTURE OF LIQUIDS ANNUAL REVIEW OF PHYSICAL CHEMISTRY ANDERSEN, H. C. 1975; 26: 145-166

  View details for Web of Science ID A1975AW32800008

• CLUSTER EXPANSIONS FOR HYDROGEN-BONDED FLUIDS .2. DENSE LIQUIDS JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C. 1974; 61 (12): 4985-4992

  View details for Web of Science ID A1974V247000006

• THEORY OF TRANSPORT IN LIQUID-METALS .1. CALCULATION OF SELF-DIFFUSION COEFFICIENTS JOURNAL OF CHEMICAL PHYSICS PROTOPAP, P., ANDERSEN, H. C., PARLEE, N. A. 1973; 59 (1): 15-25

  View details for Web of Science ID A1973Q264400002

• CLUSTER EXPANSIONS FOR HYDROGEN-BONDED FLUIDS .1. MOLECULAR ASSOCIATION IN DILUTE GASES JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C. 1973; 59 (9): 4714-4725

  View details for Web of Science ID A1973R679800020

• OPTIMIZED CLUSTER EXPANSIONS FOR CLASSICAL FLUIDS .2. THEORY OF MOLECULAR LIQUIDS JOURNAL OF CHEMICAL PHYSICS CHANDLER, D., ANDERSEN, H. C. 1972; 57 (5): 1930-?

  View details for Web of Science ID A1972N317900020

• OPTIMIZED CLUSTER EXPANSIONS FOR CLASSICAL FLUIDS .3. APPLICATIONS TO IONIC SOLUTIONS AND SIMPLE LIQUIDS JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C., CHANDLER, D., WEEKS, J. D. 1972; 57 (7): 2626-?

  View details for Web of Science ID A1972N596100003

• ROLES OF REPULSIVE AND ATTRACTIVE FORCES IN LIQUIDS - OPTIMIZED RANDOM PHASE APPROXIMATION JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C., CHANDLER, D., WEEKS, J. D. 1972; 56 (8): 3812-?

  View details for Web of Science ID A1972M268000015

• OPTIMIZED CLUSTER EXPANSIONS FOR CLASSICAL FLUIDS .1. GENERAL THEORY AND VARIATIONAL FORMULATION OF MEAN SPHERICAL MODEL AND HARD-SPHERE PERCUS-YEVICK EQUATIONS JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C., CHANDLER, D. 1972; 57 (5): 1918-?

  View details for Web of Science ID A1972N317900019

• KINETIC EQUATIONS FOR ORIENTATIONAL AND SHEAR RELAXATION AND DEPOLARIZED LIGHT SCATTERING IN LIQUIDS JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C., Pecora, R. 1971; 54 (6): 2584-?

  View details for Web of Science ID A1971J001500038

• MODE EXPANSION IN EQUILIBRIUM STATISTICAL MECHANICS .3. OPTIMIZED CONVERGENCE AND APPLICATION TO IONIC SOLUTION THEORY JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C., CHANDLER, D. 1971; 55 (4): 1497-?

  View details for Web of Science ID A1971K101100001

• MODE EXPANSION IN EQUILIBRIUM STATISTICAL MECHANICS .2. A RAPIDLY CONVERGENT THEORY OF IONIC SOLUTIONS JOURNAL OF CHEMICAL PHYSICS CHANDLER, D., ANDERSEN, H. C. 1971; 54 (1): 26-?

  View details for Web of Science ID A1971I124500004

• ROLE OF REPULSIVE FORCES IN DETERMINING EQUILIBRIUM STRUCTURE OF SIMPLE LIQUIDS JOURNAL OF CHEMICAL PHYSICS WEEKS, J. D., CHANDLER, D., ANDERSEN, H. C. 1971; 54 (12): 5237-?

  View details for Web of Science ID A1971J630300035

• RELATIONSHIP BETWEEN HARD-SPHERE FLUID AND FLUIDS WITH REALISTIC REPULSIVE FORCES PHYSICAL REVIEW A-GENERAL PHYSICS ANDERSEN, H. C., WEEKS, J. D., CHANDLER, D. 1971; 4 (4): 1597-?

  View details for Web of Science ID A1971K409600034

• MODE EXPANSION IN EQUILIBRIUM STATISTICAL MECHANICS .1. GENERAL THEORY AND APPLICATION TO CLASSICAL ELECTRON GAS JOURNAL OF CHEMICAL PHYSICS ANDERSEN, H. C., CHANDLER, D. 1970; 53 (2): 547-?

  View details for Web of Science ID A1970G908800012