Professional Education

  • Doctor of Philosophy, University of California Berkeley (2017)

All Publications

  • Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package JOURNAL OF CHEMICAL PHYSICS Epifanovsky, E., Gilbert, A. B., Feng, X., Lee, J., Mao, Y., Mardirossian, N., Pokhilko, P., White, A. F., Coons, M. P., Dempwolff, A. L., Gan, Z., Hait, D., Horn, P. R., Jacobson, L. D., Kaliman, I., Kussmann, J., Lange, A. W., Lao, K., Levine, D. S., Liu, J., McKenzie, S. C., Morrison, A. F., Nanda, K. D., Plasser, F., Rehn, D. R., Vidal, M. L., You, Z., Zhu, Y., Alam, B., Albrecht, B. J., Aldossary, A., Alguire, E., Andersen, J. H., Athavale, V., Barton, D., Begam, K., Behn, A., Bellonzi, N., Bernard, Y. A., Berquist, E. J., Burton, H. A., Carreras, A., Carter-Fenk, K., Chakraborty, R., Chien, A. D., Closser, K. D., Cofer-Shabica, V., Dasgupta, S., de Wergifosse, M., Deng, J., Diedenhofen, M., Do, H., Ehlert, S., Fang, P., Fatehi, S., Feng, Q., Friedhoff, T., Gayvert, J., Ge, Q., Gidofalvi, G., Goldey, M., Gomes, J., Gonzalez-Espinoza, C. E., Gulania, S., Gunina, A. O., Hanson-Heine, M. D., Harbach, P. P., Hauser, A., Herbst, M. F., Vera, M., Hodecker, M., Holden, Z. C., Houck, S., Huang, X., Hui, K., Huynh, B. C., Ivanov, M., Jasz, A., Ji, H., Jiang, H., Kaduk, B., Kaehler, S., Khistyaev, K., Kim, J., Kis, G., Klunzinger, P., Koczor-Benda, Z., Koh, J., Kosenkov, D., Koulias, L., Kowalczyk, T., Krauter, C. M., Kue, K., Kunitsa, A., Kus, T., Ladjanszki, I., Landau, A., Lawler, K., Lefrancois, D., Lehtola, S., Li, R. R., Li, Y., Liang, J., Liebenthal, M., Lin, H., Lin, Y., Liu, F., Liu, K., Loipersberger, M., Luenser, A., Manjanath, A., Manohar, P., Mansoor, E., Manzer, S. F., Mao, S., Marenich, A., Markovich, T., Mason, S., Maurer, S. A., McLaughlin, P. F., Menger, M. J., Mewes, J., Mewes, S. A., Morgante, P., Mullinax, J., Oosterbaan, K. J., Paran, G., Paul, A. C., Paul, S. K., Pavosevic, F., Pei, Z., Prager, S., Proynov, E., Rak, A., Ramos-Cordoba, E., Rana, B., Rask, A. E., Rettig, A., Richard, R. M., Rob, F., Rossomme, E., Scheele, T., Scheurer, M., Schneider, M., Sergueev, N., Sharada, S. M., Skomorowski, W., Small, D. W., Stein, C. J., Su, Y., Sundstrom, E. J., Tao, Z., Thirman, J., Tornai, G. J., Tsuchimochi, T., Tubman, N. M., Veccham, S., Vydrov, O., Wenzel, J., Witte, J., Yamada, A., Yao, K., Yeganeh, S., Yost, S. R., Zech, A., Zhang, I., Zhang, X., Zhang, Y., Zuev, D., Aspuru-Guzik, A., Bell, A. T., Besley, N. A., Bravaya, K. B., Brooks, B. R., Casanova, D., Chai, J., Coriani, S., Cramer, C. J., Cserey, G., DePrince, A., DiStasio, R. A., Dreuw, A., Dunietz, B. D., Furlani, T. R., Goddard, W. A., Hammes-Schiffer, S., Head-Gordon, T., Hehre, W. J., Hsu, C., Jagau, T., Jung, Y., Klamt, A., Kong, J., Lambrecht, D. S., Liang, W., Mayhall, N. J., McCurdy, C., Neaton, J. B., Ochsenfeld, C., Parkhill, J. A., Peverati, R., Rassolov, V. A., Shao, Y., Slipchenko, L., Stauch, T., Steele, R. P., Subotnik, J. E., Thom, A. W., Tkatchenko, A., Truhlar, D. G., Van Voorhis, T., Wesolowski, T. A., Whaley, K., Woodcock, H., Zimmerman, P. M., Faraji, S., Gill, P. W., Head-Gordon, M., Herbert, J. M., Krylov, A. 2021; 155 (8)

    View details for DOI 10.1063/5.0055522

    View details for Web of Science ID 000687352200007

  • Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations (vol 22, pg 26838, 2020) PHYSICAL CHEMISTRY CHEMICAL PHYSICS Yang, J., Pei, Z., Deng, J., Mao, Y., Wu, Q., Yang, Z., Wang, B., Aikens, C. M., Liang, W., Shao, Y. 2021

    View details for DOI 10.1039/d1cp90057a

    View details for Web of Science ID 000634377900001

  • Elucidating the Electronic Structure of a Delayed Fluorescence Emitter via Orbital Interactions, Excitation Energy Components, Charge-Transfer Numbers, and Vibrational Reorganization Energies. The journal of physical chemistry letters Pei, Z., Ou, Q., Mao, Y., Yang, J., Lande, A. d., Plasser, F., Liang, W., Shuai, Z., Shao, Y. 2021: 2712–20


    Recently, Wang and co-workers carried out frontier molecule orbital engineering in the design of m-Cz-BNCz, a thermally activated delayed fluorescence (TADF) molecule that emits pure green light at an external quantum efficiency of 27%. To further understand the underlying molecular design principles, we employed four advanced electronic structure analysis tools. First, an absolutely localized molecular orbitals (ALMO-) based analysis indicates an antibonding combination between the highest occupied molecular orbitals (HOMOs) of the donor 3,6-di-tert-butylcarbazole fragment and the acceptor BNCz fragment, which raises the HOMO energy and red-shifts the fluorescence emission wavelength. Second, excitation energy component analysis reveals that the S1-T1 gap is dominated by two-electron components of the excitation energies. Third, charge transfer number analysis, which is extended to use fragment-based Hirshfeld weights, indicates that the S1 and T1 excited states of m-Cz-BNCz (within time-dependent density functional theory) have notable charge transfer characters (27% for S1 and 12% for T1). This provides a balance between a small single-triplet gap and a substantial fluorescence intensity. Last, a vibrational reorganization energy analysis pinpoints the torsional motion between the BNCz and Cz moieties of m-Cz-BNCz as the source for its wider emission peak than that of p-Cz-BNCz. These four types of analyses are expected to be very valuable in the study and design of other TADF and functional dye molecules.

    View details for DOI 10.1021/acs.jpclett.1c00094

    View details for PubMedID 33705139

  • Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts CHEMICAL SCIENCE Mao, Y., Loipersberger, M., Kron, K. J., Derrick, J. S., Chang, C. J., Sharada, S., Head-Gordon, M. 2021; 12 (4): 1398–1414

    View details for DOI 10.1039/d0sc05327a

    View details for Web of Science ID 000614615000023

  • Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations. Physical chemistry chemical physics : PCCP Yang, J., Pei, Z., Deng, J., Mao, Y., Wu, Q., Yang, Z., Wang, B., Aikens, C. M., Liang, W., Shao, Y. 2020


    In this article, we report a scheme to analyze and visualize the energy density fluctuations during the real-time time-dependent density functional theory (RT-TDDFT) simulations. Using Ag4-N2 complexes as examples, it is shown that the grid-based Kohn-Sham energy density can be computed at each time step using a procedure from Nakai and coworkers. Then the instantaneous energy of each molecular fragment (such as Ag4 and N2) can be obtained by partitioning the Kohn-Sham energy densities using Becke or fragment-based Hirshfeld (FBH) scheme. A strong orientation-dependence is observed for the energy flow between the Ag4 cluster and a nearby N2 molecule in the RT-TDDFT simulations. Future applications of such an energy density analysis in electron dynamics simulations are discussed.

    View details for DOI 10.1039/d0cp04206d

    View details for PubMedID 33170198

  • Probing radical-molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals PHYSICAL CHEMISTRY CHEMICAL PHYSICS Mao, Y., Levine, D. S., Loipersberger, M., Horn, P. R., Head-Gordon, M. 2020; 22 (23): 12867–85


    Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical-molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical-molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A "polarize-then-depolarize" (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the "vertical" and "adiabatic" variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H2O˙F and FH˙OH. It is then applied to several chemically interesting radical-molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H2O) and ˙OH(H2O)2), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH3CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical-molecule interactions.

    View details for DOI 10.1039/d0cp01933j

    View details for Web of Science ID 000543038500002

    View details for PubMedID 32510096

  • Analysis and visualization of energy densities. II. Insights from linear-response time-dependent density functional theory calculations. Physical chemistry chemical physics : PCCP Pei, Z. n., Yang, J. n., Deng, J. n., Mao, Y. n., Wu, Q. n., Yang, Z. n., Wang, B. n., Aikens, C. M., Liang, W. n., Shao, Y. n. 2020


    Inspired by the analysis of Kohn-Sham energy densities by Nakai and coworkers, we extended the energy density analysis to linear-response time-dependent density functional theory (LR-TDDFT) calculations. Using ethylene-tetrafluoroethylene and oxyluciferin-water complexes as examples, distinctive distribution patterns were demonstrated for the excitation energy densities of local excitations (within a molecular fragment) and charge-transfer excitations (between molecular fragments). It also provided a simple way to compute the effective energy of both hot carriers (particle and hole) from charge-transfer excitations via an integration of the excitation energy density over the donor and acceptor grid points.

    View details for DOI 10.1039/d0cp04207b

    View details for PubMedID 33216085

  • Constructing Spin-Adiabatic States for the Modeling of Spin-Crossing Reactions. I. A Shared-Orbital Implementation. International journal of quantum chemistry Tao, Y. n., Pei, Z. n., Bellonzi, N. n., Mao, Y. n., Zou, Z. n., Liang, W. n., Yang, Z. n., Shao, Y. n. 2020; 120 (6)


    In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of N2O, singlet-triplet conversion in CH2, and CO addition to Fe(CO)4], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.

    View details for DOI 10.1002/qua.26123

    View details for PubMedID 32773885

    View details for PubMedCentralID PMC7409987

  • Excited state diabatization on the cheap using DFT: Photoinduced electron and hole transfer. The Journal of chemical physics Mao, Y. n., Montoya-Castillo, A. n., Markland, T. E. 2020; 153 (24): 244111


    Excited state electron and hole transfer underpin fundamental steps in processes such as exciton dissociation at photovoltaic heterojunctions, photoinduced charge transfer at electrodes, and electron transfer in photosynthetic reaction centers. Diabatic states corresponding to charge or excitation localized species, such as locally excited and charge transfer states, provide a physically intuitive framework to simulate and understand these processes. However, obtaining accurate diabatic states and their couplings from adiabatic electronic states generally leads to inaccurate results when combined with low-tier electronic structure methods, such as time-dependent density functional theory, and exorbitant computational cost when combined with high-level wavefunction-based methods. Here, we introduce a density functional theory (DFT)-based diabatization scheme that directly constructs the diabatic states using absolutely localized molecular orbitals (ALMOs), which we denote as Δ-ALMO(MSDFT2). We demonstrate that our method, which combines ALMO calculations with the ΔSCF technique to construct electronically excited diabatic states and obtains their couplings with charge-transfer states using our MSDFT2 scheme, gives accurate results for excited state electron and hole transfer in both charged and uncharged systems that underlie DNA repair, charge separation in donor-acceptor dyads, chromophore-to-solvent electron transfer, and singlet fission. This framework for the accurate and efficient construction of excited state diabats and evaluation of their couplings directly from DFT thus offers a route to simulate and elucidate photoinduced electron and hole transfer in large disordered systems, such as those encountered in the condensed phase.

    View details for DOI 10.1063/5.0035593

    View details for PubMedID 33380087

  • Computational Analysis of Electron Transfer Kinetics for CO2 Reduction with Organic Photoredox Catalysts. The journal of physical chemistry. A Kron, K. J., Gomez, S. J., Mao, Y. n., Cave, R. J., Mallikarjun Sharada, S. n. 2020


    We present a fundamental description of the electron transfer (ET) step from substituted oligo(p-phenylene) (OPP) radical anions to CO2, with the larger goal of assessing the viability of underexplored, organic photoredox routes for utilization of anthropogenic CO2. This work varies the electrophilicity of para-substituents to OPP and probes the dependence of rate coefficients and interfragment interactions on the substituent Hammett parameter, σ p , using constrained density functional theory (CDFT) and energy decomposition analysis (EDA). Large electronic couplings across substituents indicates an adiabatic electron transfer process for reactants at contact. As one might intuitively expect, free energy changes dominate trends in ET rate coefficients in most cases, and rates increase with substituent electron-donating ability. However, we observe an unexpected dip in rate coefficients for the most electron-donating groups, due to the combined impact of flattening free energies and a steep increase in reorganization energies. Our analysis shows that, with decreasing σ p , flattening OPP LUMO levels lower the marginal increase in free energy. EDA reveals trends in electrostatics and charge transfer interactions between the catalyst and substrate fragments that influence free energy changes across substituents. Reorganization energies do not exhibit a direct dependence on σ p and are largely similar across systems, with the exception of substituents containing lone pairs of electrons that exhibit significant deformation upon electron transfer. Our study therefore suggests that while a wide range of ET rates are observed, there is an upper limit to rate enhancements achievable by only tuning the substituent electrophilicity.

    View details for DOI 10.1021/acs.jpca.0c03065

    View details for PubMedID 32491858

  • Constructing spin-adiabatic states for the modeling of spin-crossing reactions. I. A shared-orbital implementation INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY Tao, Y., Pei, Z., Bellonzi, N., Mao, Y., Zou, Z., Liang, W., Yang, Z., Shao, Y. 2019

    View details for DOI 10.1002/qua.26123

    View details for Web of Science ID 000504110300001

  • Accurate and efficient DFT-based diabatization for hole and electron transfer using absolutely localized molecular orbitals. The Journal of chemical physics Mao, Y., Montoya-Castillo, A., Markland, T. E. 2019; 151 (16): 164114


    Diabatic states and the couplings between them are important for quantifying, elucidating, and predicting the rates and mechanisms of many chemical and biochemical processes. Here, we propose and investigate approaches to accurately compute diabatic couplings from density functional theory (DFT) using absolutely localized molecular orbitals (ALMOs). ALMOs provide an appealing approach to generate variationally optimized diabatic states and obtain their associated forces, which allows for the relaxation of the donor and acceptor orbitals in a way that is internally consistent in how the method treats both the donor and acceptor states. Here, we show that one can obtain more accurate electronic couplings between ALMO-based diabats by employing the symmetrized transition density matrix to evaluate the exchange-correlation contribution. We demonstrate that this approach yields accurate results in comparison to other commonly used DFT-based diabatization methods across a wide array of electron and hole transfer processes occurring in systems ranging from conjugated organic molecules, such as thiophene and pentacene, to DNA base pairs. We also show that this approach yields accurate diabatic couplings even when combined with lower tiers of the DFT hierarchy, opening the door to combining it with quantum dynamics approaches to provide an ab initio treatment of nonadiabatic processes in the condensed phase.

    View details for DOI 10.1063/1.5125275

    View details for PubMedID 31675855

  • Accurate prediction of electronic coupling for hole and electron transfer problems using DFT-based approaches Mao, Y., Markland, T. AMER CHEMICAL SOC. 2019
  • Probing radical-neutral interactions and "improper" hydrogen bonds with analysis tools based on absolutely localized molecular orbitals Mao, Y., Head-Gordon, M. AMER CHEMICAL SOC. 2019
  • Probing Blue-Shifting Hydrogen Bonds with Adiabatic Energy Decomposition Analysis JOURNAL OF PHYSICAL CHEMISTRY LETTERS Mao, Y., Head-Gordon, M. 2019; 10 (14): 3899–3905


    The physical origin of blue-shifting hydrogen bonds remains a subject of debate, although many plausible explanations have been proposed. Using a molecular property decomposition analysis based on absolutely localized molecular orbitals, we investigated several representative F3CH···Y (Y = H2O, NH3, Cl-) complexes. We reveal that features of a blue-shifting H-bond already appear on the frozen surface where both polarization and charge transfer (CT) are "turned off", and that the final frequency shift observed depends on the strength of CT. Further decomposition of forces at the frozen level shows that Pauli repulsion is the only component that shortens the C-H bond in the short-range, while both permanent electrostatics and dispersion lengthen the bond. The effects of these forces from the medium to long-range are also discussed. Our analysis provides a complete picture for blue-shifting H-bonds and suggests two necessary conditions for their features to be observed at equilibrium structures: (i) stronger Pauli repulsion than the combination of electrostatic and dispersion forces; (ii) relatively weak CT that is insufficient to compensate for the blue-shifting effect of the frozen interaction.

    View details for DOI 10.1021/acs.jpclett.9b01203

    View details for Web of Science ID 000476694300012

    View details for PubMedID 31241961

  • Energy Decomposition Analysis for Interactions of Radicals: Theory and Implementation at the MP2 Level with Application to Hydration of Halogenated Benzene Cations and Complexes between CO2-· and Pyridine and Imidazole. The journal of physical chemistry. A Loipersberger, M. n., Lee, J. n., Mao, Y. n., Das, A. K., Ikeda, K. n., Thirman, J. n., Head-Gordon, T. n., Head-Gordon, M. n. 2019; 123 (44): 9621–33


    To study intermolecular interactions involving radicals at the correlated level, the energy decomposition analysis scheme for second-order Mo̷ller-Plesset perturbation theory based on absolutely localized molecular orbitals (ALMO-MP2-EDA) is generalized to unrestricted and restricted open-shell MP2. The benefit of restricted open-shell MP2 is that it can provide accurate binding energies for radical complexes where density functional theory can be error-prone due to delocalization errors. As a model application, the open-shell ALMO-MP2-EDA is applied to study the first solvation step of halogenated benzene radical cations, where both halogen- and hydrogen-bonded isomers are possible. We determine that the lighter halogens favor the hydrogen-bonded form, while the iodine-substituted species prefers halogen bonding due to larger polarizability and charge transfer at the halogen. As a second application, relevant to the activation of CO2 in photoelectrocatalysis, complexes of CO2-· interacting with both pyridine and imidazole are analyzed with ALMO-MP2-EDA. The results reveal the importance of charge transfer into the π* orbital of the heterocycle in controlling the stability of the carbamate binding mode, which is favored for pyridine but not for imidazole.

    View details for DOI 10.1021/acs.jpca.9b08586

    View details for PubMedID 31621324

  • Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis CHEMICAL SCIENCE Mao, Y., Head-Gordon, M., Shao, Y. 2018; 9 (45): 8598–8607


    It is common to introduce electron-donating or electron-withdrawing substituent groups into functional conjugated molecules (such as dyes) to tune their electronic structure properties (such as frontier orbital energy levels) and photophysical properties (such as absorption and emission wavelengths). However, there lacks a generally applicable tool that can unravel the underlying interactions between orbitals from a substrate molecule and those from its substituents in modern electronic structure calculations, despite the long history of qualitative molecular orbital theory. In this work, the absolutely localized molecular orbitals (ALMO) based analysis is extended to analyze the effects of substituent groups on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a given system. This provides a bottom-up avenue towards quantification of effects from distinct physical origins (e.g. permanent electrostatics/Pauli repulsion, mutual polarization, inter-fragment orbital mixing). For the example case of prodan (a typical dye molecule), it is found that inter-fragment orbital mixing plays a key role in narrowing the HOMO-LUMO gap of the naphthalene core. Specifically, an out-of-phase mixing of high-lying occupied orbitals on the naphthalene core and the dimethylamino group leads to an elevated HOMO, whereas an in-phase combination of LUMOs on the naphthalene core and the propionyl group lowers the LUMO energy of the entire molecule. We expect this ALMO-based analysis to bridge the gap between concepts from qualitative orbital interaction analysis and quantitative electronic structure calculations.

    View details for DOI 10.1039/c8sc02990c

    View details for Web of Science ID 000451072300011

    View details for PubMedID 30568785

    View details for PubMedCentralID PMC6253684

  • Large Hydrogen-Bond Mismatch between TMAO and Urea Promotes Their Hydrophobic Association CHEM Xie, W., Cha, S., Ohto, T., Mizukami, W., Mao, Y., Wagner, M., Bonn, M., Hunger, J., Nagata, Y. 2018; 4 (11): 2615–27
  • On the Computational Characterization of Charge-Transfer Effects in Noncovalently Bound Molecular Complexes JOURNAL OF CHEMICAL THEORY AND COMPUTATION Mao, Y., Ge, Q., Horn, P. R., Head-Gordon, M. 2018; 14 (5): 2401–17


    Charge-transfer (CT) is an important binding force in the formation of intermolecular complexes, and there have been a variety of theoretical models proposed to quantify this effect. These approaches, which typically rely on a definition of a "CT-free" state based on a partition of the system, sometimes yield significantly different results for a given intermolecular complex. Two widely used definitions of the "CT-free" state, the absolutely localized molecular orbitals (ALMO) method (where only on-fragment orbital mixings are permitted) and the constrained density functional theory (CDFT) approach (where fragment electron populations are fixed), are carefully examined in this work. Natural bond orbital (NBO) and the regularized symmetry-adapted perturbation theory (SAPT) are also briefly considered. Results for the ALMO and CDFT definitions of CT are compared on a broad range of model systems, including hydrogen-bonding systems, borane complexes, metal-carbonyl complexes, and complexes formed by water and metal cations. For most of these systems, CDFT yields a much smaller equilibrium CT energy compared to that given by the ALMO-based definition. This is mainly because the CDFT population constraint does not fully inhibit CT, which means that the CDFT "CT-free" state is in fact CT-contaminated. Examples of this contamination include (i) matching forward and backward donation (e.g., formic acid dimer) and (ii) unidirectional CT without changing fragment populations. The magnitude of the latter effect is quantified in systems such as the water dimer by employing a 3-space density constraint in addition to the orbital constraint. Furthermore, by means of the adiabatic EDA, it is shown that several observable effects of CT, such as the "pyramidalization" of the planar BH3 molecule upon the complexation with Lewis bases, already appear on the "CT-free" CDFT surface. These results reveal the essential distinctions between the ALMO and CDFT definitions of CT and suggest that the former is more consistent with accepted understanding of the role of CT in intermolecular binding.

    View details for DOI 10.1021/acs.jctc.7b01256

    View details for Web of Science ID 000431926500011

    View details for PubMedID 29614855

  • Energy decomposition analysis for exciplexes using absolutely localized molecular orbitals JOURNAL OF CHEMICAL PHYSICS Ge, Q., Mao, Y., Head-Gordon, M. 2018; 148 (6): 064105


    An energy decomposition analysis (EDA) scheme is developed for understanding the intermolecular interaction involving molecules in their excited states. The EDA utilizes absolutely localized molecular orbitals to define intermediate states and is compatible with excited state methods based on linear response theory such as configuration interaction singles and time-dependent density functional theory. The shift in excitation energy when an excited molecule interacts with the environment is decomposed into frozen, polarization, and charge transfer contributions, and the frozen term can be further separated into Pauli repulsion and electrostatics. These terms can be added to their counterparts obtained from the ground state EDA to form a decomposition of the total interaction energy. The EDA scheme is applied to study a variety of systems, including some model systems to demonstrate the correct behavior of all the proposed energy components as well as more realistic systems such as hydrogen-bonding complexes (e.g., formamide-water, pyridine/pyrimidine-water) and halide (F-, Cl-)-water clusters that involve charge-transfer-to-solvent excitations.

    View details for DOI 10.1063/1.5017510

    View details for Web of Science ID 000425299800005

    View details for PubMedID 29448791

  • Assessing many-body contributions to intermolecular interactions of the AMOEBA force field using energy decomposition analysis of electronic structure calculations JOURNAL OF CHEMICAL PHYSICS Demerdash, O., Mao, Y., Liu, T., Head-Gordon, M., Head-Gordon, T. 2017; 147 (16): 161721


    In this work, we evaluate the accuracy of the classical AMOEBA model for representing many-body interactions, such as polarization, charge transfer, and Pauli repulsion and dispersion, through comparison against an energy decomposition method based on absolutely localized molecular orbitals (ALMO-EDA) for the water trimer and a variety of ion-water systems. When the 2- and 3-body contributions according to the many-body expansion are analyzed for the ion-water trimer systems examined here, the 3-body contributions to Pauli repulsion and dispersion are found to be negligible under ALMO-EDA, thereby supporting the validity of the pairwise-additive approximation in AMOEBA's 14-7 van der Waals term. However AMOEBA shows imperfect cancellation of errors for the missing effects of charge transfer and incorrectness in the distance dependence for polarization when compared with the corresponding ALMO-EDA terms. We trace the larger 2-body followed by 3-body polarization errors to the Thole damping scheme used in AMOEBA, and although the width parameter in Thole damping can be changed to improve agreement with the ALMO-EDA polarization for points about equilibrium, the correct profile of polarization as a function of intermolecular distance cannot be reproduced. The results suggest that there is a need for re-examining the damping and polarization model used in the AMOEBA force field and provide further insights into the formulations of polarizable force fields in general.

    View details for DOI 10.1063/1.4999905

    View details for Web of Science ID 000414177600022

    View details for PubMedID 29096520

  • Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis JOURNAL OF CHEMICAL THEORY AND COMPUTATION Mao, Y., Shao, Y., Dziedzic, J., Skylaris, C., Head-Gordon, T., Head-Gordon, M. 2017; 13 (5): 1963–79


    The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH3, NH4+, CN-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

    View details for DOI 10.1021/acs.jctc.7b00089

    View details for Web of Science ID 000401221300011

    View details for PubMedID 28430427

  • Energy decomposition analysis in an adiabatic picture PHYSICAL CHEMISTRY CHEMICAL PHYSICS Mao, Y., Horn, P. R., Head-Gordon, M. 2017; 19 (8): 5944–58


    Energy decomposition analysis (EDA) of electronic structure calculations has facilitated quantitative understanding of diverse intermolecular interactions. Nevertheless, such analyses are usually performed at a single geometry and thus decompose a "single-point" interaction energy. As a result, the influence of the physically meaningful EDA components on the molecular structure and other properties are not directly obtained. To address this gap, the absolutely localized molecular orbital (ALMO)-EDA is reformulated in an adiabatic picture, where the frozen, polarization, and charge transfer energy contributions are defined as energy differences between the stationary points on different potential energy surfaces (PESs), which are accessed by geometry optimizations at the frozen, polarized and fully relaxed levels of density functional theory (DFT). Other molecular properties such as vibrational frequencies can thus be obtained at the stationary points on each PES. We apply the adiabatic ALMO-EDA to different configurations of the water dimer, the water-Cl- and water-Mg2+/Ca2+ complexes, metallocenes (Fe2+, Ni2+, Cu2+, Zn2+), and the ammonia-borane complex. This method appears to be very useful for unraveling how physical effects such as polarization and charge transfer modulate changes in molecular properties induced by intermolecular interactions. As an example of the insight obtained, we find that a linear hydrogen bond geometry for the water dimer is preferred even without the presence of polarization and charge transfer, while the red shift in the OH stretch frequency is primarily a charge transfer effect; by contrast, a near-linear geometry for the water-chloride hydrogen bond is achieved only when charge transfer is allowed.

    View details for DOI 10.1039/c6cp08039a

    View details for Web of Science ID 000395869500028

    View details for PubMedID 28176997

  • Simulating the absorption spectra of helium clusters (N=70, 150, 231, 300) using a charge transfer correction to superposition of fragment single excitations JOURNAL OF CHEMICAL PHYSICS Ge, Q., Mao, Y., White, A. F., Epifanovsky, E., Closser, K. D., Head-Gordon, M. 2017; 146 (4): 044111


    Simulations of the n = 2 absorption spectra of HeN (N = 70, 150, 231, 300) clusters are reported, with nuclear configurations sampled by path integral molecular dynamics. The electronic structure is treated by a new approach, ALMO-CIS+CT, which is a formulation of configuration interaction singles (CIS) based on absolutely localized molecular orbitals (ALMOs). The method generalizes the previously reported ALMO-CIS model [K. D. Closser et al. J. Chem. Theory Comput. 11, 5791 (2015)] to include spatially localized charge transfer (CT) effects. It is designed to recover large numbers of excited states in atomic and molecular clusters, such as the entire n = 2 Rydberg band in helium clusters. ALMO-CIS+CT is shown to recover most of the error caused by neglecting charge transfer in ALMO-CIS and has comparable accuracy to standard CIS for helium clusters. For the n = 2 band, CT stabilizes states towards the blue edge by up to 0.5 eV. ALMO-CIS+CT retains the formal cubic scaling of ALMO-CIS with respect to system size. With improvements to the implementation over that originally reported for ALMO-CIS, ALMO-CIS+CT is able to treat helium clusters with hundreds of atoms using modest computing resources. A detailed simulation of the absorption spectra associated with the 2s and 2p bands of helium clusters up to 300 atoms is reported, using path integral molecular dynamics with a spherical boundary condition to generate atomic configurations at 3 K. The main features of experimentally reported fluorescence excitation spectra for helium clusters are reproduced.

    View details for DOI 10.1063/1.4973611

    View details for Web of Science ID 000394520200015

    View details for PubMedID 28147535

  • Assessing Ion-Water Interactions in the AMOEBA Force Field Using Energy Decomposition Analysis of Electronic Structure Calculations JOURNAL OF CHEMICAL THEORY AND COMPUTATION Mao, Y., Demerdash, O., Head-Gordon, M., Head-Gordon, T. 2016; 12 (11): 5422–37


    AMOEBA is a molecular mechanics force field that addresses some of the shortcomings of a fixed partial charge model, by including permanent atomic point multipoles through quadrupoles, as well as many-body polarization through the use of point inducible dipoles. In this work, we investigate how well AMOEBA formulates its non-bonded interactions, and how it implicitly incorporates quantum mechanical effects such as charge penetration (CP) and charge transfer (CT), for water-water and water-ion interactions. We find that AMOEBA's total interaction energies, as a function of distance and over angular scans for the water dimer and for a range of water-monovalent cations, agree well with an advanced density functional theory (DFT) model, whereas the water-halides and water-divalent cations show significant disagreement with the DFT result, especially in the compressed region when the two fragments overlap. We use a second-generation energy decomposition analysis (EDA) scheme based on absolutely localized molecular orbitals (ALMOs) to show that in the best cases AMOEBA relies on cancellation of errors by softening of the van der Waals (vdW) wall to balance permanent electrostatics that are too unfavorable, thereby compensating for the missing CP effect. CT, as another important stabilizing effect not explicitly taken into account in AMOEBA, is also found to be incorporated by the softened vdW interaction. For the water-halides and water-divalent cations, this compensatory approach is not as well executed by AMOEBA over all distances and angles, wherein permanent electrostatics remains too unfavorable and polarization is overdamped in the former while overestimated in the latter. We conclude that the DFT-based EDA approach can help refine a next-generation AMOEBA model that either realizes a better cancellation of errors for problematic cases like those illustrated here, or serves to guide the parametrization of explicit functional forms for short-range contributions from CP and/or CT.

    View details for DOI 10.1021/acs.jctc.6b00764

    View details for Web of Science ID 000387519400019

    View details for PubMedID 27709939

  • Variational Energy Decomposition Analysis of Chemical Bonding. 1. Spin-Pure Analysis of Single Bonds JOURNAL OF CHEMICAL THEORY AND COMPUTATION Levine, D. S., Horn, P. R., Mao, Y., Head-Gordon, M. 2016; 12 (10): 4812–20


    We have designed an energy decomposition analysis (EDA) to gain a deeper understanding of single chemical bonds, that is, those in which the interacting fragments are doublet open-shell systems but the supersystem is closed-shell. The method is a spin-pure extension of the absolutely localized molecular orbital (ALMO) EDA to the one-pair perfect pairing energy (equivalently to an active space of two electrons in two orbitals). The total interaction energy is broken up into four terms: frozen interactions, spin-coupling, polarization, and charge-transfer. A variety of single bonds are analyzed and, in addition, we use this method to show how solvation changes the nature of bonds, producing different results in the gas-phase and with explicit solvent molecules.

    View details for DOI 10.1021/acs.jctc.6b00571

    View details for Web of Science ID 000385336300009

    View details for PubMedID 27571026

  • TINKTEP: A fully self-consistent, mutually polarizable QM/MM approach based on the AMOEBA force field JOURNAL OF CHEMICAL PHYSICS Dziedzic, J., Mao, Y., Shao, Y., Ponder, J., Head-Gordon, T., Head-Gordon, M., Skylaris, C. 2016; 145 (12): 124106


    We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the onetep linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in tinker. Distributed multipole analysis is used to obtain, on the fly, a classical representation of the QM subsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA. We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations.

    View details for DOI 10.1063/1.4962909

    View details for Web of Science ID 000385562600008

    View details for PubMedID 27782640

  • Advanced Potential Energy Surfaces for Molecular Simulation JOURNAL OF PHYSICAL CHEMISTRY B Albaugh, A., Boateng, H. A., Bradshaw, R. T., Demerdash, O. N., Dziedzic, J., Mao, Y., Margul, D. T., Swails, J., Zeng, Q., Case, D. A., Eastman, P., Wang, L., Essex, J. W., Head-Gordon, M., Pande, V. S., Ponder, J. W., Shao, Y., Skylaris, C., Todorov, I. T., Tuckerman, M. E., Head-Gordon, T. 2016; 120 (37): 9811-9832


    Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

    View details for DOI 10.1021/acs.jpcb.6b06414

    View details for Web of Science ID 000384034100001

    View details for PubMedID 27513316

  • Probing non-covalent interactions with a second generation energy decomposition analysis using absolutely localized molecular orbitals PHYSICAL CHEMISTRY CHEMICAL PHYSICS Horn, P. R., Mao, Y., Head-Gordon, M. 2016; 18 (33): 23067–79


    An energy decomposition analysis (EDA) separates a calculated interaction energy into as many interpretable contributions as possible; for instance, permanent and induced electrostatics, Pauli repulsions, dispersion and charge transfer. The challenge is to construct satisfactory definitions of all terms in the chemically relevant regime where fragment densities overlap, rendering unique definitions impossible. Towards this goal, we present an improved EDA for Kohn-Sham density functional theory (DFT) with properties that have previously not been simultaneously attained. Building on the absolutely localized molecular orbital (ALMO)-EDA, this second generation ALMO-EDA is variational and employs valid antisymmetric electronic wavefunctions to produce all five contributions listed above. These contributions moreover all have non-trivial complete basis set limits. We apply the EDA to the water dimer, the T-shaped and parallel-displaced benzene dimer, the p-biphthalate dimer "anti-electrostatic" hydrogen bonding complex, the biologically relevant binding of adenine and thymine in stacked and hydrogen-bonded configurations, the triply hydrogen-bonded guanine-cytosine complex, the interaction of Cl(-) with s-triazine and with the 1,3-dimethyl imidazolium cation, which is relevant to the study of ionic liquids, and the water-formaldehyde-vinyl alcohol ter-molecular radical cationic complex formed in the dissociative photoionization of glycerol.

    View details for DOI 10.1039/c6cp03784d

    View details for Web of Science ID 000382109300033

    View details for PubMedID 27492057

  • Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation JOURNAL OF CHEMICAL PHYSICS Mao, Y., Horn, P. R., Mardirossian, N., Head-Gordon, T., Skylaris, C., Head-Gordon, M. 2016; 145 (4): 044109


    Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

    View details for DOI 10.1063/1.4959125

    View details for Web of Science ID 000381679800011

    View details for PubMedID 27475350

  • Defining the contributions of permanent electrostatics, Pauli repulsion, and dispersion in density functional theory calculations of intermolecular interaction energies JOURNAL OF CHEMICAL PHYSICS Horn, P. R., Mao, Y., Head-Gordon, M. 2016; 144 (11): 114107


    In energy decomposition analysis of Kohn-Sham density functional theory calculations, the so-called frozen (or pre-polarization) interaction energy contains contributions from permanent electrostatics, dispersion, and Pauli repulsion. The standard classical approach to separate them suffers from several well-known limitations. We introduce an alternative scheme that employs valid antisymmetric electronic wavefunctions throughout and is based on the identification of individual fragment contributions to the initial supersystem wavefunction as determined by an energetic optimality criterion. The density deformations identified with individual fragments upon formation of the initial supersystem wavefunction are analyzed along with the distance dependence of the new and classical terms for test cases that include the neon dimer, ammonia borane, water-Na(+), water-Cl(-), and the naphthalene dimer.

    View details for DOI 10.1063/1.4942921

    View details for Web of Science ID 000373384100010

    View details for PubMedID 27004862

  • Superposition of Fragment Excitations for Excited States of Large Clusters with Application to Helium Clusters JOURNAL OF CHEMICAL THEORY AND COMPUTATION Closser, K. D., Ge, Q., Mao, Y., Shao, Y., Head-Gordon, M. 2015; 11 (12): 5791–5803


    We develop a local excited-state method, based on the configuration interaction singles (CIS) wave function, for large atomic and molecular clusters. This method exploits the properties of absolutely localized molecular orbitals (ALMOs), which strictly limits the total number of excitations, and results in formal scaling with the third power of the system size for computing the full spectrum of ALMO-CIS excited states. The derivation of the equations and design of the algorithm are discussed in detail, with particular emphasis on the computational scaling. Clusters containing ∼500 atoms were used in evaluating the scaling, which agrees with the theoretical predictions, and the accuracy of the method is evaluated with respect to standard CIS. A pioneering application to the size dependence of the helium cluster spectrum is also presented for clusters of 25-231 atoms, the largest of which results in the computation of 2310 excited states per sampled cluster geometry.

    View details for DOI 10.1021/acs.jctc.5b00703

    View details for Web of Science ID 000366223400021

    View details for PubMedID 26609558

  • A cooperative hydrogen bonding system with a C-H center dot center dot center dot O hydrogen bond in ofloxacin JOURNAL OF MOLECULAR STRUCTURE Gao, X., Liu, Y., Li, H., Bian, J., Zhao, Y., Cao, Y., Mao, Y., Li, X., Xu, Y., Ozaki, Y., Wu, J. 2013; 1040: 122–28