Professional Education

  • Doctor of Philosophy, Columbia University (2016)
  • Master of Philosophy, Columbia University (2015)
  • Master of Arts, Columbia University (2013)
  • Master of Arts, CUNY Queens College (2011)
  • Bachelor of Arts, CUNY Queens College (2009)

Stanford Advisors

All Publications

  • On the advantages of exploiting memory in Markov state models for biomolecular dynamics. The Journal of chemical physics Cao, S., Montoya-Castillo, A., Wang, W., Markland, T. E., Huang, X. 2020; 153 (1): 014105


    Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.

    View details for DOI 10.1063/5.0010787

    View details for PubMedID 32640825

  • 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

  • Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches. The Journal of chemical physics Zuehlsdorff, T. J., Montoya-Castillo, A., Napoli, J. A., Markland, T. E., Isborn, C. M. 2019; 151 (7): 074111


    Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic time scale separation; the Franck-Condon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.

    View details for DOI 10.1063/1.5114818

    View details for PubMedID 31438704

  • Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics. The Journal of chemical physics Pfalzgraff, W. C., Montoya-Castillo, A., Kelly, A., Markland, T. E. 2019; 150 (24): 244109


    Methods derived from the generalized quantum master equation (GQME) framework have provided the basis for elucidating energy and charge transfer in systems ranging from molecular solids to photosynthetic complexes. Recently, the nonperturbative combination of the GQME with quantum-classical methods has resulted in approaches whose accuracy and efficiency exceed those of the original quantum-classical schemes while offering significant accuracy improvements over perturbative expansions of the GQME. Here, we show that, while the non-Markovian memory kernel required to propagate the GQME scales quartically with the number of subsystem states, the number of trajectories required scales at most quadratically when using quantum-classical methods to construct the kernel. We then present an algorithm that allows further acceleration of the quantum-classical GQME by providing a way to selectively sample the kernel matrix elements that are most important to the process of interest. We demonstrate the utility of these advances by applying the combination of Ehrenfest mean field theory with the GQME (MF-GQME) to models of the Fenna-Matthews-Olson (FMO) complex and the light harvesting complex II (LHCII), with 7 and 14 states, respectively. This allows us to show that the MF-GQME is able to accurately capture all the relevant dynamical time scales in LHCII: the initial nonequilibrium population transfer on the femtosecond time scale, the steady state-type trapping on the picosecond time scale, and the long time population relaxation. Remarkably, all of these physical effects spanning tens of picoseconds can be encoded in a memory kernel that decays only after ∼65 fs.

    View details for DOI 10.1063/1.5095715

    View details for PubMedID 31255061

  • On the exact continuous mapping of fermions SCIENTIFIC REPORTS Montoya-Castillo, A., Markland, T. E. 2018; 8
  • On the exact continuous mapping of fermions. Scientific reports Montoya-Castillo, A., Markland, T. E. 2018; 8 (1): 12929


    We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantum-classical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.

    View details for PubMedID 30154503

  • Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions The Journal of Chemical Physics Montoya-Castillo, A., Reichman, D. R. 2017; 146

    View details for DOI 10.1063/1.4975388

  • Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths The Journal of Chemical Physics Montoya-Castillo, A., Reichman, D. R. 2017; 146

    View details for DOI 10.1063/1.4973646

  • Generalized quantum master equations in and out of equilibrium: When can one win? JOURNAL OF CHEMICAL PHYSICS Kelly, A., Montoya-Castillo, A., Wang, L., Markland, T. E. 2016; 144 (18)


    Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.

    View details for DOI 10.1063/1.4948612

    View details for Web of Science ID 000377711900006

    View details for PubMedID 27179469

  • Energy Transfer from Quantum Dots to Graphene and MoS2: The Role of Absorption and Screening in Two-Dimensional Materials. Nano letters Raja, A., Montoya Castillo, A., Zultak, J., Zhang, X., Ye, Z., Roquelet, C., Chenet, D. A., van der Zande, A. M., Huang, P., Jockusch, S., Hone, J., Reichman, D. R., Brus, L. E., Heinz, T. F. 2016; 16 (4): 2328-2333


    We report efficient nonradiative energy transfer (NRET) from core-shell, semiconducting quantum dots to adjacent two-dimensional sheets of graphene and MoS2 of single- and few-layer thickness. We observe quenching of the photoluminescence (PL) from individual quantum dots and enhanced PL decay rates in time-resolved PL, corresponding to energy transfer rates of 1-10 ns(-1). Our measurements reveal contrasting trends in the NRET rate from the quantum dot to the van der Waals material as a function of thickness. The rate increases significantly with increasing layer thickness of graphene, but decreases with increasing thickness of MoS2 layers. A classical electromagnetic theory accounts for both the trends and absolute rates observed for the NRET. The countervailing trends arise from the competition between screening and absorption of the electric field of the quantum dot dipole inside the acceptor layers. We extend our analysis to predict the type of NRET behavior for the near-field coupling of a chromophore to a range of semiconducting and metallic thin film materials.

    View details for DOI 10.1021/acs.nanolett.5b05012

    View details for PubMedID 26928675

  • Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics. The Journal of chemical physics Montoya-Castillo, A., Reichman, D. R. 2016; 144 (18): 184104


    We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.

    View details for DOI 10.1063/1.4948408

    View details for PubMedID 27179468

  • Extending the applicability of Redfield theories into highly non-Markovian regimes JOURNAL OF CHEMICAL PHYSICS Montoya-Castillo, A., Berkelbach, T. C., Reichman, D. R. 2015; 143 (19)


    We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna-Matthews-Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.

    View details for DOI 10.1063/1.4935443

    View details for Web of Science ID 000366524700011

    View details for PubMedID 26590528

  • Charge Hopping Dynamics along a Disordered Chain in Quantum Environments: Comparative Study of Different Rate Kernels JOURNAL OF PHYSICAL CHEMISTRY B Jang, S., Montoya-Castillo, A. 2015; 119 (24): 7659-7665


    This work presents a computational study of charge hopping dynamics along a one-dimensional chain with Gaussian site energy disorder and linearly coupled quantum bath. Time-dependent square displacements are calculated directly from numerical solutions of Pauli master equations, for five different rate kernels: exact Fermi golden rule (FGR) rate expression, stationary phase interpolation (SPI) approximation, semiclassical (SC) approximation, classical Marcus rate expression, and Miller-Abrahams expression. All results demonstrate diffusive behavior in the steady state limit. The results based on the FGR rate expression show that the charge transport in the quantum bath can be much more sensitive to the disorder than the prediction from the classical Marcus expression. While the SPI approximation captures this general trend reasonably well, the SC approximation tends to be unreliable at both quantitative and qualitative levels and becomes even worse than the classical Marcus expression under certain conditions. These results offer useful guidance in the choice of approximate rate kernels for larger-scale simulations and also demonstrate significant but fragile positive effects of quantum environments on the charge hopping dynamics.

    View details for DOI 10.1021/jp511933m

    View details for Web of Science ID 000356754800055

    View details for PubMedID 25803833

  • ESR analyses for teeth from the open-air site at Attirampakkam, India: Clues to complex U uptake and paleoenvironmental change Joint Meeting of the 2nd International Conference on Biodosimetry/7th International Symposium on Electron Paramagnetic Resonance Dosimetry and Applications Blackwell, B. A., Montoya, A., Blickstein, J. I., Skinner, A. R., Pappu, S., Gunnell, Y., Taieb, M., Kumar, A., Lundberg, J. A. PERGAMON-ELSEVIER SCIENCE LTD. 2007: 1243–49