1
|
Schiltz C, Rappoport D, Mandelshtam VA. Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP). J Chem Phys 2023; 158:2890485. [PMID: 37184023 DOI: 10.1063/5.0146682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 04/24/2023] [Indexed: 05/16/2023] Open
Abstract
The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with ab initio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.
Collapse
Affiliation(s)
- Colin Schiltz
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Dmitrij Rappoport
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | | |
Collapse
|
2
|
Rossi M. Progress and challenges in ab initio simulations of quantum nuclei in weakly bonded systems. J Chem Phys 2021; 154:170902. [PMID: 34241065 DOI: 10.1063/5.0042572] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Atomistic simulations based on the first-principles of quantum mechanics are reaching unprecedented length scales. This progress is due to the growth in computational power allied with the development of new methodologies that allow the treatment of electrons and nuclei as quantum particles. In the realm of materials science, where the quest for desirable emergent properties relies increasingly on soft weakly bonded materials, such methods have become indispensable. In this Perspective, an overview of simulation methods that are applicable for large system sizes and that can capture the quantum nature of electrons and nuclei in the adiabatic approximation is given. In addition, the remaining challenges are discussed, especially regarding the inclusion of nuclear quantum effects (NQEs) beyond a harmonic or perturbative treatment, the impact of NQEs on electronic properties of weakly bonded systems, and how different first-principles potential energy surfaces can change the impact of NQEs on the atomic structure and dynamics of weakly bonded systems.
Collapse
Affiliation(s)
- Mariana Rossi
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
3
|
Riera M, Hirales A, Ghosh R, Paesani F. Data-Driven Many-Body Models with Chemical Accuracy for CH4/H2O Mixtures. J Phys Chem B 2020; 124:11207-11221. [DOI: 10.1021/acs.jpcb.0c08728] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Alan Hirales
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Raja Ghosh
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
| |
Collapse
|
4
|
Riera M, Yeh EP, Paesani F. Data-Driven Many-Body Models for Molecular Fluids: CO2/H2O Mixtures as a Case Study. J Chem Theory Comput 2020; 16:2246-2257. [DOI: 10.1021/acs.jctc.9b01175] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Eric P. Yeh
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
| |
Collapse
|
5
|
Brown SE. From ab initio data to high-dimensional potential energy surfaces: A critical overview and assessment of the development of permutationally invariant polynomial potential energy surfaces for single molecules. J Chem Phys 2019; 151:194111. [PMID: 31757150 DOI: 10.1063/1.5123999] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The representation of high-dimensional potential energy surfaces by way of the many-body expansion and permutationally invariant polynomials has become a well-established tool for improving the resolution and extending the scope of molecular simulations. The high level of accuracy that can be attained by these potential energy functions (PEFs) is due in large part to their specificity: for each term in the many-body expansion, a species-specific training set must be generated at the desired level of theory and a number of fits attempted in order to obtain a robust and reliable PEF. In this work, we attempt to characterize the numerical aspects of the fitting problem, addressing questions which are of simultaneous practical and fundamental importance. These include concrete illustrations of the nonconvexity of the problem, the ill-conditionedness of the linear system to be solved and possible need for regularization, the sensitivity of the solutions to the characteristics of the training set, and limitations of the approach with respect to accuracy and the types of molecules that can be treated. In addition, we introduce a general approach to the generation of training set configurations based on the familiar harmonic approximation and evaluate the possible benefits to the use of quasirandom sequences for sampling configuration space in this context. Using sulfate as a case study, the findings are largely generalizable and expected to ultimately facilitate the efficient development of PIP-based many-body PEFs for general systems via automation.
Collapse
Affiliation(s)
- Sandra E Brown
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| |
Collapse
|
6
|
Kapil V, Engel E, Rossi M, Ceriotti M. Assessment of Approximate Methods for Anharmonic Free Energies. J Chem Theory Comput 2019; 15:5845-5857. [DOI: 10.1021/acs.jctc.9b00596] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Affiliation(s)
- Venkat Kapil
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Edgar Engel
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Mariana Rossi
- Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| |
Collapse
|
7
|
Kohno BH, Mallory JD, Mandelshtam VA. Magic numbers, quantum delocalization, and orientational disordering in anionic hydrogen and deuterium clusters. J Chem Phys 2019; 150:204305. [PMID: 31153193 DOI: 10.1063/1.5099255] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Diffusion Monte Carlo (DMC) method was applied to anionic hydrogen clusters H-(H2)n (n = 1-16, 32) and their deuterated analogs using a polarizable all-atom potential energy surface (PES) developed by Calvo and Yurtsever. For the hydrogen clusters, the binding energy ΔEn appears to be a smooth function of the cluster size n, thus contradicting the previous claim that n = 12 is a "magic number" cluster. The structures of the low energy minima of the PES for these clusters belong to the icosahedral motif with the H2 molecules aligned toward the central H- ion. However, their ground state wavefunctions are highly delocalized and resemble neither the structures of the global nor local minima. Moreover, the strong nuclear quantum effects result in a nearly complete orientational disordering of the H2 molecules. For the deuterium clusters, the ground state wavefunctions are localized and the D2 molecules are aligned toward the central D- ion. However, their structures are still characterized as disordered and, as such, do not display size sensitivity. In addition, DMC simulations were performed on the mixed H-(H2)n(D2)p clusters with (n, p) = (6, 6) and (16, 16). Again, in contradiction to the previous claim, we found that the "more quantum" H2 molecules prefer to reside farther from the central H- ion than the D2 molecules.
Collapse
Affiliation(s)
- Bridgett H Kohno
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Joel D Mallory
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | | |
Collapse
|
8
|
Brown SE, Götz AW, Cheng X, Steele RP, Mandelshtam VA, Paesani F. Monitoring Water Clusters “Melt” Through Vibrational Spectroscopy. J Am Chem Soc 2017; 139:7082-7088. [DOI: 10.1021/jacs.7b03143] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
| | | | - Xiaolu Cheng
- Department
of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, United States
| | - Ryan P. Steele
- Department
of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, United States
| | | | | |
Collapse
|
9
|
Brown SE, Mandelshtam VA. Self-consistent phonons: An accurate and practical method to account for anharmonic effects in equilibrium properties of general classical or quantum many-body systems. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.06.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
10
|
Zacharias M, Patrick CE, Giustino F. Stochastic Approach to Phonon-Assisted Optical Absorption. PHYSICAL REVIEW LETTERS 2015; 115:177401. [PMID: 26551142 DOI: 10.1103/physrevlett.115.177401] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Indexed: 06/05/2023]
Abstract
We develop a first-principles theory of phonon-assisted optical absorption in semiconductors and insulators which incorporates the temperature dependence of the electronic structure. We show that the Hall-Bardeen-Blatt theory of indirect optical absorption and the Allen-Heine theory of temperature-dependent band structures can be derived from the present formalism by retaining only one-phonon processes. We demonstrate this method by calculating the optical absorption coefficient of silicon using an importance sampling Monte Carlo scheme, and we obtain temperature-dependent line shapes and band gaps in good agreement with experiment. The present approach opens the way to predictive calculations of the optical properties of solids at finite temperature.
Collapse
Affiliation(s)
- Marios Zacharias
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - Christopher E Patrick
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - Feliciano Giustino
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| |
Collapse
|
11
|
Hermes MR, Hirata S. Stochastic many-body perturbation theory for anharmonic molecular vibrations. J Chem Phys 2015; 141:084105. [PMID: 25173003 DOI: 10.1063/1.4892614] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm(-1) and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Collapse
Affiliation(s)
- Matthew R Hermes
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| |
Collapse
|
12
|
|
13
|
Hermes MR, Hirata S. Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces. J Chem Phys 2014; 141:244111. [DOI: 10.1063/1.4904220] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew R. Hermes
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| |
Collapse
|
14
|
Saller MAC, Habershon S. Basis Set Generation for Quantum Dynamics Simulations Using Simple Trajectory-Based Methods. J Chem Theory Comput 2014; 11:8-16. [DOI: 10.1021/ct500657f] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Maximilian A. C. Saller
- Department
of Chemistry and
Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom
| | - Scott Habershon
- Department
of Chemistry and
Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom
| |
Collapse
|
15
|
Coughtrie DJ, Tew DP. The Nosé-Hoover looped chain thermostat for low temperature thawed Gaussian wave-packet dynamics. J Chem Phys 2014; 140:194106. [PMID: 24852529 DOI: 10.1063/1.4875517] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have used a generalised coherent state resolution of the identity to map the quantum canonical statistical average for a general system onto a phase-space average over the centre and width parameters of a thawed Gaussian wave packet. We also propose an artificial phase-space density that has the same behaviour as the canonical phase-space density in the low-temperature limit, and have constructed a novel Nosé-Hoover looped chain thermostat that generates this density in conjunction with variational thawed Gaussian wave-packet dynamics. This forms a new platform for evaluating statistical properties of quantum condensed-phase systems that has an explicit connection to the time-dependent Schrödinger equation, whilst retaining many of the appealing features of path-integral molecular dynamics.
Collapse
Affiliation(s)
- David J Coughtrie
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - David P Tew
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| |
Collapse
|
16
|
Patrick CE, Giustino F. Unified theory of electron-phonon renormalization and phonon-assisted optical absorption. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:365503. [PMID: 25134725 DOI: 10.1088/0953-8984/26/36/365503] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the Herzberg-Teller effect and to phonon-assisted optical absorption in indirect band gap materials. In addition, our theory predicts sub-gap phonon-assisted optical absorption in direct gap materials, as well as an exponential edge which we tentatively assign to the Urbach tail. We also consider a semiclassical approach to the calculation of optical absorption spectra which simultaneously captures energy-level renormalization and phonon-assisted transitions and is especially suited to first-principles electronic structure calculations. We demonstrate this approach by calculating the phonon-assisted optical absorption spectrum of bulk silicon.
Collapse
|
17
|
Herman MF. Improving the efficiency of Monte Carlo surface hopping calculations. J Phys Chem B 2014; 118:8026-33. [PMID: 24650188 DOI: 10.1021/jp501139s] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A surface hopping method with a Monte Carlo procedure for deciding whether to hop at each step along the classical trajectories used in the semiclassical calculation is discussed. It is shown for a simple one-dimensional model problem that the numerical efficiency of the method can be improved by averaging over several copies of the sections of each trajectory that span the interaction regions. The use of Sobol sequences in the selection of the initial momentum for the trajectories is also explored. It is found that accurate results can be obtained with relatively small trajectory samples.
Collapse
Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University , New Orleans, Louisiana 70118, United States
| |
Collapse
|
18
|
Georgescu I, Jitomirskaya S, Mandelshtam VA. On the ground state calculation of a many-body system using a self-consistent basis and quasi-Monte Carlo: An application to water hexamer. J Chem Phys 2013; 139:204104. [DOI: 10.1063/1.4829836] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
|
19
|
Habershon S. Path integral density matrix dynamics: A method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems. J Chem Phys 2013; 139:104107. [DOI: 10.1063/1.4819322] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
20
|
|