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Hashem Y, Foust K, Kaledin M, Kaledin AL. Fitting Potential Energy Surfaces by Learning the Charge Density Matrix with Permutationally Invariant Polynomials. J Chem Theory Comput 2023; 19:5690-5700. [PMID: 37561135 PMCID: PMC10501011 DOI: 10.1021/acs.jctc.3c00586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Indexed: 08/11/2023]
Abstract
The electronic energy in the Hartree-Fock (HF) theory is the trace of the product of the charge density matrix (CDM) with the one-electron and two-electron matrices represented in an atomic orbital basis, where the two-electron matrix is also a function of the same CDM. In this work, we examine a formalism of analytic representation of a generic molecular potential energy surface (PES) as a sum of a linearly parameterized HF and a correction term, the latter formally representing the electron correlation energy, also linearly parameterized, by expressing the elements of CDM using permutationally invariant polynomials (PIPs). We show on a variety of numerical examples, ranging from exemplary two-electron systems HeH+ and H3+ to the more challenging cases of methanium (CH5+) fragmentation and high-energy tautomerization of formamide to formimidic acid that such a formulation requires significantly fewer, 10-20% of PIPs, to accomplish the same accuracy of the fit as the conventional representation at practically the same computational cost.
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Affiliation(s)
- Younos Hashem
- Department
of Chemistry & Biochemistry, Kennesaw
State University, 370 Paulding Ave NW, Box # 1203, Kennesaw 30144, Georgia
| | - Katheryn Foust
- Department
of Chemistry & Biochemistry, Kennesaw
State University, 370 Paulding Ave NW, Box # 1203, Kennesaw 30144, Georgia
| | - Martina Kaledin
- Department
of Chemistry & Biochemistry, Kennesaw
State University, 370 Paulding Ave NW, Box # 1203, Kennesaw 30144, Georgia
| | - Alexey L. Kaledin
- Cherry
L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, 1515 Dickey Drive, Atlanta 30322, Georgia
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Omodemi O, Kaledin M, Kaledin AL. Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis. J Comput Chem 2022; 43:1495-1503. [PMID: 35737590 DOI: 10.1002/jcc.26952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2022] [Accepted: 06/09/2022] [Indexed: 11/07/2022]
Abstract
A linearly parameterized functional form for a Cartesian representation of molecular dipole polarizability tensor surfaces (PTS) is described. The proposed expression for the PTS is a linearization of the recently reported power series ansatz of the original Applequist model, which by construction is non-linear in parameter space. This new approach possesses (i) a unique solution to the least-squares fitting problem; (ii) a low level of the computational complexity of the resulting linear regression procedure, comparable to those of the potential energy and dipole moment surfaces; and (iii) a competitive level of accuracy compared to the non-linear PTS model. Calculations of CH4 PTS, with polarizabilities fitted to 9000 training set points with the energies up to 14,000 cm-1 show an impressive level of accuracy of the linear PTS model obtained with ~1600 parameters: ~1% versus 0.3% RMSE for the non-linear vs. linear model on a test set of 1000 configurations.
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Affiliation(s)
- Oluwaseun Omodemi
- Department of Chemistry & Biochemistry, Kennesaw State University, Kennesaw, Georgia, USA
| | - Martina Kaledin
- Department of Chemistry & Biochemistry, Kennesaw State University, Kennesaw, Georgia, USA
| | - Alexey L Kaledin
- Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia, USA
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Boutwell D, Pierre-Jacques D, Cochran O, Dyke J, Salazar D, Tyler C, Kaledin M. Intramolecular Proton Transfer in the Hydrogen Oxalate Anion and the Cooperativity Effects of the Low-Frequency Vibrations: A Driven Molecular Dynamics Study. J Phys Chem A 2022; 126:583-592. [PMID: 35049313 DOI: 10.1021/acs.jpca.1c09686] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We report first-principles molecular dynamics (MD) and dipole-driven molecular dynamics (μ-DMD) simulations of the hydrogen oxalate anion at the MP2/aug-cc-pVDZ level of theory. We examine the role of vibrational coupling between the OH stretching bands, that is, the fundamental and a few combination bands spanning the 2900-3100 cm-1 range, and several of the low-frequency bending and stretching fundamental modes. The low-frequency modes between 300 and 825 cm-1 play a crucial role in the proton-transfer motion. Strong involvement of CO2 and CCO bending and the CC stretching vibrations indicate that these large amplitude motions cause the shortening of the O···O distance and thus promote H+ transfer to the other oxygen by bringing it over the 3.4 kcal/mol barrier. Analysis of resonant μ-DMD trajectories shows that the complex spectral feature near 825 cm-1, closely corresponding to both an overtone of two quanta of 425 cm-1 and a combination band of low-frequency CO2 rocking (300 cm-1) and CCO bending (575 cm-1) modes, is involved in the proton transfer. μ-DMD shows that exciting the system at these mode combinations leads to faster barrier activation than exciting at the OH fundamental mode.
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Affiliation(s)
- Dalton Boutwell
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Dominick Pierre-Jacques
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Olivia Cochran
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Jason Dyke
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Dayana Salazar
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Ciara Tyler
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Martina Kaledin
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Ave NW, Box # 1203, Kennesaw, Georgia 30144, United States
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Omodemi O, Sprouse S, Herbert D, Kaledin M, Kaledin AL. On the Cartesian Representation of the Molecular Polarizability Tensor Surface by Polynomial Fitting to Ab Initio Data. J Chem Theory Comput 2021; 18:37-45. [PMID: 34958587 DOI: 10.1021/acs.jctc.1c01015] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We describe an approach to constructing an analytic Cartesian representation of the molecular dipole polarizability tensor surface in terms of polynomials in interatomic distances with a training set of ab initio data points obtained from a molecular dynamics (MD) simulation or by any other available means. The proposed formulation is based on a perturbation treatment of the unmodified point dipole polarizability model of Applequist [ J. Am. Chem. Soc. 1972, 94, 2952] and is shown here to be, by construction (i) free of short-range or other singularities or discontinuities, (ii) symmetric and translationally invariant, and (iii) nonreliant on a body-fixed coordinate system. Permutational invariance of like nuclei is demonstrated to be readily applicable, making this approach useful for highly fluxional and reactive systems. Derivation of the method is described in detail, adding brief didactic numerical examples of H2 and H2O and concluding with an MD simulation of the Raman spectrum of H5O2+ at 300 K with the polarizability tensor fitted to CCSD(T)/aug-cc-pVTZ data obtained using the HBB-4B potential [ J. Chem. Phys. 2005, 122, 044308].
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Affiliation(s)
- Oluwaseun Omodemi
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Avenue NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Sarah Sprouse
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Avenue NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Destyni Herbert
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Avenue NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Martina Kaledin
- Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Avenue NW, Box # 1203, Kennesaw, Georgia 30144, United States
| | - Alexey L Kaledin
- Cherry L. Emerson Center for Scientific Computation, Emory University, 1515 Dickey Drive, Atlanta, Georgia 30322, United States
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