Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties

<div> <div> <div> <p>The introduction of machine-learning (ML) algorithms to quantum mechanics enables rapid evaluation of otherwise intractable expressions at the cost of prior training on appropriate benchmarks. Many computational bottlenecks in the evaluation of accurate electronic structure theory could potentially benefit from the application of such models, from reducing the complexity of the underlying wave function parameter space to circumventing the complications of solving the electronic Schrödinger equation entirely. Applications of ML to electronic structure have thus far been focused on learning molecular properties (mainly the energy) from geometric representations. While this line of study has been quite successful, highly accurate models typically require a “big data” approach with thousands of train- ing data points. Herein, we propose a general, systematically improvable scheme for wave function-based ML of arbitrary molecular properties, inspired by the underlying equations that govern the canonical approach to computing the properties. To this end, we combine the established ML machinery of the t-amplitude tensor representation with a new reduced density matrix representation. The resulting model provides quantitative accuracy in both the electronic energy and dipoles of small molecules using only a few dozen training points per system. </p> </div> </div> </div>

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Machine-Learning Coupled Cluster Properties through a Density Tensor Representation

10.26434/chemrxiv.12056178 ◽

2020 ◽

Author(s):

Benjamin Peyton ◽

Connor Briggs ◽

Ruhee D'Cunha ◽

Johannes T. Margraf ◽

Thomas Crawford

Keyword(s):

Machine Learning ◽

Wave Function ◽

Electronic Structure ◽

Electronic Energy ◽

Molecular Properties ◽

Structure Theory ◽

Function Parameter ◽

Tensor Representation ◽

Cluster Properties ◽

The Cost

<div> <div> <div> <p>The introduction of machine-learning (ML) algorithms to quantum mechanics enables rapid evaluation of otherwise intractable expressions at the cost of prior training on appropriate benchmarks. Many computational bottlenecks in the evaluation of accurate electronic structure theory could potentially benefit from the application of such models, from reducing the complexity of the underlying wave function parameter space to circumventing the complications of solving the electronic Schrödinger equation entirely. Applications of ML to electronic structure have thus far been focused on learning molecular properties (mainly the energy) from geometric representations. While this line of study has been quite successful, highly accurate models typically require a “big data” approach with thousands of train- ing data points. Herein, we propose a general, systematically improvable scheme for wave function-based ML of arbitrary molecular properties, inspired by the underlying equations that govern the canonical approach to computing the properties. To this end, we combine the established ML machinery of the t-amplitude tensor representation with a new reduced density matrix representation. The resulting model provides quantitative accuracy in both the electronic energy and dipoles of small molecules using only a few dozen training points per system. </p> </div> </div> </div>

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Tailored multilevel approaches in vibrational structure theory: A route to quantum mechanical vibrational spectra for complex systems

International Journal of Quantum Chemistry ◽

10.1002/qua.26375 ◽

2020 ◽

Vol 121 (3) ◽

Author(s):

Carolin König

Keyword(s):

Complex Systems ◽

Vibrational Spectra ◽

Vibrational Structure ◽

Structure Theory ◽

Quantum Mechanical ◽

Multilevel Approaches

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Vibrational structure in the carbon 1s ionization of hydrocarbons: Calculation using electronic structure theory and the equivalent-cores approximation

The Journal of Chemical Physics ◽

10.1063/1.476646 ◽

1998 ◽

Vol 109 (3) ◽

pp. 1041-1051 ◽

Cited By ~ 77

Author(s):

T. Darrah Thomas ◽

Leif J. Saethre ◽

Stacey L. Sorensen ◽

Svante Svensson

Keyword(s):

Electronic Structure ◽

Vibrational Structure ◽

Electronic Structure Theory ◽

Structure Theory

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Calculation of the vibrational wave function of polyatomic molecules

The Journal of Chemical Physics ◽

10.1063/1.480840 ◽

2000 ◽

Vol 112 (6) ◽

pp. 2655-2667 ◽

Cited By ~ 81

Author(s):

Per-Olof Åstrand ◽

Kenneth Ruud ◽

Peter R. Taylor

Keyword(s):

Wave Function ◽

Polyatomic Molecules ◽

Vibrational Wave Function

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Augmented Lagrangian Method for Optimizing Non-Orthogonal Orbitals

10.26434/chemrxiv.13239665.v1 ◽

2020 ◽

Author(s):

Masato Sumita ◽

Naruki Yoshikawa

Keyword(s):

Wave Function ◽

Potential Energy Surfaces ◽

Augmented Lagrangian ◽

State Energy ◽

Augmented Lagrangian Method ◽

Lagrangian Method ◽

Spin Coupling ◽

Structure Theory ◽

Coupling Coefficients ◽

Molecular Wave Function

<p>We applied augmented Lagrangian method to optimize molecular wave function based on non-orthogonal orbitals (Spin coupled wave function; SCWF) for its grand-state energy. </p><p>In contrast to the orthogonal-orbital-based electronic structure theory, SCWF includes spin eigenfunctions to satisfy the eigen states as the operator </p><p>of the square of the spin. </p><p>To obtain the ground-state energy of SCWF, therefore, it is necessary to optimize the orbital and the spin-coupling coefficients simultaneously. </p><p>In this study, the spin-coupling and the orbital coefficients are optimized with the augmented Lagrangian method under the constrain of normality of the wave function.</p><p>We employed this SCWF method to compute dissociative potential energy surfaces (PESs) of H<sub>2</sub>, H<sub>2</sub><sup>-</sup>, He<sub>2</sub><sup>+</sup>, and HLi. The obtained PESs by the SCWF method are close to these by full configuration interaction theory. These results indicate that the augmented Lagrangian method is effective to optimize SCWF.</p>

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