scholarly journals Atom-Centered Potentials with Dispersion-Corrected Minimal-Basis-Set Hartree–Fock: An Efficient and Accurate Computational Approach for Large Molecular Systems

2018 ◽  
Vol 14 (2) ◽  
pp. 726-738 ◽  
Author(s):  
Viki Kumar Prasad ◽  
Alberto Otero-de-la-Roza ◽  
Gino A. DiLabio
Keyword(s):  
Computational Approach ◽  
Basis Set ◽  
Minimal Basis ◽  
Molecular Systems ◽  
Hartree Fock

The simplified ab initio method calculation of linear polarizability

1973 ◽  
Vol 26 (5) ◽  
pp. 921 ◽  
Author(s):  
RD Brown ◽  
GR Williams
Keyword(s):  
Ab Initio ◽  
Small Molecules ◽  
Basis Set ◽  
Basis Sets ◽  
Orbital Method ◽  
Polarizability Anisotropy ◽  
Minimal Basis ◽  
Hartree Fock ◽  
Numerical Performance ◽  
Experimental Values

The simplified ab-initio molecular-orbital method described previously is particularly suited to the calculation of polarizabilities by the non-perturbative coupled Hartree-Fock technique. Trial calculations on CO and HF, for which comparison with corresponding ab-initio calculations is possible, show that the method gives an adequate numerical performance. Minimal basis set calculations in general tend to give values that are considerably too low because of inadequate flexibility of the basis and this is the origin of the large discrepancy between theory and experiment, especially for small molecules. ��� Results are also reported for N2O and O3. For these larger systems the SAI results with minimal basis sets are noticeably nearer experimental values. The polarizability anisotropy for N2O is particularly well reproduced by the SAI method. �

scholarly journals Hirshfeld atom like refinement with alternative electron density partitions

IUCrJ ◽  
2020 ◽  
Vol 7 (6) ◽  
pp. 1199-1215 ◽  
Author(s):  
Michał Leszek Chodkiewicz ◽  
Magdalena Woińska ◽  
Krzysztof Woźniak
Keyword(s):  
Quantum Chemistry ◽  
Electron Density ◽  
Structural Parameters ◽  
Accurate Determination ◽  
Basis Set ◽  
Hydrogen Atoms ◽  
Minimal Basis ◽  
Bond Lengths ◽  
Hartree Fock ◽  
Systematic Effects

Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree–Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

scholarly journals Pentagon functions for scattering of five massless particles

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
D. Chicherin ◽  
V. Sotnikov
Keyword(s):  
Phase Space ◽  
Numerical Evaluation ◽  
Public Library ◽  
Basis Set ◽  
Particle Scattering ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Analytic Expressions ◽  
Transcendental Functions ◽  
Branch Cuts

Abstract We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

scholarly journals Reduction of the molecular hamiltonian matrix using quantum community detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Susan M. Mniszewski ◽  
Pavel A. Dub ◽  
Sergei Tretiak ◽  
Petr M. Anisimov ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Community Detection ◽  
Slater Determinant ◽  
Hamiltonian Matrix ◽  
Approximate Methods ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Molecular Hamiltonian ◽  
Structure Problem ◽  
Modularity Maximization ◽  
Chemical Knowledge

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

scholarly journals Computational Methods for Ab Initio Molecular Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Eric Paquet ◽  
Herna L. Viktor
Keyword(s):  
Molecular Dynamics ◽  
Quantum Mechanics ◽  
Ab Initio ◽  
First Principles ◽  
Density Functional ◽  
Path Integrals ◽  
Ab Initio Molecular Dynamics ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Computational Perspective

Ab initio molecular dynamics is an irreplaceable technique for the realistic simulation of complex molecular systems and processes from first principles. This paper proposes a comprehensive and self-contained review of ab initio molecular dynamics from a computational perspective and from first principles. Quantum mechanics is presented from a molecular dynamics perspective. Various approximations and formulations are proposed, including the Ehrenfest, Born–Oppenheimer, and Hartree–Fock molecular dynamics. Subsequently, the Kohn–Sham formulation of molecular dynamics is introduced as well as the afferent concept of density functional. As a result, Car–Parrinello molecular dynamics is discussed, together with its extension to isothermal and isobaric processes. Car–Parrinello molecular dynamics is then reformulated in terms of path integrals. Finally, some implementation issues are analysed, namely, the pseudopotential, the orbital functional basis, and hybrid molecular dynamics.

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