Comparison of path integral and density functional techniques in a model two-electron system

1989 ◽  
Vol 93 (14) ◽  
pp. 5628-5632 ◽  
Author(s):  
Randall W. Hall
Keyword(s):  
Path Integral ◽  
Density Functional ◽  
Electron System

Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

In silico study of binding affinity of nitrogenous bicyclic heterocycles: fragment-to-fragment approach

2020 ◽  
Vol 15 (2) ◽  
pp. 49-59
Author(s):  
Yevheniia Velihina ◽  
Nataliya Obernikhina ◽  
Stepan Pilyo ◽  
Maryna Kachaeva ◽  
Oleksiy Kachkovsky ◽  
...  
Keyword(s):  
Amino Acids ◽  
Binding Affinity ◽  
In Silico ◽  
Density Functional ◽  
Energy Levels ◽  
Aromatic Amino Acids ◽  
Electron System ◽  
High Energy ◽  
Proton Donor ◽  
Stabilization Energy

The binding affinity of model aromatic amino acids and heterocycles and their derivatives condensed with pyridine were investigated in silico and are presented in the framework of fragment-to-fragment approach. The presented model describes interaction between pharmacophores and biomolecules. Scrupulous data analysis shows that expansion of the π-electron system by heterocycles annelation causes the shifting up of high energy levels, while the appearance of new the dicoordinated nitrogen atom is accompanied by decreasing of the donor-acceptor properties. Density Functional Theory (DFT) wB97XD/6-31(d,p)/calculations of π-complexes of the heterocycles 1-3 with model fragments of aromatic amino acids, which were formed by π-stack interaction, show an increase in the stabilization energy of π-complexes during the moving from phenylalanine to tryptophan. DFT calculation of pharmacophore complexes with model proton-donor amino acid by the hydrogen bonding mechanism (H-B complex) shows that stabilization energy (DE) increases from monoheterocycles to their condensed derivatives. The expansion of the π-electron system by introducing phenyl radicals to the oxazole cycle as reported earlier [18] leads to a decrease in the stabilization energy of the [Pharm-BioM] complexes in comparison with the annelated oxazole by the pyridine cycle.

Density Functional Approaches to Relativistic Quantum Mechanics

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Electron Density ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Electron System ◽  
State Density ◽  
Dft Methods ◽  
Particle Wave Function ◽  
Spatial Coordinates

The wave function is an elusive and somewhat mysterious object. Nobody has ever observed the wave function directly: rather, its existence is inferred from the various experiments whose outcome is most rationally explained using a wave function interpretation of quantum mechanics. Further, the N-particle wave function is a rather complicated construction, depending on 3N spatial coordinates as well as N spin coordinates, correlated in a manner that almost defies description. By contrast, the electron density of an N-electron system is a much simpler quantity, described by three spatial coordinates and even accessible to experiment. In terms of the wave function, the electron density is expressed as . . . ρ(r) = N ∫ Ψ* (r1,r2,...,rN)Ψ (r1,r2,...,rN)dr2dr3 ...drN (14.1) . . . where the sum over spin coordinates is implicit. It might be much more convenient to have a theory based on the electron density rather than the wave function. The description would be much simpler, and with a greatly reduced (and constant) number of variables, the calculation of the electron density would hopefully be faster and less demanding. We also note that given the correct ground state density, we should be able to calculate any observable quantity of a stationary system. The answer to these hopes is density functional theory, or DFT. Over the past decade, DFT has become one of the most widely used tools of the computational chemist, and in particular for systems of some size. This success has come despite complaints about arbitrary parametrization of potentials, and laments about the absence of a universal principle (other than comparison with experiment) that can guide improvements in the way the variational principle has led the development of wave-function-based methods. We do not intend to pursue that particular discussion, but we note as a historical fact that many important early contributions to relativistic quantum chemistry were made using DFT-like methods. Furthermore, there is every reason to try to extend the success of nonrelativistic DFT methods to the relativistic domain. We suspect that their potential for conquering a sizable part of this field is at least as large as it has been in the nonrelativistic domain.

scholarly journals Using a monomer potential energy surface to perform approximate path integral molecular dynamics simulation of ab initio water at near-zero added cost

2019 ◽  
Vol 21 (1) ◽  
pp. 409-417 ◽  
Author(s):  
Daniel C. Elton ◽  
Michelle Fritz ◽  
Marivi Fernández-Serra
Keyword(s):  
Molecular Dynamics ◽  
Density Functional Theory ◽  
Molecular Dynamics Simulation ◽  
Potential Energy ◽  
Path Integral ◽  
Liquid Water ◽  
Density Functional ◽  
Energy Surface ◽  
Dynamics Simulation ◽  
Functional Theory

We present a new approximate method for doing path integral molecular dynamics simulation with density functional theory and show the utility of the method for liquid water.

Density functional theory is straying from the path toward the exact functional

Science ◽  
2017 ◽  
Vol 355 (6320) ◽  
pp. 49-52 ◽  
Author(s):  
Michael G. Medvedev ◽  
Ivan S. Bushmarinov ◽  
Jianwei Sun ◽  
John P. Perdew ◽  
Konstantin A. Lyssenko
Keyword(s):  
Density Functional Theory ◽  
Density Distribution ◽  
Ground State ◽  
Electron Density Distribution ◽  
Density Functional ◽  
Electron System ◽  
The Other ◽  
Functional Theory ◽  
The Core ◽  
Exact Density

The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

scholarly journals Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory

2003 ◽  
Vol 02 (02) ◽  
pp. 301-322 ◽  
Author(s):  
Manoj K. Harbola ◽  
Arup Banerjee
Keyword(s):  
Density Functional Theory ◽  
Perturbation Theory ◽  
Electron Density ◽  
Current Density ◽  
Density Functional ◽  
Electron System ◽  
Time Dependent ◽  
Functional Theory ◽  
Thomas Fermi ◽  
Alkali Metal Clusters

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6 is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.

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