Study of NO and CO dissociation on the (100) Cu surface using density functional theory and the topological analysis of the electronic density and its Laplacian

1996 ◽  
Vol 74 (6) ◽  
pp. 1014-1020 ◽  
Author(s):  
Yosslen Aray ◽  
Jesús Rodríguez
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Good Description ◽  
Topological Analysis ◽  
Molecular Graph ◽  
Electronic Density ◽  
Functional Theory ◽  
Hartree Fock ◽  
Local Charge ◽  
Charge Concentration

Molecular orbital ab initio Hartree–Fock, post-Hartree–Fock at the MP2 and QCISD levels, and density functional theory calculations of the dipole moment, the topology of the electronic density, ρ(r), and its Laplacian, [Formula: see text], for CO and NO molecules are reported. The results obtained confirm that density functional methods provide remarkably good electronic properties and a good description of the topology of ρ(r) and [Formula: see text]. The Becke exchange functional with the correlation functional of Lee, Yang, and Parr was used to calculate the electronic density of the (100) Cu surface. Topological analysis of ρ(r) shows that the crystal graph corresponds to square pyramids between the atoms of the top of the surface and the atoms of the second layer The topological analysis of [Formula: see text] shows that the atomic graph of the Cu surface exhibits one (3,−3) local charge concentration surrounded by four (3,+1) local charge depletion points. Additionally, there is a (3,+3) local depletion in the midpoint between each of four contiguous Cu atoms corresponding to the active site for the adsorption of the (3,−3) local charge concentration on the C atom of the CO or the N atom of the NO molecule. The larger value of the [Formula: see text] at the nonbonded charge concentration on the atoms and the geometrical configuration of these critical points favor the interaction of the NO over the CO molecule with the (100) Cu surface. This result is in accord with the known reaction barriers for these molecules. Key words: density functional theory, Laplacian of the electronic density, (100) Cu surface, carbon monoxide, nitrogen monoxide, molecular graph, atomic graph.

scholarly journals Towards a density functional theory of molecular fragments. What is the shape of atoms in molecules?

2020 ◽  
Vol 44 (170) ◽  
pp. 269-279
Author(s):  
Victor H. Chávez ◽  
Adam Wasserman
Keyword(s):  
Density Functional Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Density Functional ◽  
Computational Cost ◽  
Atoms In Molecules ◽  
Electronic Density ◽  
Functional Theory ◽  
New Methods ◽  
The Cost

In some sense, quantum mechanics solves all the problems in chemistry: The only thing one has to do is solve the Schrödinger equation for the molecules of interest. Unfortunately, the computational cost of solving this equation grows exponentially with the number of electrons and for more than ~100 electrons, it is impossible to solve it with chemical accuracy (~ 2 kcal/mol). The Kohn-Sham (KS) equations of density functional theory (DFT) allow us to reformulate the Schrödinger equation using the electronic probability density as the central variable without having to calculate the Schrödinger wave functions. The cost of solving the Kohn-Sham equations grows only as N3, where N is the number of electrons, which has led to the immense popularity of DFT in chemistry. Despite this popularity, even the most sophisticated approximations in KS-DFT result in errors that limit the use of methods based exclusively on the electronic density. By using fragment densities (as opposed to total densities) as the main variables, we discuss here how new methods can be developed that scale linearly with N while providing an appealing answer to the subtitle of the article: What is the shape of atoms in molecules?

scholarly journals An investigation of the performance of a hybrid of Hartree-Fock and density functional theory

1992 ◽  
Vol 44 (S26) ◽  
pp. 319-331 ◽  
Author(s):  
Peter M. W. Gill ◽  
Benny G. Johnson ◽  
John A. Pople ◽  
Michael J. Frisch
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Hartree Fock

scholarly journals Effect of Hartree–Fock pseudopotentials on local density functional theory calculations

2018 ◽  
Vol 20 (27) ◽  
pp. 18844-18849 ◽  
Author(s):  
Hengxin Tan ◽  
Yuanchang Li ◽  
S. B. Zhang ◽  
Wenhui Duan
Keyword(s):  
Density Functional Theory ◽  
Band Gap ◽  
Density Functional ◽  
Local Density ◽  
Density Functional Theory Calculations ◽  
Optimal Choice ◽  
Functional Theory ◽  
Hartree Fock ◽  
Local Density Functional Theory ◽  
Local Density Functional

Optimal choice of the element-specific pseudopotential improves the band gap.

Theoretical Methods

1992 ◽  
Author(s):  
John A. Tossell ◽  
David J. Vaughan
Keyword(s):  
Density Functional Theory ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Point Group ◽  
Theoretical Background ◽  
Wave Functions ◽  
General Reference ◽  
Functional Theory ◽  
Hartree Fock ◽  
Self Consistent Field

In this chapter, the most important quantum-mechanical methods that can be applied to geological materials are described briefly. The approach used follows that of modern quantum-chemistry textbooks rather than being a historical account of the development of quantum theory and the derivation of the Schrödinger equation from the classical wave equation. The latter approach may serve as a better introduction to the field for those readers with a more limited theoretical background and has recently been well presented in a chapter by McMillan and Hess (1988), which such readers are advised to study initially. Computational aspects of quantum chemistry are also well treated by Hinchliffe (1988). In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first; that is, the “localized” side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (CI) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. The focus then shifts to the “delocalized” side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field Xα method (MS-SCF-Xα) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is followed by discussion of empirical simulation, and we conclude by mentioning a recent approach incorporating density-functional theory and molecular dynamics (Car and Parrinello, 1985).

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