skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Split electrons in partition density functional theory
Partition density functional theory is a density embedding method that partitions a molecule into fragments by minimizing the sum of fragment energies subject to a local density constraint and a global electron-number constraint. To perform this minimization, we study a two-stage procedure in which the sum of fragment energies is lowered when electrons flow from fragments of lower electronegativity to fragments of higher electronegativity. The global minimum is reached when all electronegativities are equal. The non-integer fragment populations are dealt with in two different ways: (1) An ensemble approach (ENS) that involves averaging over calculations with different numbers of electrons (always integers) and (2) a simpler approach that involves fractionally occupying orbitals (FOO). We compare and contrast these two approaches and examine their performance in some of the simplest systems where one can transparently apply both, including simple models of heteronuclear diatomic molecules and actual diatomic molecules with two and four electrons. We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts, and they tend to retain integer numbers of electrons. We establish the conditions under which the ENS populations can become fractional and observe that, even in those cases, the total charge transferred is always lower in ENS than in FOO. Similarly, the FOO fragment dipole moments provide an upper bound to the ENS dipoles. We explain why and discuss the implications.  more » « less
Award ID(s):
1900301
PAR ID:
10346879
Author(s) / Creator(s):
;
Date Published:
Journal Name:
The Journal of Chemical Physics
Volume:
156
Issue:
22
ISSN:
0021-9606
Page Range / eLocation ID:
224113
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, International Journal of Quantum Chemistry)
    Abstract The accuracy of charge‐transfer excitation energies, solvatochromic shifts, and other environmental effects calculated via various density‐embedding techniques depend critically on the approximations employed for the nonadditive noninteracting kinetic energy functional,. Approximating this functional remains an important challenge in electronic‐structure theory. To assist in the development and testing of approximations for, we derive two virial relations for fragments in molecules. These establish separate connections between the nonadditive kinetic energies of the noninteracting and interacting systems of electrons, and quantities such as the electron‐nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn‐Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules. 
    more » « less
  2. ; (, RSC Advances)
    Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all period 2 homodiatomics plus Mo 2 , Cr 2 , ClO, ClO − , and Mo 2 (acetate) 4 . Using Manz's bond order equation with DDEC6 partitioning, the Mo–Mo bond order was 4.12 in Mo 2 and 1.46 in Mo 2 (acetate) 4 with a sum of bond orders for each Mo atom of ∼4. Our study informs both chemistry research and education. As a learning aid, we introduce an analogy between bond orders in materials and message transmission in computer networks. We also introduce the first working quantitative heuristic model for all period 2 homodiatomic bond orders. This heuristic model incorporates s–p mixing to give heuristic bond orders of ¾ (Be 2 ), 1¾ (B 2 ), 2¾ (C 2 ), and whole number bond orders for the remaining period 2 homodiatomics. 
    more » « less
  3. ; ; ; (, Electronic Structure)
    Abstract Density functional theory and ab initio multi-reference calculations are performed to examine the stability and electronic structure of boron complexes that host diffuse electrons in their periphery. Such complexes (solvated electron precursors or SEPs) have been experimentally identified and studied theoretically for several s- and d-block metals. For the first time, we demonstrate that a p-block metalloid element can form a stable SEP when appropriate ligands are chosen. We show that three ammonia and one methyl ligands can displace two of the three boron valence electrons to a peripheral 1s-type orbital. The shell model for these outer electrons is identical to previous SEP systems (1s, 1p, 1d, 2s). Further, we preformed the first examination of a molecular system consisting of two SEPs bridged by a hydrocarbon chain. The electronic structure of these dimers is very similar to that of traditional diatomic molecules forming bonding and anti-bonding σ and π orbitals. Their ground state electronic structure resembles that of two He atoms, and our results indicate that the excitation energies are nearly independent of the chain length for four carbon atoms or longer. These findings pave the way for the development of novel materials similar to expanded metals and electrides. 
    more » « less
  4. ; ; (, The Journal of Chemical Physics)
    Standard approximations for the exchange–correlation functional in Kohn–Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing inter-fragment interactions. Here, we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the multi-fragment overlap approximation (MFOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly correlated linear hydrogen chains. The MFOA, when used in combination with the LDA for the fragments, improves LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. MFOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly correlated hydrogen chains. Moreover, with an additional correction to the partition energy that is specific to the one-dimensional LDA, the approximation is shown to produce dissociation energies in quantitative agreement with calculations based on the density matrix renormalization group method. 
    more » « less
  5. ; (, Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales)
    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 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email