The energy as a functional of the charge density and the charge-density susceptibility: A simple, exact, nonlocal expression for the electronic energy of a molecule

Hunt, Katharine L. C.
April 2002
Journal of Chemical Physics;4/1/2002, Vol. 116 Issue 13, p5440
Academic Journal
Simple, new expressions relate the electronic potential energy 〈V〉 and the total electronic energy E of a molecule to its averaged electron density 〈ρ[sub e](r)〉, the nonlocal charge-density susceptibility χ[sub e](r, r′;iω), the nuclear positions {R[sub N]}, and the nuclear charges {Z[sub N]}. The expressions derived in this work are exact nonrelativistically, within the Born-Oppenheimer approximation. The results give a nonlocal form for the electronic energy in density functional theory. The virial theorem for a system with Coulomb forces is used to derive the expectation value of the kinetic energy in terms of the expectation values of the potential energy and the derivatives of the potential energy operator with respect to nuclear coordinates; gradient expansions of the kinetic energy functional are not needed. Exchange and correlation effects on 〈V〉 and E are determined by an integral of the charge-density susceptibility χ[sub e](r, r′;iω), over imaginary frequencies. The results for 〈V〈 and E are first derived by use of the fluctuation-dissipation theorem and the symmetry properties of the charge-density susceptibility with respect to a change in the sign of ω. Identical results are derived by integration of χ[sub e](r, r′, iω) over imaginary frequencies and use of the closure relation.


Related Articles

  • Critical Bonding in Positive Homonuclear Diatomic Molecular Ions. Hogreve, H. // Few-Body Systems;Jan2004, Vol. 34 Issue 1/3, p143 

    Bonding in homonuclear diatoms with positive excess charge is considered. Focusing mainly onto two-electron systems, we analyze the explanation of barrier formation by avoided crossings of potential energy curves, and replace it by a description yielding a universal scenario for transitions from...

  • An adaptive potential energy surface generation method using curvilinear valence coordinates. Richter, F.; Carbonniere, P.; Dargelos, A.; Pouchan, C. // Journal of Chemical Physics;6/14/2012, Vol. 136 Issue 22, p224105 

    An automatic Born-Oppenheimer potential energy surface (PES) generation method AGAPES is presented designed for the calculation of vibrational spectra of large rigid and semi-rigid polyatomic molecules within the mid-infrared energy range. An adaptive approach guided by information from...

  • Symmetry-invariant reaction-path potentials. Ischtwan, Josef; Collins, Michael A. // Journal of Chemical Physics;6/1/1991, Vol. 94 Issue 11, p7084 

    A general method is presented for constructing a molecular potential-energy surface, based on a reaction path, which is invariant to operations of the complete nuclear permutation inversion group. The method is illustrated with a number of examples, including an approximate potential for NH+3+D2...

  • On the intersection of two potential energy surfaces of the same symmetry. Systematic characterization using a Lagrange multiplier constrained procedure. Manaa, M. Riad; Yarkony, David R. // Journal of Chemical Physics;10/1/1993, Vol. 99 Issue 7, p5251 

    Two nonrelativistic Born–Oppenheimer potential energy surfaces of the same space-spin symmetry may intersect on a surface of dimension N-2, where N is the number of internal nuclear degrees of freedom. Characterization of this entire surface can be quite costly. An algorithm, employing...

  • Temperature Dependence of the Polarizability of Sodium Clusters: An all-electron Density Functional Study. Calaminici, Patrizia; Köster, Andreas M.; Martinez, Gabriel U. Gamboa // AIP Conference Proceedings;11/29/2007, Vol. 963 Issue 1, p207 

    In this contribution we report first-principle all-electron density functional theory (DFT) calculations on small sodium clusters with less than 10 atoms employing the linear combination of Gaussian type orbital DFT program deMon2k. Born-Oppenheimer molecular dynamics (BOMD) simulations over...

  • First-principles computational studies of the torsional potential energy surface of the sec-butyl radical. Chen, Ya Kun; Wang, Yan Alexander // Canadian Journal of Chemistry;Dec2011, Vol. 89 Issue 12, p1469 

    First-principles calculations were carried out to investigate the torsional potential energy surface (PES) of the sec-butyl radical. All the wave function methods employed predict a cis-like stable conformation with a dihedral angle of about 47° in addition to the trans-like global minimum...

  • Direct calculation of anharmonic vibrational states of polyatomic molecules using potential energy surfaces calculated from density functional theory. Wright, Nicholas J.; Gerber, R. Benny // Journal of Chemical Physics;2/8/2000, Vol. 112 Issue 6 

    Potential energy surface points computed from variants of density functional theory (DFT) are used to calculate directly the anharmonic vibrational frequencies of H[sub 2]O, Cl[sup -]H[sub 2]O, and (H[sub 2]O)[sub 2]. The method is an adaptation to DFT of a recent algorithm for direct...

  • Ab initio calculation of the rotational--vibrational energy levels of H[sup +][sub 3] and its... Polyansky, Oleg L.; Tennyson, Jonathan // Journal of Chemical Physics;3/15/1999, Vol. 110 Issue 11, p5056 

    Studies the surfaces fitted to the Born-Oppenheimer potential energy, electronic relativistic correction and adiabatic correction data. Nonadiabatic corrections to the Born-Oppenheimer approximation; Extra term in the nuclear motion Hamiltonian for triatomics; Spectroscopic data from calculations.

  • Does N[sup -][sub 2] exist? A coupled-cluster study. Gutsev, Gennady L.; Rozyczko, Piotr B. // Journal of Chemical Physics;3/15/1999, Vol. 110 Issue 11, p5137 

    Calculates potential energy curves of the ground-state N[sub 2] molecule and its doublet N[sub 2][sup -] anion at the coupled-cluster level with single and double excitations and with noniterative triples. Decaying of the anion to its neutral parent; Existence of the anion within the...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics