The weak orthogonality functional in explicitly correlated pair theories

Tew, David P.; Klopper, Wim; Manby, Frederick R.
November 2007
Journal of Chemical Physics;11/7/2007, Vol. 127 Issue 17, p174105
Academic Journal
Recent advances have seen the convergence of the R12 and Gaussian geminal explicitly correlated methods, such that the principal remaining distinction is the way in which the many-electron integrals are handled. Here we examine the weak orthogonality functional and the resolution of the identity and find that the first, although exact in the limit of infinite basis, introduces a conflict between the physical description of the electronic cusp and the satisfaction of the strong orthogonality constraint. This leads us to propose an improved weak orthogonality functional where the explicitly correlated pair functions are almost orthogonal to the occupied orbitals by construction. For applications where 95%-98% accuracy in the total correlation energy is sufficient, we recommend use of the strong orthogonality functional in combination with the resolution of the identity for three- and four-electron integral evaluations.


Related Articles

  • Scheme for adding electron–nucleus cusps to Gaussian orbitals. Ma, A.; Towler, M. D.; Drummond, N. D.; Needs, R. J. // Journal of Chemical Physics;6/8/2005, Vol. 122 Issue 22, p224322 

    A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom,...

  • Analytical Hartree-Fock gradients with respect to the cell parameter for systems periodic in three dimensions. Doll, K.; Dovesi, R.; Orlando, R. // Theoretical Chemistry Accounts: Theory, Computation, & Modeling;Dec2004, Vol. 112 Issue 5/6, p394 

    Analytical Hartree-Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of three-dimensional periodicity. The code is based on Gaussian-type orbitals, and the summation of the Coulomb energy is performed with the Ewald...

  • Theory and software for large Quantum Monte Carlo super-computer simulations over exponential type orbitals. Hoggan, Philip E. // AIP Conference Proceedings;3/9/2009, Vol. 1102 Issue 1, p152 

    Slater-type orbitals (STO) are rarely used as atomic basis sets for molecular structure and property calculations, since integrals are expensive to evaluate, reliable basis sets are scarce and exact properties such as Kato’s cusp condition and the correct exponential decay of the electron...

  • Density-functional studies of plasmons in small metal clusters. Ke-Yan Lian; Sałek, Paweł; Mingxing Jin; Dajun Ding // Journal of Chemical Physics;5/7/2009, Vol. 130 Issue 17, p174701 

    We study the formation of plasmon modes of small gold clusters by modeling the excitation spectra. The shape change of the longitudinal mode as a function of cluster size is studied using time-dependent Kohn–Sham theory and Gaussian basis sets. The presence of d electrons in gold atoms...

  • On the acceleration of the convergence of singular operators in Gaussian basis sets. Pachucki, Krzysztof; Cencek, Wojciech; Komasa, Jacek // Journal of Chemical Physics;5/8/2005, Vol. 122 Issue 18, p184101 

    Gaussian type wave functions do not reproduce the interparticle cusps which result in a slow convergence of the expectation values of the operators involved in calculations of the relativistic and QED energy corrections. Methods correcting this deficiency are the main topic discussed in this...

  • Theoretical calculation of the electronic states with spin—orbit effects of the molecule LiCs. Elkork, N.; Houalla, D.; Korek, M. // Canadian Journal of Physics;Oct2009, Vol. 87 Issue 10, p1079 

    The potential energy curves of the molecule LiCs have been calculated for the 55 low-lying electronic states in the Ω-representation. Using an ab initio method the calculation is based on a nonempirical pseudo-potential in the interval 3.0ao≤ R ≤ 40.0ao of the internuclear...

  • Hierarchy of model Kohn–Sham potentials for orbital-dependent functionals: A practical alternative to the optimized effective potential method. Kohut, Sviataslau V.; Ryabinkin, Ilya G.; Staroverov, Viktor N. // Journal of Chemical Physics;5/14/2014, Vol. 140 Issue 18, p18A535-1 

    We describe a method for constructing a hierarchy of model potentials approximating the functional derivative of a given orbital-dependent exchange-correlation functional with respect to electron density. Each model is derived by assuming a particular relationship between the self-consistent...

  • A six-dimensional H2–H2 potential energy surface for bound state spectroscopy. Hinde, Robert J. // Journal of Chemical Physics;4/21/2008, Vol. 128 Issue 15, p154308 

    We present a six-dimensional potential energy surface for the (H2)2 dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer’s center of mass. The surface is intended to describe...

  • Diagnostics of molecular orbital quality. Jia Deng; Gilbert, Andrew T. B.; Gill, Peter M. W. // Canadian Journal of Chemistry;Aug2010 Part 1 of 2, Vol. 88 Issue 8, p754 

    We discuss several measures of the quality of a molecular orbital. Each requires only that the orbital be associated with a well-defined Fock operator and is thus applicable to both Hartree-Fock and density functional orbitals. One of the measures, the y diagnostic, ranges from y = 0 (perfect)...


Read the Article


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

Try another library?
Sign out of this library

Other Topics