Multicenter and multiparticle integrals for explicitly correlated cartesian gaussian‐type functions

1996

J. Phys. Chem.

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Nonadiabatic variational calculations for the positronium molecule, Ps 2 ) (e + e -) 2 , a cluster composed of two electrons and two positrons, is the subject of theoretical investigation. In particular, calculations of the twophoton annihilation rate as well as estimation of the lifetime at the nonrelativistic level of theory are presented in detail. In all calculations the nonadiabatic four-body wave function is expanded in terms of explicitly correlated Gaussian functions. The energy of the center-of-mass motion is effectively eliminated from the total nonrelativistic energy through the modified variational principle based on the internal Hamiltonian. With the wave function expanded in terms of 300 basis functions, which leads to a total energy equal to -0.515 980 au and a binding energy equal to 0.435 eV, the lifetime of the system is estimated to be 0.907 ns.

Section: Appendix Amentioning

confidence: 99%

Lifetime of Positronium Molecule. Study with Boys' Explicitly Correlated Gaussians

Kozłowski

1996

J. Phys. Chem.

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“…In order to derive the gradients, we will need the molecular integral formulas for the basis functions (2). The required molecular integrals have been published before in several formats 3–5, 10 so we will only quote the integral formulas here. The format of the integral formulas used here is somewhat unique, though, so full derivations are provided in the .…”

Section: Molecular Integralsmentioning

confidence: 99%

“…The group of Komasa, Cencek, and Rychlewski has done much excellent work with ECGs 5–9 setting energy benchmarks for several small systems. Adamowicz and Kozlowski 10, 11 were the first to implement analytical gradients and Hessians in the optimization of wave functions in a basis of single‐center ECGs. Kinghorn 12–15, in collaboration with Poshusta and Adamowicz, applied analytical gradients to the optimization of single‐center Singer ECGs for atomic and diatomic non‐Born–Oppenheimer systems.…”

Section: Introductionmentioning

confidence: 99%

Analytical gradients for Singer's multicenter n‐electron explicitly correlated Gaussians

Cafiero

Int J of Quantum Chemistry

2001

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ABSTRACT:Analytical gradients for Singer's basis of n-electron multicenter explicitly correlated Gaussian functions are derived and implemented to variationally optimize the energy and wave function of molecular systems within the Born-Oppenheimer approximation. Wave functions are optimized with respect to ( 1 2 n(n + 1) + 3n) nonlinear variational parameters and one linear coefficient per term in the basis set. Preliminary results for the ground states of H 3 + and H 3 suggest that the method can be more flexible and can achieve lower energies than previously reported calculations.

“…In this case, the calculations will require evaluation of integrals with Cartesian Gaussian cluster functions such as previously demonstrated. 9 In order for our approach to provide a viable alternative for nonadiabatic calculations of many-body systems, it should be demonstrated whether the internal energy of the nonadiabatic system can be evaluated with a sufficient accuracy. There are two aspects to this question.…”

Section: Effective Elimination Of Center-of-mass Motionmentioning

confidence: 99%

Implementation of analytical first derivatives for evaluation of the many-body nonadiabatic wave function with explicitly correlated Gaussian functions

Kozłowski

The Journal of Chemical Physics

1992

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Analytic first-order properties from explicitly correlated many-body perturbation theory and Gaussian geminal basis J. Chem. Phys. 108, 7946 (1998); 10.1063/1.476235Newton-Raphson optimization of the manybody nonadiabatic wave function expressed in terms of explicitly correlated Gaussian functions An effective method for generating nonadiabatic manybody wave function using explicitly correlated Gaussian type functions J. Chem. Phys. 95, 6681 (1991); A nonadiabatic many-particle wave function is generated using an expansion in terms of explicitly correlated Gaussian-type basis functions. In this approach, motions of all particles are correlated at the same time, and electrons and nuclei are distinguished via permutational symmetry. We utilize our newly proposed nonadiabatic variational approach [Po M. Kozlowski and L. Adamowicz, J. Chem. Phys. 95, 6681 (1991) 1, which does not require the separation of the internal and external motions. The analytical first derivative of the variational functional with respect to the nonlinear parameters appearing in the basis functions are derived and implemented to find the minimum. Numerical examples for the ground state of the hydrogen molecule are presented.