TY - JOUR

T1 - Energy and energy gradient matrix elements with N -particle explicitly correlated complex Gaussian basis functions with L=1

AU - Bubin, Sergiy

AU - Adamowicz, Ludwik

N1 - Funding Information:
This work has been supported by the National Science Foundation. We would also like to thank University of Arizona Center of Computing and Information Technology for using their supercomputer resources. Table I. Convergence of the total energy (in a.u.) of the positronium molecule in the state with L = 1 and negative parity. Basis size This work Varga et al. a 100 − 0.334 400 893 − 0.334 399 869 200 − 0.334 407 545 − 0.334 405 047 300 − 0.334 408 147 400 − 0.334 408 266 3 − 0.334 407 971 500 − 0.334 408 295 5 800 − 0.334 408 177 1200 − 0.334 408 234 1600 − 0.334 408 265 8 a We only show the lowest values from works in Refs. 11 and 12 . Table II. Convergence of the total energy (in a.u.) of the beryllium atom in the 2 P 1 state. Basis size This work Komasa et al. a 100 − 14.471 732 323 150 − 14.472 759 879 − 14.472 212 762 200 − 14.473 101 103 300 − 14.473 326 695 − 14.473 207 488 400 − 14.473 393 969 600 − 14.473 431 855 − 14.473 390 922 800 − 14.473 442 537 1200 − 14.473 442 016 a Reference 4 .

PY - 2008

Y1 - 2008

N2 - In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N -particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

AB - In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N -particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

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U2 - 10.1063/1.2894866

DO - 10.1063/1.2894866

M3 - Article

C2 - 18361554

AN - SCOPUS:41049100529

SN - 0021-9606

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 11

M1 - 114107

ER -