Keeper L. Sharkey

Born-Oppenheimer and non-Born-Oppenheimer, atomic and molecular calculations with explicitly correlated Gaussians.

This paper is part of the 2012 Quantum Chemistry thematic issue. Sergiy Bubin,*,† Michele Pavanello,*,‡ Wei-Cheng Tung, Keeper L. Sharkey, and Ludwik Adamowicz* †Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, United States ‡Department of Chemistry, Rutgers University Newark, Newark, New Jersey 07102, United States Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, United States

Analytical energy gradient in variational calculations of the two lowest P3 states of the carbon atom with explicitly correlated Gaussian basis functions

Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n-electron atomic systems with two p-electrons and (n−2) s-electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited P3 state of the carbon atom. For the former the lo...

Refinement of the experimental energy levels of higher 2D Rydberg states of the lithium atom with very accurate quantum mechanical calculations.

Very accurate variational non-relativistic calculations are performed for four higher Rydberg (2)D states (1s(2)nd(1), n = 8,..., 11) of the lithium atom ((7)Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the (2)S 1s(2)2s(1) ground state.

An algorithm for calculating atomic D states with explicitly correlated Gaussian functions

An algorithm for the variational calculation of atomic D states employing n-electron explicitly correlated gaussians is developed and implemented. The algorithm includes formulas for the first derivatives of the hamiltonian and overlap matrix elements determined with respect to the gaussian nonlinear exponential parameters. The derivatives are used to form the energy gradient which is employed in the variational energy minimization. The algorithm is tested in the calculations of the two lowest D states of the lithium and beryllium atoms. For the lowest D state of Li the present result is lower than the best previously reported result.

An algorithm for non-Born-Oppenheimer quantum mechanical variational calculations of N = 1 rotationally excited states of diatomic molecules using all-particle explicitly correlated Gaussian functions

An algorithm for quantum mechanical variational calculations of bound states of diatomic molecules corresponding to the total angular momentum quantum number equal to one (N = 1) is derived and implemented. The approach employs all-particle explicitly correlated Gaussian function for the wave-function expansion. The algorithm is tested in the calculations of the N = 1, v = 0, ..., 22 states of the HD(+) ion.

Charge asymmetry in rovibrationally excited HD + determined using explicitly correlated all-particle Gaussian functions

Very accurate non-Born-Oppenheimer quantum-mechanical calculations are performed to determine the average values of the interparticle distances and the proton-deuteron density function for the rovibrationally excited HD(+) ion. The states corresponding to excitations to all bound vibrational states (v = 0, ..., 22) and simultaneously excited to the first excited rotational state (N = 1) are considered. To describe each state up to 8000 explicitly correlated all-particle Gaussian functions are used. The nonlinear parameters of the Gaussians are variationally optimized using a procedure that employs the analytical energy gradient determined with respect to these parameters. The results show an increasing asymmetry in the electron distribution with the vibrational excitation as the electron density shifts towards deuteron and away from the proton.

An algorithm for quantum mechanical finite-nuclear-mass variational calculations of atoms with L = 3 using all-electron explicitly correlated Gaussian basis functions.

A new algorithm for quantum-mechanical nonrelativistic calculation of the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for atoms with an arbitrary number of s electrons and with three p electrons, or one p electron and one d electron, or one f electron is developed and implemented. In particular the implementation concerns atomic states with L = 3 and M = 0. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. The approach is employed to perform test calculations on the lowest (2)F state of the two main isotopes of the lithium atom, (7)Li and (6)Li.

Non-Born–Oppenheimer variational method for calculation of rotationally excited binuclear systems

An algorithm for direct non-Born–Oppenheimer quantum mechanical variational calculations of bound states of binuclear systems with Coulombic interactions corresponding to the total angular momentum quantum number equal to one (N = 1) is derived and implemented. Contributions corresponding to each of the particles being angularly excited are taken into account. All-particle explicitly correlated Gaussian basis functions with Cartesian angular factors are used in the approach. The method is tested in the calculations of various three-particle systems including heteronuclear electronic (HD+) and muonic (e.g. ) ions.

Charge asymmetry in the rovibrationally excited HD molecule.

The recently developed method for performing all-particle non-Born-Oppenheimer variational calculations on diatomic molecular systems excited to the first excited rotational state and simultaneously vibrationally excited is employed to study the charge asymmetry and the level lifetimes of the HD molecule. The method uses all-particle explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians are optimized with the aid of the analytical energy gradient determined with respect to these parameters.

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions.

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground (4)S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.