Nikita Kirnosov

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.

Nuclear–nuclear correlation function from non-Born–Oppenheimer calculations of diatomic rovibrational states with total angular momentum equal to two (N = 2). Charge asymmetry in HD

ABSTRACT The HD molecule in rovibrational states where the total angular momentum quantum number is equal to two (N = 2) is characterised with quantum mechanical calculations without assuming the Born–Oppenheimer (BO) approximation. Explicitly correlated all-particle Gaussian functions are used in the calculations. The convergence of the total non-BO energies of the considered states with the basis set size is analysed. The calculations of the averaged interparticle distances demonstrate the asymmetry of the electronic charge distribution. The algorithm to calculate the nuclear–nuclear correlation function for the N = 2 states is derived and implemented. Plots of this function for different rovibrational states provide a visual representation of the molecular structure. GRAPHICAL ABSTRACT

Charge asymmetry and rovibrational excitations of HD

ABSTRACT Average values of the interparticle distances for rovibrationally excited HD+ are calculated using a method where the Born–Oppenheimer (BO) approximation is not assumed. The difference between the proton–electron and deuteron–electron distances is used to describe the charge asymmetry in the system. All-particle one-centre explicitly correlated Gaussian functions are used in the calculations of the HD+ rovibrational states. In this work, the non-BO method is extended to calculate the rovibrational states corresponding to the total rotational quantum number of two (N = 2). The algorithms for calculating the Hamiltonian and overlap matrix elements, and the matrix elements of the analytical energy gradient determined with respect to the exponential parameters of the Gaussians, are presented. The gradient is employed in the variational optimisation of the parameters, which is key in obtaining very accurate rovibrational energies in the calculations. The algorithm for calculating the average interparticle distances is also shown. The charge asymmetry of HD+ near the dissociation limit occurs, as expected, with the electron preferentially being near to the deuteron. The asymmetry for a particular vibrational level increases with rotational excitations. The rovibrational transition energies are also calculated and compared with available experimental data.

Computational and photoelectron spectroscopic study of the dipole-bound anions, indole(H2O)1,2−

We report our joint computational and anion photoelectron spectroscopic study of indole-water cluster anions, indole(H2O)1,2 (-). The photoelectron spectra of both cluster anions show the characteristics of dipole-bound anions, and this is confirmed by our theoretical computations. The experimentally determined vertical electron detachment (VDE) energies for indole(H2O)1 (-) and indole(H2O)2 (-) are 144 meV and 251 meV, respectively. The corresponding theoretically determined VDE values for indole(H2O)1 (-) and indole(H2O)2 (-) are 124 meV and 255 meV, respectively. The vibrational features in the photoelectron spectra of these cluster anions are assigned as the vibrations of the water molecule.

Direct non-Born-Oppenheimer variational calculations of all bound vibrational states corresponding to the first rotational excitation of D2 performed with explicitly correlated all-particle Gaussian functions

Direct variational calculations where the Born-Oppenheimer approximation is not assumed are done for all rovibrational states of the D2 molecule corresponding to first excited rotational level (the N = 1 states). All-particle explicitly correlated Gaussian basis functions are used in the calculations. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters. The results allow to determine the ortho-para spin isomerization energies as a function of the vibrational quantum number.

A comparison of two types of explicitly correlated Gaussian functions for non-Born-Oppenheimer molecular calculations using a model potential

A new functional form of the explicitly correlated Gaussian-type functions (later called Gaussians or ECGs) for performing non-Born-Oppenheimer (BO) calculations of molecular systems with an arbitrary number of nuclei is presented. In these functions, the exponential part explicitly depends on all interparticle distances and the preexponential part depends only on the distances between the nuclei. The new Gaussians are called sin/cos-Gaussians and their preexponential part is a product of sin and/or cos factors. The effectiveness of the new Gaussians in describing non-BO pure vibrational states is investigated by comparing them with r(m)-Gaussians containing preexponential multipliers in the form of non-negative powers of internuclear distances (the internuclear distance in the diatomic case). The testing is performed for a diatomic system with the nuclei interacting through a Morse potential. It shows that the new sin/cos-Gaussian basis set is capable of providing equally accurate results as obtained with the r(m)-Gaussians. However, especially for lower vibrational states, more sin/cos-Gaussians are needed to reach a similar accuracy level as obtained with the r(m)-Gaussians. Implementation of the sin/cos-Gaussians in non-BO calculations of diatomic and, in particular, of triatomic systems, which will follow, will provide further assessment of the efficiency of the new functions.