Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of ditritium using all-particle explicitly correlated Gaussian functions

Very accurate variational calculations of the complete pure vibrational spectrum of the ditritium (T2) molecule are performed within the framework where the Born-Oppenheimer approximation is not assumed. After separating out the center-of-mass motion from the total laboratory-frame Hamiltonian, T2 becomes a three-particle problem. States corresponding to the zero total angular momentum, which are pure vibrational states, are spherically symmetric in this framework. The wave functions of these states are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. In the calculations the total energies, the dissociation energies, and expectation values of some operators dependent on interparticle distances are determined

Non-Born–Oppenheimer calculations of the BH molecule

Variational calculations employing explicitly correlated Gaussian basis functions have been performed for the ground state of the boron monohydride molecule BH and for the boron atom B . Up to 2000 Gaussians were used for each system. The calculations did not assume the Born–Oppenheimer BO approximation. In the optimization of the wave function, we employed the analytical energy gradient with respect to the Gaussian exponential parameters. In addition to the total nonrelativistic energies, we computed scalar relativistic corrections mass-velocity and Darwin . With those added to the total energies, we estimated the dissociation energy of BH. The non-BO wave functions were also used to compute some expectation values involving operators dependent on the interparticle distance

Fundamental vibrational transitions of the 3He 4He+ and 7LiH+ ions calculated without assuming the Born-Oppenheimer approximation and with including leading relativistic corrections

Very accurate variational calculations of the fundamental pure vibrational transitions of the 3He 4He+ and 7LiH+ ions are performed within the framework that does not assume the Born-Oppenheimer BO approximation. The non-BO wave functions expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance are used to calculate the leading relativistic corrections. Up to 10 000 Gaussian functions are used for each state. It is shown that the experimental 3He 4He+ fundamental transitions is reproduced within 0.06 cm−1 by the calculations. A similar precision is expected for the calculated, but still unmeasured, fundamental transition of 7LiH+. Thus, three-electron diatomic systems are calculated with a similar accuracy as two-electron system

Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D2 with including relativistic corrections

In this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D2 molecule performed within the framework where the Born-Oppenheimer (BO) approximation is not assumed. After the elimination of the center-of-mass motion, D2 becomes a threeparticle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α2 (where α = 1/c is the fine structure constant) calculated as expectation values of the operators representing these effect

Fundamental vibrational transitions of the 3He 4He+ and 7LiH+ ions calculated without assuming the Born-Oppenheimer approximation and with including leading relativistic corrections

Very accurate variational calculations of the fundamental pure vibrational transitions of the 3He 4He+ and 7LiH+ ions are performed within the framework that does not assume the Born-Oppenheimer BO approximation. The non-BO wave functions expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance are used to calculate the leading relativistic corrections. Up to 10 000 Gaussian functions are used for each state. It is shown that the experimental 3He 4He+ fundamental transitions is reproduced within 0.06 cm−1 by the calculations. A similar precision is expected for the calculated, but still unmeasured, fundamental transition of 7LiH+. Thus, three-electron diatomic systems are calculated with a similar accuracy as two-electron system

Complete pure vibrational spectrum of HD calculated without the Born-Oppenheimer approximation and including relativistic corrections

All 18 bound pure vibrational levels of the HD molecule have been calculated within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states have been corrected for the relativistic effects of the order of α2 (where α is the fine structure constant), calculated using the perturbation theory with the nonrelativistic non-BO wave functions being the zero-order approximation. The calculations were performed by expanding the non-BO wave functions in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and by performing extensive optimization of the Gaussian nonlinear parameters. Up to 10 000 basis functions were used for each stat

Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of ditritium using all-particle explicitly correlated Gaussian functions

Very accurate variational calculations of the complete pure vibrational spectrum of the ditritium (T2) molecule are performed within the framework where the Born-Oppenheimer approximation is not assumed. After separating out the center-of-mass motion from the total laboratory-frame Hamiltonian, T2 becomes a three-particle problem. States corresponding to the zero total angular momentum, which are pure vibrational states, are spherically symmetric in this framework. The wave functions of these states are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. In the calculations the total energies, the dissociation energies, and expectation values of some operators dependent on interparticle distances are determined

Vibrational transitions of the 7LiH+ ion calculated without the Born–Oppenheimer approximation and with leading relativistic corrections

We recently presented very accurate calculations of the fundamental vibrational frequency of the 7LiH+ and 3He4He+ ions [Stanke et al., Phys. Rev. A 79, 060501(R) (2009)] performed without the Born–Oppenheimer approximation and included leading relativistic corrections. The accuracy of those calculations was estimated to be of the order of 0.06 cm−1. In the present work we extend the calculations to the remaining pure vibrational states of 7LiH+ and similarly accurate results are generated. They may lead to the experimental search for still unidentified lines corresponding to those transition

Vibrational transitions of the 7LiH+ ion calculated without the Born–Oppenheimer approximation and with leading relativistic corrections

We recently presented very accurate calculations of the fundamental vibrational frequency of the 7LiH+ and 3He4He+ ions [Stanke et al., Phys. Rev. A 79, 060501(R) (2009)] performed without the Born–Oppenheimer approximation and included leading relativistic corrections. The accuracy of those calculations was estimated to be of the order of 0.06 cm−1. In the present work we extend the calculations to the remaining pure vibrational states of 7LiH+ and similarly accurate results are generated. They may lead to the experimental search for still unidentified lines corresponding to those transition

Non-Born–Oppenheimer calculations of the BH molecule

Variational calculations employing explicitly correlated Gaussian basis functions have been performed for the ground state of the boron monohydride molecule BH and for the boron atom B . Up to 2000 Gaussians were used for each system. The calculations did not assume the Born–Oppenheimer BO approximation. In the optimization of the wave function, we employed the analytical energy gradient with respect to the Gaussian exponential parameters. In addition to the total nonrelativistic energies, we computed scalar relativistic corrections mass-velocity and Darwin . With those added to the total energies, we estimated the dissociation energy of BH. The non-BO wave functions were also used to compute some expectation values involving operators dependent on the interparticle distance