Non‐Born–Oppenheimer Variational Calculations of Atoms and Molecules with Explicitly Correlated Gaussian Basis Functions

Bubin, Sergiy; Cafiero, Mauricio; Adamowicz, Ludwik

doi:10.1002/0471739464.ch6

Cited by 80 publications

(114 citation statements)

References 2 publications

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“…Even, non-negative numbers in the 0-250 range are used for the m k powers. This range was found sufficient in our previous works [4,5] to effectively describe the nucleus-nucleus correlation and the vibrational oscillations of the wave functions representing pure vibrational states of small diatomic molecules. In the optimization of the linear and nonlinear parameters of the ECGs, {c k }, {A k }, and {m k }, for each state in the present work we use the Rayleigh quotient, E = min c Hc c Sc , which, subjected to the orthogonality condition for excited states, yields the generalized eigenvalue problem,…”

Section: The Methods Used In the Calculationsmentioning

confidence: 77%

“…As we have shown in previous works [4][5][6], good basis functions for non-BO calculations of rotationless states of a diatomic molecule with only σ electrons that possess all the above-mentioned desirable features are explicitly correlated Gaussian (ECG) functions multiplied by powers of the internuclear distance. These functions have been used in our previous calculations of the HD molecule [1,2].…”

Section: Introductionmentioning

confidence: 95%

“…We start this article with a brief description of the method we used (a more complete description of the method can be found in our recent reviews [4,5]). We also briefly describe the procedure used to calculate the relativistic corrections.…”

Section: Introductionmentioning

confidence: 99%

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

2011

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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 α 2 (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 state.

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Section: The Methods Used In the Calculationsmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 95%

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

2011

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“…The most rigorous non-BO methods are aimed to solve the all-particle Schrödinger equation of small atomic and molecular systems as accurately as possible, taking into account the translational and rotational invariance of the molecular Hamiltonian. Within this framework, the methodological contributions from Adamowicz and collaborators [17][18][19] have the longest history (for a very recent review, see Ref. 19).…”

Section: Introductionmentioning

confidence: 99%

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

Aguirre

Villarreal

Delgado‐Barrio

et al. 2013

The Journal of Chemical Physics

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An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO-MOLPRO interface allows to include highlevel electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code. Different model systems illustrate the implementation: 4 He 2 dimer as a protype of a weakly bound van der Waals system; isotopomers of [He-H-He] + molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations. The possible improvements and future developments are outlined.

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“…[4][5][6][7][8] Our goal in that development has been to describe the rovibrational spectra of those systems with similar accuracy as had been achieved before for two-electron molecules [9][10][11][12] and as currently being achieved by the state-ofthe-art experiments. The advances in computer hardware and software for numerical calculations make such calculations possible.…”

mentioning

confidence: 99%

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

Bubin

Stanke

Adamowicz

2011

The Journal of Chemical Physics

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Pure vibrational transitions of a three-electron 7 LiH + ion are still unknown experimentally even though it can be readily produced in experimental conditions by a photoinduced electron detachment. This makes the theoretical calculations of pure vibrational transitions an important prerequisite to any attempt to measure them. In a paper published four years ago 1 we described calculations of six pure vibrational states of 7 LiH + performed at the nonrelativistic level without assuming the Born-Oppenheimer (BO) approximation. In the calculations we employed explicitly correlated Gaussian basis functions multipled by powers of the internuclear distance. In more recent work 2 we applied the non-BO approach to calculate the fundamental vibrational transitions of the 3 He 4 He + and 7 LiH + ions. In the calculations we also included the leading relativistic corrections determined with the use of firstorder perturbation theory with the non-BO wave function as the zero-order approximation. For 3 He 4 He + the calculations reproduced within 0.06 cm −1 the fundamental vibrational transition, which is known with very high accuracy of about 0.001 cm −1 . 3 In that work we also calculated the fundamental transition of 7 LiH + . As the approach used in the 7 LiH + calculations was the same as used for 3 He 4 He + , a similar accuracy was claimed for the 7 LiH + transition. In the present work we use the approach to refine the theoretical predictions of the energies of higher pure vibrational transitions of 7 LiH + .Nearly all quantum-mechanical molecular calculations are performed assuming the BO approximation with the nuclei placed at fixed positions. Well established procedures and functional basis sets have been developed for such calculations. The BO electronic calculations generate a potential energy surface (potential energy curve for a diatomic molecule) which is subsequently used to determine vibrational states of the molecule. When the electrons and the a) Author to whom correspondence should be addressed. Electronic mail: sergiy.bubin@vanderbilt.edu.nuclei of the molecular system are treated on equal footing, as in the non-BO approach, unconventional basis functions for expanding the wave function need to be used. There are two major features which such basis functions need to describe. The first concerns the correlation effects of the coupled motions of the nuclei and the electrons and not just electrons as in the BO calculation. One way to effectively and accurately describe those effects is the use of basis functions that explicitly depend on the electron-electron, electronnucleus, and nucleus-nucleus distances. The second feature concerns the symmetry of the non-BO state under consideration. As the molecular Hamiltonian obtained after separation of the system's center of mass motion is spherically symmetric (isotropic), the basis functions have to reflect this symmetry. In particular, in the calculations of pure vibrational states (more precisely, the states with zero total angular momentum) the basis function...

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Non‐Born–Oppenheimer Variational Calculations of Atoms and Molecules with Explicitly Correlated Gaussian Basis Functions

Cited by 80 publications

References 2 publications

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

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

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

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

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