Nonadiabatic energies of the ground state of the hydrogen molecule

Wolniewicz, L.

doi:10.1063/1.469753

Cited by 244 publications

(238 citation statements)

References 20 publications

Supporting

Mentioning

204

Contrasting

Order By: Relevance

“…The present value of the dissociation energy D 0 ͑H 2 ͒ is consistent with, but more precise than, the result of the ab initio calculations of Wolniewicz 4 ͑D 0 ͑H 2 ͒ th = 36 118.069 cm −1 ͒ and the most recent experimental result of Zhang et al 3 ͑D 0 ͑H 2 ͒ exp = 36 118.062͑10͒ cm −1 ͒. Table III and Fig.…”

Section: The Dissociation Energy Of Hsupporting

confidence: 76%

“…4 Our new result thus represents a test for future calculations of E i ͑H 2 ͒ and also of D 0 ͑H 2 ͒ in combination with precise values of E i ͑H͒ and D 0 ͑H 2 + ͒ as explained in more detail in the next subsection.…”

Section: B the Ionization Energy Of Hmentioning

confidence: 99%

“…We present here a measurement of the second energy interval, which when combined with the other two, enables us to derive a more precise value of the ionization energy of ortho-H 2 . The ionization energy E i ͑H 2 ͒ and the dissociation energy D 0 ͑H 2 ͒ of para-H 2 can also be derived from this new measurement by including previous results on the ionization energy of the hydrogen atom, 7 the dissociation energy of H 2 + , 4 and the rotational energy level intervals for the lowest vibronic states of the neutral molecule and the cation. [8][9][10][11] …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Determination of the ionization and dissociation energies of the hydrogen molecule

Liu

Salumbides²,

Hollenstein³

et al. 2009

The Journal of Chemical Physics

185

193

View full text Add to dashboard Cite

The transition wave number from the EF 1 ⌺ g + ͑v =0,N =1͒ energy level of ortho-H 2 to the 54p1 1 ͑0͒ Rydberg state below the X + 2 ⌺ g + ͑v + =0,N + =1͒ ground state of ortho-H 2 + has been measured to be 25 209.997 56Ϯ ͑0.000 22͒ statistical Ϯ ͑0.000 07͒ systematic cm −1 . Combining this result with previous experimental and theoretical results for other energy level intervals, the ionization and dissociation energies of the hydrogen molecule have been determined to be 124 417.491 13͑37͒ and 36 118.069 62͑37͒ cm −1 , respectively, which represents a precision improvement over previous experimental and theoretical results by more than one order of magnitude. The new value of the ionization energy can be regarded as the most precise and accurate experimental result of this quantity, whereas the dissociation energy is a hybrid experimental-theoretical determination.

show abstract

Section: The Dissociation Energy Of Hsupporting

confidence: 76%

Section: B the Ionization Energy Of Hmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of the ionization and dissociation energies of the hydrogen molecule

Liu

Salumbides²,

Hollenstein³

et al. 2009

The Journal of Chemical Physics

185

193

View full text Add to dashboard Cite

show abstract

“…(5), are extremely difficult to compute with the exponential functions. As far as we know, the only accurate molecular calculations of the Breit term within the exponential basis set were performed by Ko los and Wolniewicz [57,59] for various electronic states of H 2 .…”

Section: Relativistic Qed and Adiabatic Correctionsmentioning

confidence: 99%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

et al. 2015

View full text Add to dashboard Cite

In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order α 2 are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0 ± 1.9 cm −1 , in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

show abstract

“…[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

View full text Add to dashboard Cite

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...

show abstract

Nonadiabatic energies of the ground state of the hydrogen molecule

Cited by 244 publications

References 20 publications

Determination of the ionization and dissociation energies of the hydrogen molecule

Determination of the ionization and dissociation energies of the hydrogen molecule

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

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

Contact Info

Product

Resources

About