Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σg+ term values

Abstract

The mass-correction function is evaluated for selected excited states of the hydrogen molecule within a single-state non-adiabatic treatment. Its qualitative features are studied under the avoided crossing of the EF with the GK state and also for the outer well of the HH state. For the HH state, a negative mass correction is obtained for the vibrational motion near the outer minimum, which accounts for most of the deviation between experiment and earlier theoretical work. * Electronic address: matyus@chem.elte.hu This work represents the first steps towards a fully coupled non-adiabatic calculation of the EF -GK-HH-etc. singlet-gerade manifold of H 2 including the formerly neglected mass-correction terms which appear in the multi-state effective non-adiabatic Hamiltonian recently formulated [1]. Relying on the condition of adiabatic perturbation theory [2] that the electronic band must be separated from the rest of the electronic spectrum by a finite gap over the relevant dynamical range, already a single-state treatment delivers insight into the extremely rich non-adiabatic dynamics of electronically excited hydrogen. Motivated by these ideas and after careful inspection of the singlet gerade manifold (Figure 1), we have selected the lowerenergy region of the EF and the outer well of the HH state, often labelled withH, for a single-state non-adiabatic study. Concerning the computational methodology, we used the QUANTEN computer program [3-6] to accurately solve the electronic Schrödinger equation for the selected states using floating, explicitly correlated Gaussian functions. The mass-correction functions were also computed with QUANTEN according to the procedure described in Refs. [5, 6]. The resulting non-adiabatic corrections to the (effective) vibrational and rotational mass are shown in Figures 2 and 3. These numerical examples shed light on qualitative properties of the mass-correction functions, which can be understood by remembering the appearance of the R a reduced resolvent in the masscorrection tensor of the selected a electronic state [1, 2],Note that this is the Cartesian form of the tensor, and the general transformation of the KEO, including also the coordinate-dependent M aa,ij elements, to arbitrary curvilinear coordinates has been worked out in Ref. [5]. From this general expression, the specific results for a diatomic molecule with spherical polar coordinates, giving rise to the vibrational and rotational corrections, were derived and used in Refs. [5,6]. The single-state non-adiabatic mass-correction term has been discovered-and rediscovered several times in the past and has been used for the ground electronic state of diatomics [6,7,[7][8][9], for an approximate treatment of the water molecule

Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ $^1Σ_\text{g}^+$ manifold of molecular hydrogen

“…This feature was computed already in Ref. [21], and it was found that correction of the constant, nuclear (proton) mass by this non-adiabatic term the deviation of theory and experiment is reduced by an order of magnitude, i.e., from ca. 1 cm −1 to ca.…”

“…The single-state mass correction, Eq. ( 8), has been formulated several times [13][14][15][16] and was successfully used in spectroscopic applications [15,[17][18][19][20][21][22]. We are not aware of any computation with the multi-state expression, Eqs.…”

“…III has been implemented in the in-house developed computer program named QUANTEN (QUANTum mechanical description of Electrons and atomic Nuclei). QUANTEN has recent applications including non-relativistic energy upper and lower bounds, non-adiabatic, pre-Born-Oppenheimer, perturbative and variational relativistic computations [21][22][23][24][25][26][27][28][29][30][31][32]. The program contains a (stochastic and deterministic) non-linear variational engine and an integral library for variants of explicitly correlated Gaussian (ECG) functions.…”

“…(We note that in both the single-state adiabatic and non-adiabatic computations relativistic and leading-order QED corrections were included in Ref. [21]. )…”

Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

“…For a quantitative description of the high-resolution spectroscopic measurements of atoms [1,2] and molecules [3,4], calculations of highly accurate energies are required corresponding to an at least parts-per-billion (ppb) relative precision [5][6][7]. To ensure a ppb-level of convergence for atomic and molecular energies, it is necessary to use explicitly correlated basis functions [6,[8][9][10]. Although fast convergence of the energy with respect to the basis set size is ensured, most explicitly correlated functions are highly specialised to the particular system.…”