Very accurate potential energy curve of the LiH molecule

Abstract

We present very accurate calculations of the ground-state potential energy curve (PEC) of the LiH molecule performed with all-electron explicitly correlated Gaussian functions with shifted centers. The PEC is generated with the variational method involving simultaneous optimization of all Gaussians with an approach employing the analytical first derivatives of the energy with respect to the Gaussian nonlinear parameters (i.e., the exponents and the coordinates of the shifts). The LiH internuclear distance is varied between 1.8 and 40 bohrs. The absolute accuracy of the generated PEC is estimated as not exceeding 0.3 cm(-1). The adiabatic corrections for the four LiH isotopologues, i.e., (7)LiH, (6)LiH, (7)LiD, and (6)LiD, are also calculated and added to the LiH PEC. The aforementioned PECs are then used to calculate the vibrational energies for these systems. The maximum difference between the computed and the experimental vibrational transitions is smaller than 0.9 cm(-1). The contribution of the adiabatic correction to the dissociation energy of (7)LiH molecule is 10.7 cm(-1). The magnitude of this correction shows its importance in calculating the LiH spectroscopic constants. As the estimated contribution of the nonadiabatic and relativistic effects to the ground state dissociation energy is around 0.3 cm(-1), their inclusion in the LiH PEC calculation seems to be the next most important contribution to evaluate in order to improve the accuracy achieved in this work.

Electronic structure and time-dependent description of rotational predissociation of LiH

“…Special investigations were devoted to dipole moments 24,25 and ionic states of LiH 26,27,28 . Recently, Tung et al 29 and Holka et al 30 performed very accurate calculations of the ground and some excited state potential curves.…”

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

“…The above formula represents a general case of the expectation value of δ 3 ((b ⊗ I 3 ) T r − ξ) and, with an appropriate choice of vector (b ⊗ I 3 ), it can be used to calculate matrix elements of operators representing δ 3 (r i j ) in the Darwin termĤ I I d2 (13) and δ 3 (r ia ) in the Darwin termĤ I I d1 (12). The matrix elements ⟨δ 3 (r i j )⟩ and ⟨δ 3 (r ia )⟩ are obtained by setting bb T ⊗ I 3 = J i j and bb T ⊗ I 3 = J ii , respectively.…”

“…6 They showed that careful optimization of the non-linear parameters of the ECGs not only yields accurate nonrelativistic energies but also very well converged leading relativistic corrections, even in the traditional approach employing the Pauli Hamiltonian. Recently we have used ECGs in very accurate calculations of some two-, three-, and four-electron systems, H + 3 , 7-10 LiH + , 11 LiH, 12 He + 2 , 13 and (H 2 ) 2 . 14 The calculations produced the most a) Electronic address: monika@fizyka.umk.pl b) Electronic address: epalikot@doktorant.umk.pl c) Electronic address: ludwik@email.arizona.edu accurate nonrelativistic ground-state potential-energy surfaces (PESs) for these systems ever calculated.…”

Orbit-orbit relativistic correction calculated with all-electron molecular explicitly correlated Gaussians

“…The calculations are performed employing the basis sets containing 2400 ECGs generated in Ref. 9 As there have not been any previous high-accuracy calculations of the OO correction for a four-electron molecular system before, no comparison can be made in this case. However, as the value of the correction changes by about 20% when the internuclear distance increases from 2 to 10 a.u., it can be expected to have a non-negligible effect on the rovibrational transition energies when the correction is included in the LiH PES.…”

“…With this the upper part of the rovibrational spectrum of this system (in the 20 000-30 000 cm −1 spectral range) will be studied. More exact determination of the rovibrational spectrum will also be performed for the LiH molecule, 9 as well as for other small molecules with more than two nuclei and/or more than two electrons (e.g., H 3 , LiH + 2 , and HeH − ). In Sec.…”