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Analytical potential energy function and spectroscopic parameters for the ground and excited states of NaH

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Abstract

A set of energies at different internuclear distances for the ground electronic state and two excited electronic states of NaH molecule have been calculated using valence internally contracted multireference configuration interaction(MRCI) including Davidson correction and three basis sets. Then, a potential energy curve (PEC) for each state was determined by extrapolating MRCI energies to the complete basis sets limit. Based on the PECs, accurate vibrational energy levels and rotational constants were determined. The computational PECs are were fitted to analytical potential energy functions using the Murrell–Sorbie potential function. Then, accurate spectroscopic parameters were calculated. Compared with experimental results, values obtained with the basis set extrapolation yield a potential energy curve that gives accurate vibrational energy levels, rotational constants and spectroscopic parameters for the NaH molecule.

Introduction

It is well known that the alkali hydride molecules, such as LiH and NaH are of astrophysical importance and the photodissociation is one of the channels for the destruction of these alkali hydride molecules in interstellar clouds The calculation of photodissociation cross section of NaH from the ν″=0 level of the ground state (X 1Σ+) to the excited B1Π state has previously been done by Kirby and Dalgarno [1] using a conventional method. Bhattacharjee et al. [2] have studied the photodissociation of NaH molecule via B1Π state from the ground X 1Σ+ state by solving the time-dependent Schrödinger equation using the Fourier grid Hamiltonian method. Some sets of potential energy curves (PEC) in the literature [3], [4], [5] are used in their calculations. Recently, Taylor and Newman [6] obtained PEC and spectroscopic and electric properties for the ground state of NaH and NaD using different basis sets and extrapolation schemes. However, their PEC are combined by CCSD(T) and UCCSD(T) energies. Therefore there remain some arbitrary components, although the computational results are accord well with experiments. Moreover, their PEC is not fitted to analytical function, and multireference configuration interaction (MRCI) calculations are not employed in the energy calculations. This will affect the accuracies of dynamical calculation results, which are based on the PEC. Accurate analytical potential energy function (APEF) is necessary to obtain satisfactory results for calculations of these sorts. In the present work, we focus on obtaining accurate PECs at high-level theoretical computational level, and APEF using least-square fitting tool. To evaluate the liability of the PEC and APEF, vibrational energy levels and spectroscopic parameters are also calculated systemically and compared with the experimental data and other theoretical work available at present.

Section snippets

Computational approach

In this work Valence internally contracted MRCI [7](a), (b) calculations (including Davidson [8] correction) and large basis sets are used to generate all ab initio potential energy data. We use a series of aug-cc-pVxZ(x=D,T,Q) basis sets on hydrogen [9]. Adding core polarization functions to second row compounds has been shown to increase the basis set convergence [10] and we, consequently, employ a cc-pVCxZ(x=D,T,Q) series of basis sets on sodium [11]. Hereafter, BS1, BS2 and BS3 will be use

Results and discussion

The PECs of X1Σ+ state are computed using MRCI method including Davidson correction with three basis sets (BS1, BS2 and BS3) in order to observe the effects of basis sets on the molecular properties. Based on the PECs, the vibrational energy levels and rotational constants are determined by solving one-dimensional Schrödinger equation of nuclear motion. These calculations are realized with program Level 7.5 [13].

The calculational results of the molecular vibrational and rotational properties

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