Article

# Calibration-quality adiabatic potential energy surfaces for H-3(+) and its isotopologues

Gorlaeus Laboratories, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands.

The Journal of Chemical Physics (Impact Factor: 2.95). 05/2012; 136(18):184303. DOI: 10.1063/1.4711756 Source: PubMed

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**ABSTRACT:**For high-precision calculations of rovibrational states of light molecules, it is essential to include non-adiabatic corrections. In the absence of crossings of potential energy surfaces, they can be incorporated in a single surface picture through coordinate-dependent vibrational and rotational reduced masses. We present a compact method for their evaluation and relate in particular the vibrational mass to a well defined nuclear core mass derived from a Mulliken analysis of the electronic density. For the rotational mass we propose a simple, but very effective parametrization. The use of these masses in the nuclear Schrödinger equation yields numerical data for the corrections of a much higher quality than can be obtained with optimized constant masses, typically better than 0.1 cm(-1). We demonstrate the method for H(2), H(2) (+), and singly deuterated isotopologues. Isotopic asymmetry does not present any particular difficulty. Generalization to polyatomic molecules is straightforward. - [Show abstract] [Hide abstract]

**ABSTRACT:**The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H rovibrational spectrum is reproduced at the 0.1 cm(-1) accuracy level up to 16 600 cm(-1) above the ground state. - [Show abstract] [Hide abstract]

**ABSTRACT:**The molecular ion is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro-vibrational spectrum of is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm(-1) relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm(-1). Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro-vibrational data show that an accuracy of the order of 0.1 cm(-1) is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.