The importance of proton tunneling in chemical and biological systems is well known, e.g. for the DNA base pairing, as discussed by Löwdin [

1]. The phenomenon of potential barrier penetration plays an important role in many branches of physics: quantum field theory, fission of atomic nuclei, scanning tunneling microscopy and solid state physics [

2]. Theoretical studies of proton tunneling require the knowledge of multi-dimensional potential energy surfaces (PES’s) which are difficult to obtain from

ab initio calculations, especially for electronically excited states. From the theoretical point of view proton transfer in the ground electronic state is more easily tractable. Extensive experimental and theoretical studies have been reported for multidimensional proton tunneling in tropolone [

3,

4,

5,

6,

7,

8,

9,

10,

11,

12,

13]. Vener et al. [

10] studied theoretically multidimensional proton tunneling in tropolone by using adiabatic separation of variables. Smedarchina et al. [

11] used the instanton approach to account for tunnelling splittings. Takada and Nakamura [

12] on the base of high accuracy

ab initio calculations proposed a model potential energy surface (PES) for the electronically ground

$\tilde{X}$ state and employed it to analyze the proton tunnelling dynamics. Wójcik et al. [

13] reported the results of the high accuracy

ab initio MO calculations of the potential energy surfaces in the excited Ã state of tropolone, and by fitting the two- and three-dimensional analytical model potentials to these surfaces and solving the multidimensional vibrational problems, interpreted the existing experimental data. Other systems for which tunnelling have been studied include malonaldehyde [

14,

15,

16,

17], formic acid [

18], hydrogen-oxalate anion [

16], substituted tropolone [

19,

20] and 5-methyl-9-hydroxyphenalenone (OH and OD) [

21], methanol tetramer [

22] and hydrogen carbonate dimer ion [

23]. Recently a mixed quantum-classical approach has been used to study dynamics of hydrogen-bonded systems [

24,

25].

System which draws our attention in the present paper is benzoic acid dimer. It is present in the structure of the crystal [

26,

27,

28]. Its proton transfer has been recently studied by inelastic neutron scattering by Plazanet et al. [

29] and Fillaux et al. [

30]. Vibrational spectra of benzoic acid have been reported in Refs. [

31,

32]. In this article we present the results of high accuracy

ab initio MO and DFT calculations of the potential energy surfaces for the ground state of benzoic acid dimer in the stable and saddle point structures, and by fitting the two-dimensional analytical model potentials to these surfaces and solving the multidimensional vibrational problems, we predict the effects of excitations of the low-frequency in- and out-of-plane modes on the proton tunnelling splittings.

This paper is organized as follows. The results of our quantum chemical calculations for the ground state of benzoic acid dimer are presented in Sec. II. Model studies of the tunnelling are discussed in Sec. III. Concluding remarks are given in Sec. IV.