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Ab Initio Study of Different Acid Molecules Interacting with H2O

Using the Gaussian-03 for ab initio calculations, we have studied interaction of different acid molecules with a single water molecule. The molecular and supermolecular optimized structures were found with the Becke-3-Lee-Yang-Parr (B3LYP-hybrid potential) calculations of density-functional theory (DFT) methods as well as the Moeller-Plesset second-order perturbation theory, using the basis set of Aug-cc-pVDZ quality and the CRENBL ECP effective core potential for molecules containing heavy iodine atom. Possible isomers of studied acids and supermolecules, consisting of acid molecules coupled with a single water molecule, are shown. Energies, zero-point energies (ZPEs), thermal enthalpies and free energies, as well as the corresponding binding energies for the theoretical methods were calculated. It was found that optimized structures of supermolecular isomers with lowest energies corresponding to the global minimum on the potential energy surfaces can be different for both theories. The simplest structure acids H2S and H2Se, forming acid-water supermolecules, can give clear evidence of disagreement of the two theoretical methods concerning optimization of lowest energy structures, because the B3LYP-DFT method gives the lowest-energy structure for the first supermolecular isomer, but the MP2 method for the second possible isomer. A dramatic difference between potential energy surfaces for both theories applying to the optimized structure finding of the H2SO3-H2O supermolecular isomers was found, because MP2 supermolecular geometries cannot exist for the corresponding B3LYP-DFT ones, for which the frequency characteristics of the supermolecular isomers were also calculated. In general, the binding energies and ZPE ones for the MP2 method are 10-15% larger than those for the B3LYP-DFT method.


Introduction
One of today recurrent topics of physical chemistry and chemical physics is the theoretical investigation of gas-phase clusters [1][2][3][4], including hydrogen-bonded complexes. The interaction of an acid molecule with water can lead to many different structures that could depend on chosen level of theory. It is well-known that the hydration process has important implications in the context of atmospheric chemistry and aerosol, because there occur reaction mechanisms of introduction of substantial amount of gas phase chlorine and bromine compounds into the marine troposphere [5][6]. The development of supersonic jet nozzles allowed extensive studying of different molecular clusters in complicated experiments, for instance, see in Refs. [7][8][9][10][11]. On the other hand, ab initio theoretical studies are widely used in addition to experimental investigations. Thus, a large set of the structural and thermochemical data were obtained in this theoretical study with quantum-mechanical methods.
Iodic acid with the chemical formula HIO 3 can be obtained as a white solid and is an insoluble compound, unlike chloric acid or bromic acid. Perchloric acid (HClO 4 ) is an oxoacid of chlorine and is a colorless liquid soluble in water. Perchloric acid is a strong super-acid completely dissociating in an aqueous solution comparable in strength to sulfuric acid (H 2 SO 4 ) or nitric acid (). Perbromic acid (HBrO 4 ) is a strong acid and strongly oxidizing, and is the least stable of the halogen (VII) acids. Per-iodic acid (HIO 4 ) has heavy iodine atom and is widely used in organic chemistry for structural analysis.
On the other hand, there is much work on experimental and theoretical investigations of strong nitric super-acid (HNO 3 ) that is a highly corrosive and toxic acid that can cause severe burns. Example interesting theoretical and experimental studies of nitric acid can be found in Refs. [30][31][32][33][34][35][36] and [37][38][39][40][41][42], respectively. Also, there exist much theoretical (in general, density-functional theory or DFT) and experimental work on studying the strong sulfur-containing super-acid, H 2 SO 4 , see Refs. [43][44][45][46] as well as Refs. [47][48][49][50] of DFT-study. It is thought that due to experimental difficulties in investigations of the Sulfurous acid H 2 SO 3 , less attention is paid to the acid study [51][52], and it is little known about the so-called Sulfonic acid, which has the same chemical formula H 2 SO 3 . The sulfur-containing acid with the simplest chemical formula H 2 S (Sulfane or Hydrogen sulfide) is a covalent hydride structurally related to water (H 2 O) since oxygen and sulfur occur in the same periodic table group. Hydrogen sulfide is weakly acidic, and references on the acid studies can be found in [53][54][55][56]. Hydrogen selenide (H 2 Se) is the simplest hydride of selenium studied in Ref. [57], a colorless, flammable gas under standard conditions, and soluble in water. The properties of H 2 S and H 2 Se are similar. The wellknown phosphorous-containing acids, phosphoric acid (H 3 PO 4 ) and phosphorous acid (H 3 PO 3 ), were studied in Refs. [58][59][60][61][62]. Phosphoric acid (H 3 PO 4 ) also known as orthophosphoric acid or phosphoric (V) acid, is an inorganic acid and very commonly used as an aqueous solution. Phosphoric acid is also used as the electrolyte in phosphoric-acid fuel cells. Phosphorous acid [63][64], also called phosphonic acid, is one of the well-known and commonly used oxoacids of phosphorus. The other well-known acids are boric acid (H 3 BO 3 or B(OH) 3 ) also called boracic acid or orthoboric acid, and boron oxide hydroxide (metaboric acid) with the chemical formula HBO 2 . There is much work on the H 3 BO 3 and HBO 2 acids used in medicine, for instance, see Refs. [65][66][67][68][69][70]. A highly valuable precursor to many chemical compounds ranging from polymers to pharmaceuticals, hydrogen cyanide is a chemical compound with the following chemical formula HCN. A solution of hydrogen cyanide in water is called hydrocyanic acid. Hydrogen cyanide is a colorless, very poisonous, and highly volatile liquid that boils slightly above room temperature at 26 °C (78.8 °F). Recent studies on the weakly acidic hydrogen cyanide can be found in Refs. [71][72][73]. It is noted that HCN as a simplest nitrile system can act as both proton donor and proton acceptor systems in cluster formation that can be the case for water and alcohol molecules. The interaction of HCN with water can leads to two different structural motifs.

Ab initio calculations
All the calculations were performed using the GAUSSIAN-03 program [74], see also the famous books [75][76][77]. The minimum-energy molecular structures of all supermolecular isomers were completely optimized by using density-functional theory (DFT [78]) calculations employing Becke's three-parameter exchange potential [79][80] and the Lee-Yang-Parr correlation functional [81] (B3LYP) as well as the Møller-Plesset [82] second-order perturbation theory (MP2) calculations employing Dunning's augmented basis set [83][84] of the Aug-cc-pVDZ quality. In a supermolecule consisting of two molecules (for instance, in the water dimer) basis functions from one molecule can help compensate for the basis set incompleteness on the other molecule, and vice versa. This effect is known as basis set superposition error (BSSE) which will be zero in the case of a complete basis set. An approximate way of assessing the BSSE is the counterpoise (CP) correction method [85][86], in which the BSSE can be estimated as the difference between monomer energies with the regular basis and the energies calculated with the full set of basis functions for the whole supermolecules studied in this paper. In addition to the binding energies (∆E), zero-point energies (∆ZPE), the enthalpies (∆H), and the Gibbs free energies (∆G) at 298K and 1 atm are also reported for both the B3LYP and MP2 theoretical methods.
Average relativistic effective potential (AREP) and spin-orbit (SO) operators for the chemical elements of the second transition row have been published in Ref. [87], in which particular attention was focused on the portioning of the core and valence space, as well as Gaussian basis sets with contraction coefficients for the lowest energy state of each atom were introduced. Discussion of the details and complete review were given in Ref. [88]. More general reviews on the subject of effective core potentials can be also found in the literature [89][90]. The effective core potential of Ref. [87] called CRENBL ECP was used in this report to calculate structural and energetic properties of (super)-molecules containing the heavy iodine atom possessing the atomic number 53 in the periodic table of chemical elements of Mendeleev.

Results and discussion
It was found with the B3LYP-DFT methods using the basis set of Aug-CC-pVDZ quality that three possible isomers for the chemical formula H 2 SO 3 can exist. The most stable of them, the so-called Sulfurous acid (H 2 SO 3 ) possesses the lowest energy on the potential energy surface, and its molecular structure is shown in Figure 1a with both hydrogen atoms rotated towards the third molecular oxygen, which is not coupled with a hydrogen atom. The second, less stable H 2 SO 3 isomer has its ground state energy by about 1 kcal/mol smaller and opposite-directed hydrogen atoms (see the Table and Figure 1). The so-called Sulfonic acid being the third possible H 2 SO 3 isomer is the most "unstable" with its local minimum energy value of by about Hartrees that is  Table 1 with the largest binding energy Eb for the most stable H 2 SO 3 isomer. That can be explained by the way that the potential energy surfaces (PESs) for both commonlyused methods can give even qualitatively different results concerning structure optimization. Also, for Sulfonic acid it was found that the water oxygen can interact with the H 2 SO 3 molecular hydrogen coupled with sulfur

Conclusions
In this report, we have investigated the structural and energetic characteristics of the interaction of single acid molecules with a single water molecule. Both commonly-used theoretical methods, the Becke's threeparameter exchange potential with the Lee-Yang-Parr correlation functional and the second-order Møller-Plesset perturbation theory, have shown good agreement for optimized structures' finding and binding energies' calculations, using the same Dunning's basis set of Aug-cc-pVDZ quality and the CRENBL ECP effective core potential for molecules containing heavy iodine atom. However, some MP2 optimized structures of the acidwater supermolecules cannot be found for the corresponding B3LYP-DFT calculations that can be explained by the fact of uniqueness of each potential energy surface for the theoretical methods. That is even dramatic for the Sulfurous acid-water (H 2 SO 3 -H 2 O) supermolecular isomers, because the corresponding MP2 optimized structures cannot be found for the B3LYP-DFT ones with the smallest and highest (most stable structure) binding energies.