Ab initio study of β-alanine conformers in the gas phase

Twelve conformers of non-ionized β-alanine have been investigated using high level ab-initio methods. Geometry optimizations and frequency calculations have been performed at MP2/6311G(d,p) and MP2/6-311++G(d,p) levels of calculation. Relative energies, rotational constants, harmonic vibrational frequencies and infrared intensities are reported. The relevance of using basis sets including diffuse functions has been supported. A factor of 0.9814 is proposed to scale the MP2/6-311++G(d,p) vibrational frequencies. The good agreement between the theoretical results and the available experimental values supports the reliability of the MP2/6-311++G(d,p) level of theory for describing the conformational behavior of molecules with internal hydrogen bonds.


Introduction
2][3][4] In the gas phase, where these intermolecular interactions have no effect,, they exist as non-ionized species.Error!Bookmark not defined.,Error!Bookmark not defined.The study of the conformational behavior of non-ionized amino acids is important for understanding the dynamics of the peptide and protein backbones.
β-Amino acids, although much less abundant than their α partners, are also present in peptides, and in free form they show interesting pharmacological effects.They can be cyclized to β-lactams which have potential biological activity.In this respect, several methods for the synthesis of racemic β-amino acids have been developed, [5][6][7] and in the last few decades special attention has been paid to the preparation of enantiomerically pure compounds.Professor

Computational Details
All the calculations have been performed with the Gaussian 98 30 package of programs.Relaxed scan calculations were carried out for all the torsions responsible for the non-rigidity of the molecule.They were performed trough the full 360 o space with steps of 10 o , using the secondorder Møller-Plesset (MP2) method 31,32 and the 6-311G(d,p) and 6-311++G(d,p) basis sets.The minima structures were identified and considered identical if their energies differed by less than 10 -5 hartree and if the root-mean-square difference of their rotational frequencies differed by less than 30 MHz.Twelve unique conformations were then fully optimized and frequency calculations were carried out, all at MP2/6-311G(d,p) and MP2/6-311++G(d,p) levels of theory.They were verified to be minima by establishing that their matrices of second derivatives (hessians) were positive definite upon diagonalization.The hessians were all determined analytically.Relative energies were calculated at 0K and 298 K. Zero point corrections (ZPE) and thermal corrections (TCE) to energy were included.The MP2/6-311G(d,p) values were corrected by using the recommended scaling factors.The ZPE and TCE values computed at MP2/6-311++G(d,p) level have not been corrected, since, to our best knowledge, there are no scaling factors reported for that level of calculation.Twelve different conformations were found for β-alanine by varying the torsional variables describing above (Figure 2).Their values of φ 1 , φ 2 , φ 3 , and φ 4 are shown in Table I, as well as the energies relative to conformer I at 0K and at 298 K.The data is reported at two different levels of calculation: MP2/6-311G(d,p) and MP2/6-311++G(d,p).In order to present more accurate values the Zero Point Energy correction (ZPE) and the thermal correction to energy (TCE), they have been improved by using the scaling factors recommended by Scott and Radom. 33at MP2/6-311G(d,p) level of theory.The MP2/6-311++G(d,p) ZPE and TCE values have not been corrected, since, to our best knowledge, there are no scaling factors reported for that level of calculation.Conf.The relative energy values in Table 1 show a discrepancy between the results obtained with the 6-311G(d,p) and the 6-311++G(d,p) basis sets.The discrepancy could be caused by the overestimation of internal hydrogen bonds when the used basis set do not include diffuse functions, which was previously pointed out by Nielsen et al.Error!Bookmark not defined.In order to clarify that, a more detailed analysis on the possible intra-molecular interactions in β-alanine conformers is needed.Bader topological analysis 34 of the MP2/6-311G(d,p) wave functions, corresponding to all the studied conformers, were performed in order to identify and quantify all possible intra-molecular interactions (Table 2).All the hydrogen bond interactions lead to ring critical points in the corresponding conformers.The strongest internal hydrogen bond was found in conformer I, between H11 and N7.The interaction distance was found to be d (7,11) = 1.77Å, which is the shortest distance among all the found interactions.The shortest distance and the largest value of electronic charge density (ρ) and of the Laplacian of ρ, (∇ 2 ρ) at the critical points, show that the N7-H11 interaction in conformer I is the strongest one.This finding reinforces the hypothesis that non diffused basis set overestimate the effect of internal hydrogen bonds on the energy values.In our case this overestimation is found responsible for the prediction of conformer I as the most stable at MP2/6-311G(d,p) level of theory.However, there is crucial to find another way to prove that the relative energies obtained at MP2/6-311++G(d,p) are the correct ones.Two conformers of β-alanine have been previously identified by McGlone and Godfrey Error!Bookmark not defined.by using a Stark-modulated free-expansion jet spectrometer.The authors named them β-ala(x) and β-ala(y).Hereafter we are referring to them accordingly.Their observations led to identify β-ala(x) as the lowest energy conformation.Their spectroscopic derived parameters are reported in Table 3 and have been used as reference for comparing our results.Calculations on the trideutero analogues of all the studied conformers have also been performed.The data of the non-deuterated and deuterated parent species, as well as the associated changes in the rotational constants are reported in Table 3.Since the changes in the rotational constants on deuteration are a function of the amino and hydroxyl hydrogen positions, they can be use to select which of the modeling conformers correspond to those identified in reference Error!Bookmark not defined.. From the agreement on the rotational constants and on their variation, As it has been previously established, the ab-initio vibrational frequencies (ω) are typically larger than the fundamentals (υ) observed experimentally. 35A major source of this disagreement is the neglect of anharmonicity effects in the theoretical treatment.Other causes are the incomplete incorporation of electron correlation and the use of finite basis set.However, the overestimation of ab-initio vibrational frequencies is relatively uniform, and consequently frequency scaling factors are often applied.Scott and Radom Error!Bookmark not defined.recommend a scaling factor of 0.9496 for the MP2/6-311G(d,p) vibrational frequencies.However, there is no scaling factor recommended for frequencies computed at MP2/6-311++G(d,p).Analyzing the MP2/6-311G(d,p) scaled frequencies together with the MP2/6-311++G(d,p) harmonic frequencies of all the studied conformers, a scaling factor of 0.9814 has been used in the present work to correct the latter ones.The information contained in the MP2/6-311++G(d,p) theoretical vibrational frequencies and infrared intensities reported in Table IV, for the six most stable conformers of β-alanine, could help on the interpretation of experimental investigation of the gas-phase vibrational spectrum of this amino acid.
The results summarized in Table 4 show that there are some normal modes which do not change significantly from one conformer to another.The band corresponding to ω 26 (-C=O stretching) appears as the most intense one in all conformers but I, and its frequency changes very little among them, from 1777 (II, III) to 1805 (XII) cm -1 .However, some normal modes with high IR intensities shift considerably.For example the modes involving the -OH group.In conformer I the mode corresponding to the -OH stretching (ω 31 ) shifts towards lower frequencies in about 450 cm -1 , been the highest intensity vibration of this conformer, while the peak of the -OH torsion (ω 13 ) shifts towards higher frequencies in about 350 cm -1 .These changes can be explained by the strong intra-molecular hydrogen bond in conformer I, involving the hydrogen atom in the -OH group.High intensity normal modes whose frequency does not change from one conformer to another should serve as indicators of the presence of β-alanine, while characteristic shifts should help identification of β-alanine conformers.

Conclusions
Twelve different conformers of gaseous β-alanine were identified.The minima structures have been considered identical if their energies differ by less than 10 -5 hartree and if the root-meansquare difference of their rotational frequencies differ by less than 30 MHz.Geometry optimizations and frequency calculations have been performed at MP2/6-311G(d,p) and MP2/6-311++G(d,p) levels of calculation.The relevance of using basis sets including diffuse functions to correctly predict the relative energies of the conformers has been supported.
Relative energies, rotational constants, harmonic vibrational frequencies and infrared intensities are reported.A factor of 0.9814 is proposed to scale MP2/6-311++G(d,p) vibrational frequencies.
The good agreement between the theoretical results and the available experimental values supports the reliability of the MP2/6-311++G(d,p) level of theory for describing the conformational behavior of molecules with internal hydrogen bonds.

Table 2 .
Characterization of the intra-molecular interactions found in the β-alanine conformers

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calculated conformers corresponding to those observed by McGlone and Godfrey are: conformer II = β-ala(x) and conformer I β-ala(y).This validate the MP2/6-311++G(d,p) relative energies and reinforces the relevance of using basis set with diffuse functions, even if correlation methods are employed.Now, it seems reasonable to rely on the MP2/6-311++G(d,p) results and propose conformer II as the most stable one.
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