2. COMPUTATIONAL METHODOLOGY
The methodology adopted in the present work to compute the rotational and vibrational data is similar to that utilized for the spectral study of Glutamic acid in our previous such work.33 The conformers of biologically significant left-handed isomer (L )-Leucine and its isomeric species being investigated in this work are depicted in Figure 1. Note that the global minimum (lowest-energy conformer) of Leucine (EQ0#) has been verified through its structure optimization performed at different levels of quantum-mechanical theory (for details, see Ref. 10). For the present work, ab-initio Møller-Plesset 2ndorder (MP2) perturbation theory with frozen-core (fc) approximation as well as density functional theory (DFT) are utilized to compute the spectroscopic parameters.34-35 The rotational constants computed for EQ0# at different levels of the theory are provided in Table 1. These are also compared with the available experimental gas-phase data from a study by Cocinero et al.29 The computed rotational constants are found to be in good agreement with experimental one. In particular, the MP2/6-31+G(d,p) method using a Gaussian basis set, 6-31+G(d,p), resulted in a more closer agreement with deviations less than 5 MHz compared to MP2/6-311++G(d,p) method exhibiting deviations up to 7 MHz, as evident in Table 1. This observation in the present work, thereby, improves upon the previously known computational results of Cocinero et al.,29 in their prediction of rotational parameters through MP2/6-311++G(d,p) method which was used to assist their experimental results.
Besides the aforementioned wave-function based MP2 method, the DFT computations for rotational constants were also carried out. For this, a conventional hybrid exchange correlational functional, B3LYP, is employed along with a correlation consistent, cc-pVTZ and aug-cc-pVTZ, basis set.37,38 Additionally, in view of various non-covalent (dispersion) interactions in the branched structural framework of Leucine, Grimme’s D3 dispersion correction has also been employed along with a Becke-Johnson (BJ) damping function in the computaions.39,40 It is quite evident from Table 1 that DFT/B3LYP-D3(BJ)/cc-pVTZ method gives more closer values (to the experimental one) for rotational constants of global conformer, with deviation of only 5 MHz than that computed using the DFT/B3LYP-D3(BJ)/aug-cc-pVTZ method. Besides this, a recently proposed SNSD basis set,41 constituted from the polarized double-zeta (ζ) N07D basis set including the diffuse s-typefunctions on every atom and diffuse polarized (d-type ) functions on heavy atoms as well as p-type on hydrogen atoms, is also tested in besides the B3LYP-D3(BJ) method. However, though SNSD is known to be quite accurate and cost-effective for spectroscopic calculations but in the present work, it is observed to be less accurate than B3LYP-D3(BJ)/cc-pVTZ method. Moreover, in the present work, DFT calculations were also performed employing a recently recommended double hybrid functional, B2PLYP-D3(BJ),42 however, significant deviations of more than 10 MHz are observed using this method as can be seen in Table 1. Thus, overall, B3LYP-D3(BJ)/cc-pVTZ is observed to be the best DFT method although it is found to be relatively less accurate than the wave-function based ab initioMP2/6-31+G(d,p) method as clearly evident in Table 1.
On the basis of aforementioned observations for the global conformer, the rotational parameters of other isomeric species being investigated in this work were computed using their optimized geometries at both the aforementioned quantum-mechanical levels of theory, namely, MP2/6-31+G(d,p) and DFT/B3LYP-D3(BJ)/cc-pVTZ. The optimized structures were additionally validated through harmonic vibrational frequency check. However, anharmonic frequency calculations are also performed at the specified levels of the theory to accurately estimate the vibrational frequencies beyond harmonic oscillator approximation, which further provided other rotational parameters listed in Table 2, for example, the Ray’s asymmetry parameter, quartic centrifugal distortion constants, and nuclear quadrupole coupling constants. Note that for these calculations, a quartic force field (QFF) is deployed for the inter-nuclear potential in the ‘Watson’ Hamiltonian so as to account for ro-vibrational interactions.9,21 Further, for the computation of vibrational frequencies, the anharmonicity is estimated at the level of the second order vibrational perturbation theory (VPT2) which is basically rooted in the Rayleigh-Schrödinger perturbation theory.43,44 Note that the inclusion of anharmonic effects actually contribute towards an accurate estimation of both vibrational and rotational parameters,21 by aiding the evaluation of rotational constants associated with vibrationally averaged ground state. Besides this, the anharmonic calculations also provide the centrifugal distortion constants which are estimated employing Watson’s A-reduced Hamiltonian in irreducible (Ir) representation.45,46
In the present work, all the aforementioned quantum-mechanical computations are performed using Gaussian 09 program.47 The rotational parameters computed at MP2/6-31+G(d,p) level of the theory, as collected in Tables 2 and 3, were further used for generating the rotational spectral line data and simulating the rotational spectra through the PGOPHER program,48 as depicted in Figure 2 as well as listed in the Supporting Information (SI) Tables S1 and S2. Besides this, the anharmonic vibrational spectroscopic data computed for the global minimum conformer EQ0# is further compared in Table 4 with the experimental gas-phase values for Leucine available from matrix-IR and fast thermal heating experiments.30,31As evident in Table 4, DFT/B3LYP-D3(BJ)/cc-pVTZ exhibits a closer agreement with the experiment. Thus, this DFT method was employed for computing the vibrational spectral data for all other species in the complete IR region (from mid-IR to far-IR). Additionally, a VEDA4 program,49 has also been used to further characterize each mode of vibration in terms of potential energy distribution (PED) for all the conformers of Leucine and its isomeric species, as provided in supporting information SI Table S3. It should be noted that in the present work, these calculations are performed at a temperature of 298.15K, the effect of temperature on vibrational lines is not attempted in this work. However, since the rotational intensities considerably depend on the temperature, therefore, while simulating the rotational spectra and generating the line-data through PGOPHER program,45 a low temperature of 10 K is used in order to assist the search of species in cold molecular clouds as elaborated in the next section.
Table 1. Computed equilibrium rotational constants (Ae, Be, Ce) for the global minimum conformer of Leucine (EQ0#) at various levels of quantum-mechanical (MP2 and DFT) methods. The respective absolute deviations relative to the experimental values are listed in parenthesis. The best estimated values are marked in bold, for details see the text.