Thermal and Thermodynamic Parameters for Glycine (GL) Solvation in Water Theoretically

For accurate study, thermodynamic analysis is important for obtaining the individual and specific micro data to illustrate the solute-solvent interaction picture by using Gaussian 09 program. Density functional theory (DFT) were carried out on applying Gaussian 09 program packages [1]. The Beck’s 3parameters exchange functional and Lee – Yang – Paar’s correlation functions (B3LYP) were studied in DFT method [2], 6-321G (D,P) basis sets were applied to give stable geometry. In Gaussian 09 the ideal gas approximation for non-interacting particles are used for starting calculations. The very important point for the calculations is the estimation of partition function Q (V,T) which correspond to total partition function [3,4]. The aim of the work is to complete the study of the active compound glycine thermochemical properties to get light on it and explain its solvent effect (Table 1).


Introduction
For accurate study, thermodynamic analysis is important for obtaining the individual and specific micro data to illustrate the solute-solvent interaction picture by using Gaussian 09 program.
Density functional theory (DFT) were carried out on applying Gaussian 09 program packages [1]. The Beck's 3-parameters exchange functional and Lee -Yang -Paar's correlation functions (B3LYP) were studied in DFT method [2], 6-321G (D,P) basis sets were applied to give stable geometry. In Gaussian 09 the ideal gas approximation for non-interacting particles are used for starting calculations. The very important point for the calculations is the estimation of partition function Q (V,T) which correspond to total partition function [3,4]. The aim of the work is to complete the study of the active compound glycine thermochemical properties to get light on it and explain its solvent effect ( Table 1).
The necessary equations used for evaluating entropy, energy, heat capacity resulting from the calculation frequencies for glycine in water by the use of Gaussian 09 package are given below: Where NA n N and N A k B = R where N A is Avogadro's number R is the gas constant, B k is Boltzmann's constant and Q is the partition function changing into log scale we get: The thermal energy can also be obtained from the partition function: The heat capacity can be evaluated by applying equation4: Equations above mentioned will be used for estimation of the available thermodynamic for inorganic and organic compounds from the given and evaluated partition functions [5][6][7][8][9][10]. The theoretical calculations were done from the contributions for the translation, rotational motion and electronic contributions.
The data which obtained from frequency analysis by the need of partition function. For vibrational motion, we Choose the first vibrational energy K, level to be zero level, the corresponding partition function is expressed as [11].
The ZPVE was calculated for glycine in water.

HOMO and LUMO Orbitals
The HOMO and LUMO orbitals are evaluated theoretically and drawn in Figure 1 indicating the last fill orbital shape and minimum empty orbital. These orbitals obtained from alpha orbitals evaluated from Gaussian 09 package. Also, different HOMO orbitals were represented in Figure 1 which are HOMO-1, HOMO-2, HOMO-3.
HOMO as explained before in the last filled orbitals. Different loops was appeared in last HOMO orbital which is jointed in lower filled HOMO orbital. The LUMO orbital is bigger one in comparsion to the orbitals above it, like LUMO+1, LUMO+2, LUMO+3 and LUMO+4 ( Figure 1). The energy gap which is the difference between last HOMO and first LUMO orbitals is 0.2294ev. This value indicate that glycine in water can conduct electricity in good case. The energy gap between last HOMO and other LUMO orbitals increase as represented in Table indicating less conduction for large transfer of electrons.

Different contribution for Glycine in Water:
The different types of motions were studied theoretically for glycine in water and summarized as given next.

Contributions from Translation
The translational partition function was used for evaluating the translational entropy (which donate e factor which comes from Stirling's approximation: (7) The contribution to internal energy is: Finally, the heat capacity at constant volume is

Contributions from Electronic Motion
This last contribution can be calculated from the electronic partition function Where w is the degeneracy of energy level, E 0 E 1 E 2 E n is the energy in n-level.
The entropy due to electronic kinetic motion is: Since we have no temperature dependent terms in partition functions, the electronic heat capacity and electronic motion energy and internal energy are both zero

Contribution from Rotational Motion
The rotational partition function is: The entropy of rotation is given by: The contribution for rotation internal energy is: And contribution to heat capacity is: For nonlinear molecule as glycine, the rotation energy and heat capacity at constant volume is given by:   (Table 3 and Figure 3).  Reason / : Allow strongly delocalized NBO set/

Conclusion
All the thermal, classic thermodynamics, IR, NMR, statistical thermodynamic data for glycine in water were calculated using Gaussian 09 theoretically in water. The data proves the activity of glycine in water as very reactive agent. This behavior is illustrated from molecular orbitals and colligative specific properties of glycine in water.