# 311 Mp4

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## 311 mp4

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The structural stability and C-N internal rotations of phenylurea and phenylthiourea were investigated by DFT-B3LYP and ab initio MP2 and MP4//MP2 calculations with 6-311G** and/or 6-311+G** basis sets. The complex multirotor internal rotations in phenylurea and phenylthiourea were investigated at the B3LYP/6-311+G** level of theory from which several clear minima were predicted in the calculated potential energy scans of both molecules. For phenylurea two minima that correspond to non-planar- (CNCC dihedral angle of about 45 degrees ) cis (CNCO dihedral angle is near 0 degrees ) and trans (CNCO dihedral angle is near 180 degrees ) structures were predicted to have real frequency. For phenylthiourea only the non-planar-trans structure was predicted to be the low energy minimum for the molecule. The vibrational frequencies of the lowest energy non-planar-trans conformer of each of the two molecules were computed at the B3LYP level and tentative vibrational assignments were provided on the basis of normal coordinate analysis and experimental infrared and Raman data.

Quantum chemistry composite methods (also referred to as thermochemical recipes)[1][2] are computational chemistry methods that aim for high accuracy by combining the results of several calculations. They combine methods with a high level of theory and a small basis set with methods that employ lower levels of theory with larger basis sets. They are commonly used to calculate thermodynamic quantities such as enthalpies of formation, atomization energies, ionization energies and electron affinities. They aim for chemical accuracy which is usually defined as within 1 kcal/mol of the experimental value. The first systematic model chemistry of this type with broad applicability was called Gaussian-1 (G1) introduced by John Pople. This was quickly replaced by the Gaussian-2 (G2) which has been used extensively. The Gaussian-3 (G3) was introduced later.

Several variants of this procedure have been used. Removing steps 3 and 4 and relying only on the MP2 result from step 5 is significantly cheaper and only slightly less accurate. This is the G2MP2 method. Sometimes the geometry is obtained using a density functional theory method such as B3LYP and sometimes the QCISD(T) method in step 2 is replaced by the coupled cluster method CCSD(T).

The G2(+) variant, where the "+" symbol refers to added diffuse functions, better describes anions than conventional G2 theory. The 6-31+G(d) basis set is used in place of the 6-31G(d) basis set for both the initial geometry optimization, as well as the second geometry optimization and frequency calculation. Additionally, the frozen-core approximation is made for the initial MP2 optimization, whereas G2 usually uses the full calculation.[3]

The G3 is very similar to G2 but learns from the experience with G2 theory. The 6-311G basis set is replaced by the smaller 6-31G basis. The final MP2 calculations use a larger basis set, generally just called G3large, and correlating all the electrons not just the valence electrons as in G2 theory, additionally a spin-orbit correction term and an empirical correction for valence electrons are introduced. This gives some core correlation contributions to the final energy. The HLC takes the same form but with different empirical parameters.

Unlike fixed-recipe, "model chemistries", the FPD approach[9][10][11][12][13] consists of a flexible sequence of (up to) 13 components that vary with the nature of the chemical system under study and the desired accuracy in the final results. In most instances, the primary component relies on coupled cluster theory, such as CCSD(T), or configuration interaction theory combined with large Gaussian basis sets (up through aug-cc-pV8Z, in some cases) and extrapolation to the complete basis set limit. As with some other approaches, additive corrections for core/valence, scalar relativistic and higher order correlation effects are usually included. Attention is paid to the uncertainties associated with each of the components so as to permit a crude estimate of the uncertainty in the overall results. Accurate structural parameters and vibrational frequencies are a natural byproduct of the method. While the computed molecular properties can be highly accurate, the computationally intensive nature of the FPD approach limits the size of the chemical system to which it can be applied to roughly 10 or fewer first/second row atoms.

The FPD Approach has been heavily benchmarked against experiment. When applied at the highest possible level, FDP is capable to yielding a root-mean-square (RMS) deviation with respect to experiment of 0.30 kcal/mol (311 comparisons covering atomization energies, ionization potentials, electron affinities and proton affinities). In terms of equilibrium, bottom-of-the-well structures, FPD gives an RMS deviation of 0.0020 Å (114 comparisons not involving hydrogens) and 0.0034 Å (54 comparisons involving hydrogen). Similar good agreement was found for vibrational frequencies.

The T1 method.[1] is an efficient computational approach developed for calculating accurate heats of formation of uncharged, closed-shell molecules comprising H, C, N, O, F, Si, P, S, Cl and Br, within experimental error. It is practical for molecules up to molecular weight 500 a.m.u.

T1 follows the G3(MP2) recipe, however, by substituting an HF/6-31G* for the MP2/6-31G* geometry, eliminating both the HF/6-31G* frequency and QCISD(T)/6-31G* energy and approximating the MP2/G3MP2large energy using dual basis set RI-MP2 techniques, the T1 method reduces computation time by up to 3 orders of magnitude. Atom counts, Mulliken bond orders and HF/6-31G* and RI-MP2 energies are introduced as variables in a linear regression fit to a set of 1126 G3(MP2) heats of formation. The T1 procedure reproduces these values with mean absolute and RMS errors of 1.8 and 2.5 kJ/mol, respectively. T1 reproduces experimental heats of formation for a set of 1805 diverse organic molecules from the NIST thermochemical database[14] with mean absolute and RMS errors of 8.5 and 11.5 kJ/mol, respectively.

This approach, developed at the University of North Texas by Angela K. Wilson's research group, utilizes the correlation consistent basis sets developed by Dunning and co-workers.[16][17] Unlike the Gaussian-n methods, ccCA does not contain any empirically fitted term. The B3LYP density functional method with the cc-pVTZ basis set, and cc-pV(T+d)Z for third row elements (Na - Ar), are used to determine the equilibrium geometry. Single point calculations are then used to find the reference energy and additional contributions to the energy. The total ccCA energy for main group is calculated by:

The reference energy EMP2/CBS is the MP2/aug-cc-pVnZ (where n=D,T,Q) energies extrapolated at the complete basis set limit by the Peterson mixed gaussian exponential extrapolation scheme. CCSD(T)/cc-pVTZ is used to account for correlation beyond the MP2 theory:

The Complete Basis Set (CBS) methods are a family of composite methods, the members of which are: CBS-4M, CBS-QB3, and CBS-APNO, in increasing order of accuracy. These methods offer errors of 2.5, 1.1, and 0.7 kcal/mol when tested against the G2 test set. The CBS methods were developed by George Petersson and coworkers, and they make extrapolate several single-point energies to the "exact" energy.[20] In comparison, the Gaussian-n methods perform their approximation using additive corrections. Similar to the modified G2(+) method, CBS-QB3 has been modified by the inclusion of diffuse functions in the geometry optimization step to give CBS-QB3(+).[21] The CBS family of methods is available via keywords in the Gaussian 09 suite of programs.[22]

The ability of these theories to successfully reproduce the CCSD(T)/CBS (W1 and W2), CCSDT(Q)/CBS (W3), and CCSDTQ5/CBS (W4) energies relies on judicious combination of very large Gaussian basis sets with basis-set extrapolation techniques. Thus, the high accuracy of Wn theories comes with the price of a significant computational cost. In practice, for systems consisting of more than 9 non-hydrogen atoms (with C1 symmetry), even the computationally more economical W1 theory becomes prohibitively expensive with current mainstream server hardware.

The potential energy surface of HCP converting to HPC in its ground electronic state has been investigated with ab initio methods at levels up to MP2/6-311G**//MP4/6-311G** as well as TZV + + ** CASSCF. All geometries are fully optimized and compare favorably to previous theoretical and experimental values. The HCP molecule is predicted to be 85.4 kcal/mol lower in energy than its linear isomer at the-MP2/6-31G*//MP2/6-31G* level. The energy barrier for hydrogen rearrangement is found to be merely 2.3 kcal from the HPC end. CASSCF studies were initiated to clarify the low barrier and lent support to a flat surface as HPC converts to stable, linear HCP at the TZV + + ** level. CASSCF also predicts that HPC is unstable with respect to bending. Harmonic vibrational frequencies for HCP results in 5% accuracy or better. A bent triplet is found to be the lowest excited state using the CASSCF method. 041b061a72