Geometry and Basis Set

All calculations have been carried out for D3h geometries, with the B-H intemuclear distance fixed, unless otherwise noted, at 2.24 ao (where ao denotes the atomic unit of distance, or Bohr 1 ao = 0.5291772 x 10 ° m [37]). This choice is based on what is perhaps the highest-level ab initio optimization of this molecule s geometry to date [46], which predicted an equilibrium value Re = 2.2416 ao (1.1862 A, 1 A = 1.000014 x 10 10 m [37]). Though there is at present no experimental value for Re, the expectation value R0 of the B-H intemuclear distance in the vibrational ground state has been spectroscopically determined to be 2.24882 ao (1.19001 A) [40] and provides an obvious experimental upper bound for Re, inasmuch as the potential well can be safely assumed to be steeper on the inside. 

The basis set consisted of two Is, two 2s, two sets of 2p and one set (five components) of 3d real Slater-type basis functions (STFs) on boron, two Is and one set of 2p STFs on each hydrogen. It was thus of double-zeta plus polarization quality. The z axis was taken to be perpendicular to the plane of the nuclei. 

Exponential parameters were optimized at the SCF level, at the singleconfiguration spin-coupled (SC) level, and for a valence- and core-correlated OBS-GMCSC wavefunction that included eight configurations. Intermediate GMCSC wavefunctions, including three, six and seven configurations, used the exponential parameters that had been optimized at the SC level. 

Note that basis functions and orbitals are designated as o if they are invariant under reflection in the plane of the nuclei, and as n if they do change sign under the same reflection. 

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Mas, E.M. and Szalewicz, K. (1996) Effects of monomer geometry and basis set saturation on computed depth of water dimer potential, J. Chem. Phys., 104,7606-7614. 

For sake of comparison, in all studied cases, we run calculations for those geometries and basis sets with a FCI (or near FCI) available. The methods we deal with are CCSD, CAS-SDCI, (SC)2CAS-SDCI and ec-CCSD corrected from both CAS-SDCI and (SC) CAS-SDCI. The performance of the methods is examined from two aspects the total energy and the quality of the potential energy surface (PES), being this quality measured by the so-called non-parallelity error (NPE). For a given set of calculations in a dissociative curve, the NPE is defined as the difference between the maximal and minimal deviation from the exact FCI PES. 

The method is an approximate self-consistent-field (SCF) ab initio method, as it contains no empirical parameters. All of the SCF matrix elements depend entirely on the geometry and basis set, which must be orthonormal atomic orbitals. Originally, the impetus for its development was to mimic Hartree-Fock-Roothaan [5] (HFR) calculations especially for large transition metal complexes where full HFR calculations were still impossible (40 years ago). However, as we will show here, the method may be better described as an approximate Kohn-Sham (KS) density functional theory (DFT)... 

All energies in kelvin (1 phartree = 0.315778 kelvin). Geometries and basis sets are specified in Ref. 120. RPA denotes random phase approximation, S, D, and T denote single, double, and triple excitations, respectively, (2) denotes the sum of intramonomer correlation contributions through second order in W and ST(CCSD) indicates that the single and triple excitation amplitude.s were computed using the converged CCD double excitation amplitudes. 

Crystal (we tested Crystal 98 1.0) is a program for ah initio molecular and band-structure calculations. Band-structure calculations can be done for systems that are periodic in one, two, or three dimensions. A separate script, called LoptCG, is available to perform optimizations of geometry or basis sets. 

A frequency job must use the same theoretical model and basis set as produced the optimized geometry. Frequencies computed with a different basis set or procedure have no validity. We U be using the 6-31G(d) basis set for all of the examples and exercises in this chapter. This is the smallest basis set that gives satisfactory results for frequency calculations. 

Predict the zero point or thermal energy by running a frequency job at the optimized geometry, using the same method and basis set. (Note that these two steps maybe run via a single Gaussian job via the Opt Freq keyword.)... 

In this chapter we will illustrate some of the methods described in the previous sections. It is of course impossible to cover all types of bonding and geometries, but for highlighting the features we will look at the H2O molecule. This is small enough that we can employ the full spectrum of methods and basis sets. 

The changes in geometry (Table 1) and vibrational frequencies (Table 2) of 1 (A = C), as well as the differences in relative energies (Table 3) of isomers 2 and 3 with an increase in the quality of the theoretical method, emphasize the importance of electron correlation and basis set. Although the geometry of the CHj fragment does... 

We conclude this section with a comment concerning notation. To identify a computational approach, it is customary to write procedure/basis set , e.g. MP2-FC/6-311G. If the geometry is obtained by procedure 1 and basis set 1, and that geometry is then used in calculating a particular property with procedure 2 and basis set 2, this is designated by procedure 2/basis set 2//procedure 1/basis set 1 . 

This chapter has reviewed certain experimental results and computational studies involving some of the metalloporphyrins (Fe(II)P, Co(II), and others). The present investigation also explored the accuracy of several DFT methods. The geometries of MP-XO complexes and XO binding energy were found to depend very strongly on the functional and basis set used. In many cases, model systems should be described at least with a triple- quality basis set. 

The corrections in going from HF to MP2 are large (Table 7.3) and the computational effort increases dramatically for small improvements in energies and geometries. With a limited basis set such as DZP, it is clear that CCSD(T), which should be superior to MP4, cannot five up to its promise because the basis set is too small. A major conclusion is that there must be a good balance between attempted amount of electron correlation recovery and basis set size. It is advisable to use at least triple-f quality type basis sets for highly correlated methods such as coupled cluster theory. 

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