Calculations on Diatomic Molecules

Miscellaneous Calculations on Diatomic Molecules.—A variety of more approximate treatments have been tested on diatomics. Naray-Szabo has tested a method for approximate HF calculations 373 (in which the integrals are approximated) in applications to various first-row diatomics. The results were reasonable for non-polar molecules but the method fails for molecules where the atoms have very different Z, i.e. BeO and BeF, amongst others, did not give a minimum in the PE curve. 

An interesting molecule that has been little studied is SiS 12+, which should be similar to the isovalent CO, CS, and SiO. BA + P calculations at Re by Green16 give a value of ft that is 0.5 D larger than the experimental value. The diatomic molecules PN and PC were also studied by Bauschlicher and Schaefer.213 

In concluding this section, we draw attention to a paper by Roby,374 who has 

Sannigrahi and S. Noor Mohammad, Internat. J. Quantum Chem., 1973, 7, 1183. 

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Becke A D 1983 Numerical Flartree-Fock-Slater calculations on diatomic molecules J. Chem. Phys. 76 6037-45... 

The Cl procedure just described uses a fixed set of orbitals in the functions An alternative approach is to vary the forms of the MOs in each determinantal function O, in (1.300), in addition to varying the coefficients c,. One uses an iterative process (which resembles the Hartree-Fock procedure) to find the optimum orbitals in the Cl determinants. This form of Cl is called the multiconfiguration SCF (MCSCF) method. Because the orbitals are optimized, the MCSCF method requires far fewer configurations than ordinary Cl to get an accurate wave function. A particular form of the MCSCF approach developed for calculations on diatomic molecules is the optimized valence configuration (OVC) method. 

Diatomic molecules are still rather simple systems suitable for clarifying problems encountered in polyatomic molecules. Moreover, they give us additional information not obtainable from atomic calculations, Polarization functions represent a typical example. Since they correspond to orbitals unoccupied in atomic ground states, their exppnents cannot be estimated from atomic calculations. Among the calculations on diatomic molecules, very useful information on the problem of basis set composition was contributed by calculations reported by Cade, Huo, Wahl, Sales, Liu, Yoshimine and others " . Consider for example the results for the nitrogen molecules. Fig. 2.2 presents the dependence of the total energy and its components (ki-... 

As a consequence it is mandatory to use a higher level of theory in studies of 3d systems, for example, by combining CASSCF and multireference Cl calculations. A number of studies of transition-metal systems published during the last three years have followed this strategy. They range from calculations on diatomic molecules to large transition-metal complexes like ferrocene and (Mo2C1 ") . Some examples of such calculations can be found in Refs 86-96. It would be outside the scope of this review to include a comprehensive discussion of all these studies. Therefore only two illustrative examples have been selected the NiH molecule and the complex between a nickel atom and an ethene molecule. 

The values are chosen to fit the results of minimal basis set ab initio calculations on diatomic molecules. 

Electron correlation energies for small molecules have been calculated either by the independent electron-pair approximation (lEPA) or by configuration interaction (Cl). Brute force Cl in general did not give too good results Cl calculations gave a substantial part of the correlation energy only where the weakly occupied orbitals had been optimized somehow. Here one must mention the calculations on diatomic molecules by Bender and Davidson ) and by Wahl et.al. >. 

This section presents some examples of SCF wave functions for diatomic molecules. (For a summary of SCF calculations on diatomic molecules, see MulUken and Ermler, Diatomic Molecules.)... 

To overcome the deficiencies of the Hartree-Fock wave function (for example, improper behavior R oo and incorrect values), one can introduce configuration interaction (Cl), thus going beyond the Hartree-Fock approximation. Recall (Section 11.3) that in a molecular Cl calculation one begins with a set of basis functions Xi, does an SCF calculation to find SCf occupied and virtual (unoccupied) MOs, uses these MOs to form configuration (state) functions writes the molecular wave function i/ as a linear combination 2/ of the configuration functions, and uses the variation method to find the ft, s. In calculations on diatomic molecules, the basis functions can be Slater-type AOs, some centered on one atom, the remainder on the second atom. 

Becke, A. D. (1986). Completely numerical calculations on diatomic molecules in the local-density approximation. Phys. Rev. A 33,2786-2788. 

Ab initio and DFT Calculations on Diatomic Molecules. - Jaszunski, Klopper and Noga" describe an analysis of the static dipole polarizability of the Hc2 dimer using high precision CCSD(T) calculations. The results for the polarizability and its anisotropy are not significantly different from CCSD results in the literature and serve to confirm their accuracy. 

For SCF calculations on diatomic molecules, one can use Slater-type orbitals [Eq. (11.14)] centered on the various atoms of the molecule as the basis functions. (For an alternative choice, see Section 15.4.) The procedure used to find the coefficients Cj, of the basis functions in each SCF MO is discussed in Section 14.3. To have a complete set of AO basis functions, an infinite number of Slater orbitals are needed, but the true molecular Hartree-Fock wave function can be closely approximated with a reasonably small number of carefully chosen Slater orbitals. A minimal basis set for a molecular SCF calculation consists of a single basis function for each inner-sheU AO and each valence-shell AO of each atom. An extended basis set is a set that is larger than a minimal set. Minimal-basis-set SCF calculations are easier than extended-basis-set calculations, but the latter are much more accurate. 

The elements of the Hamilton and overlap matrices, i.e., (Xmini H xm2m) and XmimlXmitiz) with Xmn being the Kth atomic orbital of the mth atom, are obtained from calculations on diatomic molecules. The Hamilton operator contains the kinetic-energy operator as well as the potential. The latter is approximated as a superposition of the potentials of the isolated atoms. 

Tanpipat, N., Ah initio relativistic effective potential and relativistic configuration interaction calculations on diatomic molecules containing heavy elements (Lutecium and Lawrencium), PhD thesis. University of Tennessee, 1987. 

Calculations on diatomic molecules of transition elements have begun. but so far are restricted to the first few elements. A ligand-field theory for these molecules " based on the anticipated transition metal ion configuration (e.g., 3d for Ti + in TiO) was not successful and the configurations including one or two electrons of the transition metal ion must be considered.Cheetham and Barrow ) ground states predicted... 

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