Here are the results of a DFT calculation that I duplicated from our publication on the structure of MTO. The calculations were performed on the Gaussian 94 package system using the gradient correction of Becke and the methods of Perdew and Wang. Dunning's basis set was used for the C,O & H atoms, while the quasi-relativistic core potentials and optimized valence basis sets of Stoll and Preuss were used on the Rhenium atom.
This is the input file that I used, MTO.dat.
About the input;
The method here is that outline by Scherer in our paper on MTO (Journal of Chemical Physics Vol. 107, p. 2187, 1997). His method is very logical in that he uses well known methods from a combination of sources to obtain a very reasonable answer.
Carbon, Oxygen and Hydrogen;
It has long been known in computational chemistry that Gaussian Type Orbitals (GTOs) will run more efficiently in numerical calculations than the more accurate Slater Type Orbitals (STOs), however because some accuracy is lost in using GTOs we must use several in combination to represent one STO. Well defined GTOs for the first two rows of the period table are abundant, however few have stood the test of time like those of Thom. H. Dunning, Jr. In 1970-1 Dunning produced contracted Gaussian basis sets for the first row atoms that were large enough to allow his calculations to approach the Hartree-Fock limit. He defined the atomic basis sets in terms of a group of primitive Gaussian functions in which he had optimized the coefficients and exponents to match with more rigorous calculations done to determine the appropriate atomic parameters. The results of this work are table of coefficients and exponents that can be used as input to a structure calculation like that shown in MTO.dat above. The GTOs are versatile in that the number of variable coefficients can be relatively easily changed for increased accuracy in determination of the wavefunction. For an example of a study I did on this effect in the cyclopentadienyl complexes CpIn and CpTl click here.
Rhenium;
Rhenium is a third row transition metal, it's compounds have many interesting properties, but like all third row transition metal compounds, it has a lot of electrons (75 in it's nuetral state). The abundance of electrons greatly complicates calculation for this element because a rigorous (ab initio) calculation would require extreme amounts of computation time.
Generally the core electrons (all the way up to 60 for third row metals) are all considered together in an ab initio treatment of a such a system. This assumption can be made in general because the core electrons do not behave differently in different chemical systems. Generally it is the valence electrons that tend to change the most upon bonding.
The method of the pseudopotential has been in use for quite some time and is generally used as a substitute of a few functions for many functions. The large number of electrons in Rhenium's core would require an enormous amount of GTOs, thus in a method similar to that of Dunning, Stoll and Preuss have developed what they call non-relativistic and quasi-relativistic effective core potentials that describe the behavior of electrons even near the core where the Coulombic forces give the electrons enough kinetic energy such that their velocities approach the speed of light and thus behave relativistically. These authors optimized their psuedopotentials to reproduce observable atomic properties such as the valence energies of a multitude of electronic states. They did this without restricting any parameters of the electron configurations. They obtained their reference data from ab initio all electron calculations since experimental data on excited atomic states of transition metals are rare. The results of their studies are a set of mathematical functions that may be entered into calculations in numerical form.
The last thing needed in the input for Rhenium is a description of the valence electrons, this is done in an analogous matter to the full descriptions of carbon, oxygen and hydrogen above using GTOs. For consistency these were chosen from the same report by Stoll and Preuss because they chose the complimentary valence space to their core space. The exponents and coefficients were optimized to parameters for the 5s, 5p, 5d and 6s orbitals that were determined from all electron calculations. The input for this set of GTOs looks slightly different than the previous GTOs.
About the Method; BPW91
The methods of Density Functional Theory were used to carry out these calculations in a quick and efficient way. Density Functionals were initially developed as an alternative representation of the wavefunction in terms of electron density that more effectively treats the effects of electron-electron interaction. The method may now be better characterized as a 'semi-empirical' (uses experimental data in the theory) method rather than and ab initio (from first principles) technique. The original methods of DFT have been improved over the years by various computational chemists. A few of those improvements are used in the method BPW91, the B stands for the gradient correction of Becke who developed an improvement to the Local Density Aproximation (LDA) that allowed the electron correlation energy to approach it's proper asymptotic limit of 1/r2. This means that at large distances between ineteracting electrons the only forces felt are those of Coulombic repulsion. His correcting factor contains only one new parameter and has been shown to fit the exact Hartree-Fock values with great accuracy. The second two letters in the method's name stand for Perdew and Wang who developed an accurate and simple analytic representation of the electron-gas correlation energy. Their form of the electron correlation energy showed an improvement on the random phase approximation in regions of high electron density. It would appear that this combination of Becke's gradient correction for the long distance interaction and Perdew and Wang's method for the short distance interaction provide a complimentary description of the correlated behavior of electrons in molecular systems.
Results;
This is the output obtained from the input above, MTO.out.
These results agree quite well with
the experimental data (from our lab), and are exactly the same results
produced by Scherer in his DFT study. Calculations done on both the eclipsed
and staggered conformations of MTO allowed an estimate for the barrier
to internal rotation (a microwave observable) to be determined.
V = 1.92 kcal/mol = 20,133,000 MHz = 671.6 cm-1
I also discovered that the Gaussian94 package allows calculation of electric field gradients due to the electrons in a molecule, this combined with the electric field gradient due to the nuclei will produce splitting patterns in the microwave spectra of molecules that contain a quadrupolar nucleus (like Rhenium). In many of the transition metals this splitting can be large (on the order of the rotational constants) and thus it is in our best interests to be able to predict the magnitude of it. For example in the two Rhenium compounds Dr. Kukolich has studied this coupling ranged from -900 MHz up to +726 MHz. Typical rotation constants are in the range from 500 MHz to 4000 MHz.
Since no work has been done on calculating quadrupole coupling for nuclei bigger than Nitrogen I realize that this could be a formidable task, even impossible. But I am looking into it, and have decided to start small, and try to predict some coupling values for Nitrogen in molecules such as ammonia.
Expanding Scherer's Method;
The same methods are now being used to probe the molecule
HRe(CO)5,