MRD-CI method

P.J. Bruna, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method. J. Chem. Phys. 72, 5437-5445 (1980)... 

For longer polyenes, multireference double excitation configuration interaction (MRD-CI) approximations have been employed which select the most important electronic configurations and balance the effects of electron correlation in the ground and excited states. The MRD-CI methods provide results comparable to Q-CI or full -Cl calculations on short polyenes (Zoos and Ramasesha, 1984) and have allowed calculations to be extended to molecules with up to eight double bonds (Tavan and Schulten,... 

In this context one should also mention the rather old MRD-CI-method of Buenker and Peyerimhoff [160]. There one starts from a multideterminant reference function and improves it by Cl with single and double substitution. This method has not been designed for single states, but rather for the computation of various states simultaneously. 

The isomer lowest in energy is predicted to be the 2,5-dihydro-1,2,4-triazine 198g. The most stable structures always show two C=N double bonds. Moreover, in polar solvents, 198h should also be a dominant species [00PCCP2187]. The valence and Rydberg excited states of 1,2,3-triazine have been studied by multireference methods (MRD-CI) and the results are compared with experimental spectra [98CP39]. 

This is done in the MRD-CI/Bk method [20, 13] which we want to present in the present section. After a brief introduction of the underlying theory we will discuss the GH molecule as a test system. 

In the following, the efficiency of the Bk method in correcting a truncated CI wavefunction will be discussed. Such a calculation, in the following abbreviated as a MRD-CI/Bk calculation, consists of two steps. After choosing the reference space, all single and double excitations are generated. In the first... 

After discussing the underlying theory of the MRD-CI/BK method, we want to give a few examples, which illustrate some problems in the calculations of isotropic hfcc s. To give a feeling about the accuracy of various theoretical levels, we will compare the MRD-CI/Bk method with several other theoretical approaches. As a test system we use the H2CO+ molecule in its electronic ground state. 

Table 13 Isotropic hyperfine couplings in H2CN using the MRD-CI/Bk method with different geometries (in MHz).

The anisotropic hfccs are given in table 14. All theoretical values were calculated using the MRD-CI/Bk method but, as already mentioned, they are quite insensitive to the method of calculation. We have therefore omitted from the table most previous results given in the literature. Only the study of Feller and Davidson is included for comparison. The dependence upon the geometry is also less prominent. 

For the molecule H2CN, we compared the MRD-CI/BK method to S-CI, SD-CI, truncated MR-CI calculations and to the QCISD calculations reported in the very careful CCF investigation [10]. To give a feeling about the relia-... 

Table 14 Anisotropic hyperfine coupling constants (in MHz) of H2GN (X2B2). The values of the present work were obtained with the van Duijneveldt AO basis in combination with the MRD-CI/BK method.

Most of the studies about ESR parameters deal with molecules possessing one unpaired electron, i.e. S=l/2. Investigations on systems with S=1 are rare. To show the ability of the MRD-CI/Bk method we want to discuss the hyperfine structure of the isoelectronic molecules CCO, CNN and NCN [64]. 

Comparison of the theoretical values with the experimental findings shows that only the MRD-CI/Bk treatment yields reliable quantitative hfcc s for all the investigated molecules. Employing this method, all results lie within the experimental error bars. The S-CI method again reaches qualitative agreement with the experimental results. The deviations are between 0 and 6 MHz (0-20 %), with exception of the C center in CaGpO, for which much larger errors were found. The value of Ax deviates more than 12 MHz ( 23 %) from the experimental value (43.7 MHz vs. 57 3 MHz) for Ay an error of 15 MHz ( 71 %) is found. Comparison with the MRD-CI/Bk treatment shows that the S-CI calculations yield a value for the isotropic hfcc of Ca which is much too low (17.3 MHz vs. 30.7 MHz). 

Both the BLYP functional used in the present work and the PW86 functional in ref. [114] give Aiso(1H) values which deviate less from the experimental data than the MRD-CI/Bk results. The agreement with experimental data is even improved if the geometry is optimized using the DFT method itself (table 24, upper part). However, as already discussed in ref. [114], very often these geometries are not as good as ab initio data. 

If direct contributions are important a cancellation takes place, leading, for example, to very accurate isotropic hfcc s of / protons, as shown for H2CN and H2CO+. In such cases neither the direct nor the indirect contributions represent observables. Therefore it is unclear whether this represents an error cancellation or arises from the differences in the description of correlation effects in the MRD-CI/Bk treatment and the DFT method. 

We have in the present paper investigated two fundamentally different, yet complementary, routes to computational studies of radical hyperfine structures. On the one hand, we have the highly accurate MRCI - based approaches, which are able to predict hyperfine structures of small systems to very high accuracy. The role and importance of higher than double excitations in the configuration expansions has been elucidated by means of detailed case studies on a number of first row atoms, as well some selected molecular systems. We have also demonstrated how a newly developed method, the MRD-CI/Bk method, by means of a perturbative method is able to incorporate the effects... 

Most of the general methods developed for isolated molecules have been used to treat PH as supermolecules HF, Cl, CEPA, MPn, MRD-CI, CC, DFT, etc... They can use semi-empirical or, more often, ab initio wave functions. Let us notice that MP2 is mostly used in the last decade. Among the emerging methods, let us mention CASPT2 calculations on the excited states of H30+(59i) and DFT studies more or less arbitrarily included in quantum chemistry treatments. VB calculations are found in only one case. 

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