The performance of the density functional theory on reaction pathways requiring the multideterminantal description
Introduction
The description of reaction pathways is a great challenge for theoretical chemistry. Quantum chemistry offering potential energy surfaces (PES) for an arbitrary configuration of involved atoms is often a main tool in the reaction investigation at the microscopic level (Hehre et al., 1985). Most often chemical reactions involve breaking and forming bonds and lead to substantial differences in an electronic density distribution. Then, the proper representation of PES requires a simultaneous description of subsystems having different number of electrons. The correlation energy of reactants and products may differ substantially and its proper description is essential.
The density functional theory (DFT) (Ziegler, 1991) is developing rapidly as a cost-effective general procedure for the inclusion of correlation energy. The DFT replaces the exchange-correlation energy by a one electron integral involving the local electron spin densities or their gradients. The convenient formulation of the Kohn-Sham self consistent field procedure by the Pople's group (Pople et al., 1992) allows to express the electron density in terms of the finite set of molecular orbitals.
The decomposition reactions of NH4+ (Kaldor et al., 1989) and nitromethane (Roszak and Kaufman, 1991) are known as severe tests for the quality of the correlation description. In both cases the closed shell system is decomposed into two open shell fragments, and the restricted Hartree-Fock procedure leads to the wrong dissociation limit. The description has to be improved by inclusion of the correlation energy. The multideterminant description, even the simplest one including HOMO and LUMO orbitals only leads to the proper dissociation limit.
In this work we study the process of the NH4+ dissociation and the transformation reaction from nitromethane to methyl nitrite within the density functional theory model applying a number of possible energy functionals, representing exchange and correlation terms. Results are compared with CASSCF and FOCI calculations known to properly account for the multireference character of the wavefunction.
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Theoretical methods and computational details
The calculations for NH4+ and nitromethane have been performed applying the density functional theory approach. The adopted functionals for the exchange term include: Xα functional (Xα) (Dirac, 1930), Slater's local spin density exchange functional (S) (Slater, 1951) and Becke's (B) functional (Becke, 1988). The correlation energy has been calculated applying Lee-Yang-Parr (LYP) (Lee et al., 1988), Perdew (P86) (Perdew, 1986), local spin density correlation of Vosko-Wilk-Nusair (VWN) and (VWN5)
The deprotonation of NH4+
The study of the deprotonation reaction of NH4+ (Fig. 1) was carried out using HF, MP2, CASSCF and DFT methods. All calculations which include correlation energy are based on the restricted single determinantal wavefunction. The N-H+ dissociation pathway proceeds through an avoided crossing of two potential surfaces with the closed shell NH4+ dissociating into the open shell H(2S)+NH3+ (2A1) fragments rather then into higher energy closed shell systems H+ and NH3(1A1). The ground state
Nitromethane to methyl nitrite rearrangement
The reaction pathway of nitromethane to methyl nitrite rearrangement is known to be very sensitive to the proper description of the correlation effects (McKee, 1989; Roszak et al., 1994). The wavefunctions of nitromethane, methyl nitrite as well as the transition state, have the significant multireference character. Energy differences between the transition state and nitromethane ΔE(NM-TS) and between the transition state and methyl nitrite ΔE(MN-TS) are the most important parameters of the
Conclusions
The density functional methods have been applied for cases known to require the multireference description. The DFT calculations were based on the restricted single determinantal wave function and the computational scheme proposed by Pople et al. (Pople et al., 1992). The dissociation of (NH3-H)+ leads to an unphysical ground state of NH3 +H+ in every DFT energy functional applied when the method is based on the restricted single determinantal wavefunction, similarly to HF and MP2 methods. In
Acknowledgements
This research has been supported in part by KBN Grant No. 6 P04A 060 09 and in part by the Technical University of Wrocław under Grant No. 341-664. We wish to thank the Poznań Supercomputing and Networking Center for providing computer time.
References (24)
- et al.
Chem. Phys. Lett.
(1992) - et al.
J. Mol. Graphics
(1994) - et al.
J. Chem. Phys.
(1992) - et al.
Mol. Phys.
(1984) Phys. Rev.
(1988)J. Chem. Phys.
(1993)Proc. Cambridge Phil. Soc.
(1930)- Dunning, T. H. and Hay, P. J. (1976) In Modern Theoretical Chemistry, ed. H. F. Schaefer III, p. 1. Plenum, New...
- et al.
J. Chem. Phys.
(1984) - Frish, M. J., Trucks, G. W., Schlegel, H. B., Gill, P. M. W., Johnson, B. G., Wong, M. W., Foresman, J. B., Robb, M....