Laboratory for Physical Chemistry 2: Molecular Spin Science

Kazuo Toyota (Lecturer)

1. Current Research and Principal Research Interests

Our principal interests focus on the development and application of quantum chemical theories which are applicable to electronic structures of various types molecules in both the ground and excited states, aiming the theories feasible for sizable molecules and electronically excited states of organic high spin molecules as models for molecule-based magnetic materials. Our approach is based on the SAC-CI method. 
Nowadays the sophisticated ab initio calculations are becoming more and more useful tools for researches in the broad areas of chemistry, physics and related sciences. However, the quantitative description of the electronic structure for open-shell systems has long been a challenging subject in quantum chemistry. The long expansion of the wave function is generally required for such systems if the conventional configuration interaction (CI) method is used. This is due to the complicated correlation effects among electrons in open-shell systems. On the other hand, for closed-shell systems, it is well known that the so-called dynamical correlation effects can be treated with good accuracy by the coupled cluster (exponential) expansion with single and double excitations from the Hartree-Fock (HF) electronic configuration. The symmetry-adapted cluster (SAC) expansion is one of the coupled cluster type theories. In 1978, Nakatsuji proposed an attractive approach to the electronic structure theory for open-shell systems, called symmetry-adapted-cluster configuration-interaction (SAC-CI). In the SAC-CI method, the wave function is represented by a linear combination of excited functions from correlated one described by the SAC expansion instead of the uncorrelated HF configuration. Bypassing the explicit consideration of many-electron excitations from the HF configuration usually required for open-shell systems, the SAC-CI method remarkably reduces the degrees of freedom to describe the correlated wave functions for open-shell systems including excited states, so that computations of their complicated wave functions become feasible by invoking accessible computational resources. 
Our research activities can be categorized as follows

(1) Application of the SAC-CI method to spectroscopic studies.
The SAC-CI method has been implemented up to septet states and has been applied to various states including the ground, excited, ionized, and electron-attached states (see Ref. below). We applied the SAC-CI method to electronic spectra of pigments of industrial importance, phthalocyanines (tetrabenzotetraazaporphyrins), before the recent calculations by time dependent density functional theory (TDDFT) were reported for the molecules. The electronic structures of this class of pigments in the excited states have been studied by some groups in terms of semi empirical methods but there were few ab initio calculations for the excited states. The SAC-CI method can treat such large molecules as phthalocyanines when used with the so-called perturbation selection technique. The assignments of absorption bands up to 4.4eV were made based on the theoretical spectra by the SAC-CI method. The electronic structure of the B band in UV region calculated by us is in good agreement with that proposed by MCD experimentalists.
We apply the SAC-CI method to the absorption and emission spectroscopic analysis for triplet-triplet or quintet-quintet transitions occurring in typical high-spin hydrocarbons such as diphenylenemethylene or m-phenylene-bis(phenylmethylene). 

(2) Development of analytical gradients for the SAC/SAC-CI method: Aiming to predict general molecular properties of the ground, excited, ionized, electron attached and high spin states.
It is required to evaluate energy derivatives for predicting general molecular properties, for example, electric dipole moments, geometries, chemical shifts, etc. For the closed-shell systems, the rapid developments of the analytical gradient method have enabled us to perform geometry optimizations as routine works. However, the stable and semi stable geometries of molecules with high spin multiplicities or in the excited states are still hard to compute. We have formulated analytical expressions of the first derivatives of energies and have developed computer programs to calculate the analytical energy derivatives for the SAC-CI method. The programs have been used to calculate equilibrium geometries and adiabatic (0-0) excitation energies of the ground and excited states of some small molecules with singlet to quartet spin multiplicities.

(3) Development of an efficient localized MO based theory for very large systems.
Expanding applicability of the theory to larger systems is one of the most important subjects in modern quantum chemistry. The short-range nature of the correlation among electrons is useful to make the theory computationally less demanding without loosing substantial accuracy. This can be realized through the localization of molecular orbitals and dropping less important non-locally excited functions from the SAC and SAC-CI expansions. We also developed programs for calculating the energy gradients more economically than those based on the conventional delocalized MO formulation.

 (4) Methodological establishment of ab initio calculations for magnetic properties of organic open-shell systems. 
   Prediction for fine structure tensors of spin multiplet states from molecular systems has been a long-standing issue in chemistry since Higuchi's pioneering work. Correlating three spin problems have challenged theoreticians. Recently, experimentally determined fine structure constants from high spin states of highly symmetric molecular systems have appeared, attracting general attention. Spin correlation functions have rarely been used for calculating fine structure tensors so far. In this project, we develop methods in ab initio level for calculating fine structure tensors by invoking spin correlation functions and spin-coupled wave functions for high spin hydrocarbons and other high spin molecules of chemical importance, combining the SAC-CI method with the spin correlation functional analysis. We predict the fine structure tensors of the electronic excited states from various types of high spin molecules, serving for experimental challenges for the detection of the excited states. 

2. Selected Publications

1. "SAC-CI study of the excited states of free base tetrazaporphin", K. Toyota, J. Hasegawa, and H. Nakatsuji, Chem. Phys. Lett., 250, 437-442 (1996). 

2. "Excited states of free base phthalocyanine studied by the SAC-CI method", K. Toyota, J. Hasegawa, and H. Nakatsuji, J. Phys. Chem. A, 101, 446-451 (1997).

3. "Analytical energy gradients of the excited, ionized, and electron-attached states calculated by the SAC-CI general-R method", M. Ishida, K. Toyota, M. Ehara, and H. Nakatsuji, Chem. Phys. Lett., 347, 493-498 (2001).

4. "Analytical energy gradient of high-spin multiplet state calculated by the SAC-CI method", M. Ishida, K. Toyota, M. Ehara, and H. Nakatsuji, Chem. Phys. Lett., 350, 351-358 (2001).

5. "Elimination of singularities in molecular orbital derivatives: minimum orbital-deformation (MOD) method", K. Toyota, M. Ehara, H. Nakatsuji, Chem. Phys. Lett., 356, 1-6 (2002).

6. "SAC-CI general-R method: Theory and applications to the multi-electron processes", M. Ehara, M. Ishida, K. Toyota, and H. Nakatsuji (Ed. by K. D. Sen, "Reviews in modern quantum chemistry A celebration of the contributions of Robert G Parr", pp. 293-319), World Scientific, Singapore, in press.