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We applied the fragment molecular orbital (FMO) method, which enables total electronic calculations of large molecules at ab initio level, to the evaluation of binding affinities between the human progesterone receptor ligand-binding domain (PR LBD) and various steroidal ligands. The FMO calculations were performed on the entire structure of the PR LBD, which is composed of approximately 4,100 atoms. Our computational binding energies of PR LBD/ligand complexes agreed well with experimental binding affinities (r=0.909). Interaction energies between each ligand and specific amino acid residues were also obtained from the FMO calculations. The principal residues involved in the interactions with these ligands were Arg766 and Asn719, with some additional contribution by Gln725. The main factor determining differences in binding affinity of the various ligands was not interactions with particular residues, but with the binding-site residues closest to the ligand. The interfragment interaction energy analysis is proving to be a useful method for gaining detailed information on ligand binding.

We propose a parallelized integral-direct algorithm of the second-order Moller–Plesset perturbation theory (MP2) as a size-consistent correlated method. The algorithm is a modification of the recipe by Mochizuki et al. [(1996) Theor Chim Acta 93:211]. There is no need to communicate the bulky data of integrals across worker processes, keeping the formal fifth-power dependence on the number of basis functions. A multiple integral screening procedure is incorporated to reduce the operation costs effectively. An approximate MP2 density matrix can also be directly calculated through the integral contraction with orbital energies. We implement the MP2 code by accepting Kitaura’s fragment molecular orbital (FMO) scheme as in the program ABINIT-MP developed by Nakano et al. [(2002) Chem Phys Lett 351:475]. The error in the FMO–MP2 energies is found to be within the order of the chemical accuracy. Timing and parallel acceleration results are shown for test molecules.

The analytic energy gradient for the point charge approximation of the embedding potential is derived in the framework of unrestricted Hartree–Fock based on the fragment molecular orbital method (FMO). For this goal, we derive the necessary coupled-perturbed unrestricted Hartree–Fock equations, describing the response terms arising from the use of embedding atomic charges in dimer calculations. By a comparison to numerical gradients and with the aid of molecular dynamics, we show that the gradients have a high accuracy. A speed-up of the factor 7.3 is obtained for the largest system, when approximated potentials are used relative to the exact two-electron embedding. We apply the FMO method to polymer radicals and show that it has satisfactory accuracy in reproducing the geometries and energies of polymer radical reactions.

The completely analytic energy gradients are derived and implemented for the two-body fragment molecular orbital (FMO2) method combined with the model core potentials (MCP) and effective fragment potentials (EFP). The many-body terms in EFP require solving coupled-perturbed Hartree-Fock equations, which are derived and implemented. The molecular dynamics (MD) simulations are performed using the FMO2/MCP method for the capped alanine decamer and with the FMO2/EFP method for the zwitterionic conformer of glycine tetramer immersed in the water layer of 6.0 A (135 water molecules). The results of the MD simulations using the FMO2/EFP and FMO2/MCP gradients show that the total energy is conserved at the time steps less than 1 fs.

A new method for the resolution of an antisymmetrized product of molecular orbitals into VB structures is proposed. Here VB structures are projected from a single Slater determinant associated with the ground state using the first-order density matrix. The present theory is applied to the ground state of some conjugated hydrocarbons, and special attention is paid to the covalent type VB structures.

The reliability of theab-initio effective core potential method for calculating molecular geometries was tested for several polyatomic molecules by using the energy gradient technique. The calculated geometries are in good agreement with those of all-electron calculation not only for equilibrium but also for transition states. The heat of reaction and the activation barrier height compare very well with those of all-electron calculation as well.

An energy decomposition scheme useful for the analysis of the coupled types of interactions in strongly interacting systems is developed within the Hartree-Fock approximation. A dominant characteristic of the scheme is that it involves the interactions between vacant orbitals of component molecules, as can be justified from the third-order perturbation theory. On the basis ofab initio molecular orbital calculations, the utility of the scheme is illustrated for the BH3-NH3 complexation and the SN2 reaction of CH4 with H−. It is found that the charge transfer from electron donor (i.e. NH3 or H−) to acceptor (i.e. BH3 or CH4) is strongly coupled with the polarization of the acceptor, to contribute appreciably to the stabilization of the entire system. A specific role of this coupling mode in the progress of reactions is discussed.

The energy decomposition scheme is used with the ab initio MO of the STO-3G minimal basis to elucidate the nature of hydrogen-bondings in (HCOOH)2, (HCONH2)2 and (B(OH)3)2. The comparison of the interaction energy and its five components, together with that of the difference density map, reveals the similarity or the difference of these three systems. Each component of the global difference density represents the characteristic role of the corresponding interaction. While the effect of the exchange and charge-transfer interaction is limited to the hydrogen-bonded region, that of the polarization and the coupling terms is spread over the intramolecular bonds of each monomer. The analysis of some orbital interactions is made with respect to (HCOOH)2 and the importance of the particular charge-transfer interaction is demonstrated.

RPA theory has been applied to the calculations of the electronic spectra of some conjugated systems, considering only π-electrons explicitly. Electron repulsion integrals have been calculated using Slater AO's with appropriate orbital exponents. The present calculation shows that the correlation effect between π-electrons is rather small for the lowest π — π * transitions. Good results have been obtained, when we calculate the electron repulsion integrals using orbital exponents evaluated by Slater rule. “Effective” electron interaction in the excited states has been discussed, using the calculated results. The calculated oscillator strengths were considerably improved by RPA