Advances in transition state theory and computer simulations are providing new insights into the sources of enzyme catalysis. Both lowering of the activation free energy and changes in the generalized transmission coefficient (recrossing of the transition state, tunneling, and nonequilibrium contributions) can play a role. A framework for understanding these effects is presented, and the contributions of the different factors, as illustrated by specific enzymes, are identified and quantified by computer simulations. The resulting understanding of enzyme catalysis is used to comment on alternative proposals of how enzymes work.

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.

A Monte Carlo quantum mechanical-molecular mechanical (QM-MM) simulation method was used to determine the contributions of the solvent polarization effect to the total interaction energies between solute and solvent for amino acid side chains and nucleotide bases in aqueous solution. In the present AM1-TIP3P approach, the solute molecule is characterized by valence electrons and nucleus cores with Hartree-Fock theory incorporating explicit solvent effects into the total Hamiltonian, while the solvent is approximated by the three-point charge TIP3P model. The polarization energy contributes 10 to 20 percent of the total electrostatic energy in these systems. The performance of the hybrid AM1-TIP3P model was further validated by consideration of bimolecular complexes with water and by computation of the free energies of solvation of organic molecules using statistical perturbation theory. Excellent agreement with ab initio 6-31G(d) results and experimental solvation free energies was obtained.

A generalized hybrid orbital (GHO) method has been developed at the semiempirical level in combined quantum mechanical and molecular mechanical (QM/MM) calculations. In this method, a set of hybrid orbitals is placed on the boundary atom between the QM and MM fragments, and one of the hybrid orbitals participates in the SCF calculation for the atoms in the QM region. The GHO method provides a well-defined potential energy surface for a hybrid QM/MM system and is a significant improvement over the “link-atom” approach by saturating the QM valencies with hydrogen atoms. The method has been tested on small molecules and yields reasonable structural, energetic, and electronic results in comparison with the results of the corresponding QM and MM approximations. The GHO method will greatly increase the applicability of combined QM/MM methods to systems comprising large molecules, such as proteins.

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An energy decomposition scheme based on the block-localized wave function (BLW) method is proposed. The key of this scheme is the definition and the full optimization of the diabatic state wave function, where the charge transfer among interacting molecules is deactivated. The present energy decomposition (ED), BLW-ED, method is similar to the Morokuma decomposition scheme in definition of the energy terms, but differs in implementation and the computational algorithm. In addition, in the BLW-ED approach, the basis set superposition error is fully taken into account. The application of this scheme to the water dimer and the lithium cation–water clusters reveals that there is minimal charge transfer effect in hydrogen-bonded complexes. At the HF/aug-cc-PVTZ level, the electrostatic, polarization, and charge-transfer effects contribute 65%, 24%, and 11%, respectively, to the total bonding energy (−3.84 kcal/mol) in the water dimer. On the other hand, charge transfer effects are shown to be significant in Lewis acid–base complexes such as H3NSO3 and H3NBH3. In this work, the effect of basis sets used on the energy decomposition analysis is addressed and the results manifest that the present energy decomposition scheme is stable with a modest size of basis functions.

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The absorption of one photon by a semiconductor material usually creates one electron-hole pair. However, this general rule breaks down in a few organic semiconductors, such as pentacene and tetracene, where one photon absorption may result in two electron-hole pairs. This process, where a singlet exciton transforms to two triplet excitons, can have quantum yields as high as 200%. Singlet fission may be useful to solar cell technologies to increase the power conversion efficiency beyond the so-called Shockley-Queisser limit. Through time-resolved two-photon photoemission (TR-2PPE) spectroscopy in crystalline pentacene and tetracene, our lab has recently provided the first spectroscopic signatures in singlet fission of a critical intermediate known as the multiexciton state (also called a correlated triplet pair). More importantly, we found that population of the multiexciton state rises at the same time as the singlet state on the ultrafast time scale upon photoexcitation. This observation does not fit with the traditional view of singlet fission involving the incoherent conversion of a singlet to a triplet pair. However, it provides an experimental foundation for a quantum coherent mechanism in which the electronic coupling creates a quantum superposition of the singlet and the multiexciton state immediately after optical excitation. In this Account, we review key experimental findings from TR-2PPE experiments and present a theoretical analysis of the quantum coherent mechanism based on electronic structural and density matrix calculations for crystalline tetracene lattices. Using multistate density functional theory, we find that the direct electronic coupling between singlet and multiexciton states is too weak to explain the experimental observation. Instead, indirect coupling via charge transfer intermediate states is two orders of magnitude stronger, and dominates the dynamics for ultrafast multiexciton formation. Density matrix calculation for the crystalline tetracene lattice satisfactorily accounts for the experimental observations. It also reveals the critical roles of the charge transfer states and the high dephasing rates in ensuring the ultrafast formation of multiexciton states. In addition, we address the origins of microscopic relaxation and dephasing rates, and adopt these rates in a quantum master equation description. We show the need to take the theoretical effort one step further in the near future by combining high-level electronic structure calculations with accurate quantum relaxation dynamics for large systems.