Naoki Nakatani

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations

This paper describes an interface between the density matrix renormalization group (DMRG) method and the complete active-space self-consistent field (CASSCF) method and its analytical gradient, as well as an extension to the second-order perturbation theory (CASPT2) method. This interfacing allows large active-space multi-reference computations to be easily performed. The interface and its extension are both implemented in terms of reduced density matrices (RDMs) which can be efficiently computed via the DMRG sweep algorithm. We also present benchmark results showing that, in practice, the DMRG-CASSCF calculations scale with active-space size in a polynomial manner in the case of quasi-1D systems. Geometry optimization of a binuclear iron-sulfur cluster using the DMRG-CASSCF analytical gradient is demonstrated, indicating that the inclusion of the valence p-orbitals of sulfur and double-shell d-orbitals of iron lead to non-negligible changes in the geometry compared to the results of small active-space ca...

Platinum-catalyzed reduction of amides with hydrosilanes bearing dual Si–H groups: a theoretical study of the reaction mechanism

A platinum-catalyzed amide reduction through hydrosilylation with 1,2-bis(dimethylsilyl)benzene (BDSB) was investigated on a theoretical basis. While the platinum-catalyzed hydrosilylation of alkenes is well known, that of carbonyl groups rarely occurs. The only exception involves the use of bifunctional hydrosilanes having dual, closely located Si-H groups, which accelerate the hydrosilylation of carbonyl groups, leading to successful reduction of amides to amines under mild conditions. In the present study, we determined through density functional theory calculations that the platinum-catalyzed hydrosilylation of the C=O bond proceeds via a Pt(IV)-disilyl-dihydride intermediate with an associated activation energy of 29.6 kcal mol(-1). Although it was believed that the hydrosilylation of carbonyl groups does not occur via the classical Chalk-Harrod cycle, the computational results support a mechanism involving the insertion of the amide C=O bond into a Pt-H bond. This insertion readily occurs because a Pt-H bond in the Pt(IV)-disilyl-dihydride intermediate is highly activated due to the strong σ-donating interaction of the silyl groups. The modified Chalk-Harrod mechanism that occurs preferentially in rhodium-catalyzed hydrosilylation as well as the ionic outer sphere mechanism associated with iridium-catalyzed amide reduction were both safely ruled out as mechanisms for this platinum-catalyzed amide reduction, because of the unexpectedly large activation barrier (>40 kcal mol(-1)) for the Si-O bond formation.

Excited states of a significantly ruffled porphyrin: computational study on structure-induced rapid decay mechanism via intersystem crossing.

The compound meso-tetra-tert-butylporphyrin (H2T(t-Bu)P) is a significantly ruffled porphyrin and known as a good quencher. Compared with planar porphyrins, H2T(t-Bu)P showed bathochromic shift and rapid radiationless decay of the (1)(π, π*) excited state. Density functional theory, approximated coupled-cluster theory, and complete active space self-consistent field method level calculations were performed for the potential energy surface (PES) of the low-lying singlet and triplet states of H2T(t-Bu)P. The origin of the bathochromic shift in the absorption and fluorescence spectra was attributed to both steric distortions of the ring and electronic effects of the substituents. The nonradiative deactivation process of H2T(t-Bu)P via intersystem crossing (ISC) is proposed as (S1 → T2 → T1 → S0). Along a nonplanar distortion angle, the PESs of the S1 and T2 states are very close to each other, which suggests that many channels exist for ISC. For the T1 → S0 transition, minimum energy ISC points were located, and spin-orbit coupling (SOC) was evaluated. The present results indicate that the ISC can also occur at the T1/S0 intersection, in addition to the vibrational SOC promoted by specific normal modes.

A DFT and multi-configurational perturbation theory study on O2 binding to a model heme compound via the spin-change barrier

Dioxygen binding to a model heme compound via intersystem crossing (ISC) was investigated with a multi-state multi-configurational self-consistent field method with second-order perturbation theory (MS-CASPT2) and density functional theory (DFT) calculations. In elongated Fe-O distances, the energy levels of the S0 and T1 states are separated, which decreases the probability of intersystem crossing in these structures. At the DFT(B97D) level of calculation, the Fe-O distances of the S0 and T1 states were 1.91 and 2.92 Å, respectively. The minimum energy intersystem crossing point (MEISCP) was located as a transition state at a Fe-O distance of 2.17 Å with an energy barrier of 1.0 kcal mol(-1) from the T1 minimum. The result was verified with MS-CASPT2 calculations including the spin-orbit interaction which also showed the intersystem crossing point at a Fe-O distance of 2.05 Å. An energy decomposition analysis on the reaction coordinate showed the important contribution of the ring-shrinking mode of the porphyrin ring, indicating that the reaction coordinates which control the relative energy level of the spin-states play a key role in intersystem crossing.

Spin-Blocking Effect in CO and H2 Binding Reactions to Molybdenocene and Tungstenocene: A Theoretical Study on the Reaction Mechanism via the Minimum Energy Intersystem Crossing Point

Potential energy profiles and electronic structural interpretation of the CO and H2 binding reactions to molybdenocene and tungstenocene complexes [MCp2] (M = Mo and W, Cp = cycropentadienyl) were studied using density functional theory calculations and ab initio multiconfigurational electronic structure calculations. Experimentally observed slow H2 binding was reasonably explained in terms of the spin-blocking effect. Electronic structural analysis at the minimum-energy intersystem crossing point (MEISCP) revealed that the singly occupied molecular orbitals π-bonding/σ-antibonding character in the M-CO/H2 moiety determines the energy levels of the MEISCP. Analysis of the reaction coordinate showed that the singlet-triplet gap significantly depends on the Cp-M-Cp angle. Therefore, not only the metal-ligand distance but also the Cp-M-Cp angle is an important reaction coordinate to reach the MEISCP, the transition state of H2 binding. The role of spin-orbit coupling is also discussed.

Adsorption Energies of Carbon, Nitrogen, and Oxygen Atoms on the Low-temperature Amorphous Water Ice: A Systematic Estimation from Quantum Chemistry Calculations

We propose a new simple computational model to estimate adsorption energies of atoms and molecules to low-temperature amorphous water ice, and we present the adsorption energies of carbon (3P), nitrogen (4S), and oxygen (3P) atoms based on quantum chemistry calculations. The adsorption energies were estimated to be 14100 +- 420 K for carbon, 400 +- 30 K for nitrogen, and 1440 +-160 K for oxygen. The adsorption energy of oxygen is well consistent with experimentally reported value. We found that the binding of a nitrogen atom is purely physisorption, while that of a carbon atom is chemisorption in which a chemical bond to an O atom of a water molecule is formed. That of an oxygen atom has a dual character both physisorption and chemisorption. The chemisorption of atomic carbon also implies a possibility of further chemical reactions to produce molecules bearing a C-O bond, while it may hinder the formation of methane on water ice via sequential hydrogenation of carbon atoms. These would be of a large impact to the chemical evolution of carbon species in interstellar environments. We also investigated effects of the newly calculated adsorption energies onto chemical compositions of cold dense molecular clouds with the aid of gas-ice astrochemical simulations. We found that abundances of major nitrogen-bearing molecules, such as N2 and NH3, are significantly altered by applying the calculated adsorption energy, because nitrogen atoms can thermally diffuse on surfaces even at 10 K.

Transition States of Spin-State Crossing Reactions from Organometallics to Biomolecular Excited States

Our recent studies on spin-state crossing reactions are summarized. With a constraint optimization method, a minimum-energy intersystem-crossing point (MEISCP) was located. With an energy decomposition analysis, important reaction coordinates for the intersystem-crossing were clarified. The systems investigated were twofold; one is accelerated triplet-state quenching in metal-free biomolecules such as a significantly ruffled porphyrin and a carotenoid, and the other is spin-blocked phenomena in the ligand binding of organometallic complexes. A common finding in these spin-state crossing reactions is that there is a key reaction coordinate that leads the system toward a MEISCP, a transition state of spin-crossing reaction. This coordinate is not necessary related to the primary reaction coordinate (such as C=C twisting in carotenoid, Fe–O distance in O2 binding, M-H distance in metallocenes) but to the coordinate sensitive to the relative energy difference between the two spin states (such as bond-length alternation in carotenoid, porphyrin ring stretching in O2 binding of heme, and cyclopentadienyl (Cp)-M-Cp angle in metallocenes). This knowledge should be useful in the catalysis design and reaction control.