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The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige

We propose an efficient ${\cal O}(N^2)$-parameter ansatz that consists of a sequence of exponential operators, each of which is a unitary variant of Neuscamman's cluster Jastrow operator. The ansatz can also be derived as a decomposition of T$_2$ amplitudes of the unitary coupled cluster with generalized singles and doubles, which gives a near full-CI energy, and reproduces it by extending the exponential operator sequence. Because the cluster Jastrow operators are expressed by a product of number operators and the derived Pauli operator products, namely the Jordan-Wigner strings, are all commutative, it does not require the Trotter approximation to implement to a quantum circuit and should be a good candidate for the variational quantum eigensolver algorithm by a near-term quantum computer. The accuracy of the ansatz was examined for dissociation of a nitrogen dimer, and compared with other existing ${\cal O}(N^2)$-parameter ansatzs. Not only the original ansatzs defined in the second-quantization form but also their Trotterized variants, in which the cluster amplitudes are optimized to minimize the energy obtained with a few, typically single, Trotter steps, were examined by quantum circuit simulators., Comment: 9 pages, 3 figures

For theoretically studying molecules with fluorescence in the near-infrared region, high-accuracy determination of state energy level is required for meaningful analyses since the spectra of interest are of very narrow energy range. In particular, these molecules are in many cases handled in solution; therefore, consideration of the solvation effect is essential upon calculation together with the electronic structure of the excited state. Earlier studies showed that they cannot be described with conventional methods such as PCM-TD-DFT, yielding results far from experimental data. Here, we have developed a new method by combining a solvation theory based on statistical mechanics (RISM) and a multireference perturbation theory (CASPT2) with the extension of the density matrix renormalization group reference states for calculating the photochemical properties of near-infrared molecules and have obtained higher-accuracy prediction.

We present an extended implementation of the multireference configuration interaction (MRCI) method combined with the quantum-chemical density matrix renormalization group (DMRG). In the previous study, we introduced the combined theory, referred to as DMRGMRCI, as a method to calculate high-level dynamic electron correlation on top of the DMRG wave function that accounts for active-space (or strong) correlation using a large number of active orbitals. The DMRG-MRCI method is built on the full internal-contraction scheme for the compact reference treatment and on the cumulant approximation for the treatment of the four-particle rank reduced density matrix (4-RDM). The previous implementation achieved the MRCI calculations with the active space (24e,24o), which are deemed the record largest, whereas the inherent Nact 8 × N complexity of computation was found a hindrance to using further large active space. In this study, an extended optimization of the tensor contractions is developed by explicitly incorporating the rank reduction of the decomposed form of the cumulant-approximated 4-RDM into the factorization. It reduces the computational scaling (to Nact7 × N) as well as the cache-miss penalty associated with direct evaluation of complex cumulant reconstruction. The present scheme, however, faces the increased complexity of factorization patterns for optimally implementing the tensor contraction terms involving the decomposed 4-RDM objects. We address this complexity using the enhanced symbolic manipulation computer program for deriving and coding programmable equations. The new DMRG-MRCI implementation is applied to the determination of the stability of the iron(IV)-oxo porphyrin relative to the iron(V) electronic isomer (electromer) using the active space (29e,29o) (including four second d-shell orbitals of iron) with triple-ζ-quality atomic orbital basis sets. The DMRG-cu(4)-MRCI+Q model is shown to favor the triradicaloid iron(IV)-oxo state as the lowest energy state and characterize the iron(V) electromer as thermally inaccessible, supporting the earlier experimental and density functional studies. This conflicts with the previous MR calculations using the restricted activespace second-order perturbation theory (RASPT2) with the similar-size active space (29e,28o) reported by Pierloot et al. (Radoń, M.; Broclawik, E.; Pierloot, K. J. Chem. Theory Comput. 2011, 7, 898), showing that the hypothetical iron(V) state indicated by recent laser flash photolysis (LFP) studies is likely thermally accessible because of its underestimated relative energy.

We have developed a new computational scheme for high-accuracy prediction of the isotropic hyperfine coupling constant (HFCC) of heavy molecules, accounting for the high-level electron correlation effects, as well as the scalar-relativistic effects. For electron correlation, we employed the ab initio density matrix renormalization group (DMRG) method in conjunction with a complete active space model. The orbital-optimization procedure was employed to obtain the optimized orbitals required for accurately determining the isotropic HFCC. For the scalar-relativistic effects, we initially derived and implemented the Douglas-Kroll-Hess (DKH) hyperfine coupling operators up to the third order (DKH3) by using the direct transformation scheme. A set of 4d transition-metal radicals consisting of Ag atom, PdH, and RhH2 were chosen as test cases. Good agreement between the isotropic HFCC values obtained from DMRG/DKH3 and experiment was archived. Because there are no available gas-phase values for PdH and RhH2 radicals in the literature, the results from the present high-level theory may serve as benchmark data.

We present the development of the multistate multireference second-order perturbation theory (CASPT2) with multiroot references, which are described using the density matrix renormalization group (DMRG) method to handle a large active space. The multistate first-order wave functions are expanded into the internally contracted (IC) basis of the single-state single-reference (SS-SR) scheme, which is shown to be the most feasible variant to use DMRG references. The feasibility of the SS-SR scheme comes from two factors: first, it formally does not require the fourth-order transition reduced density matrix (TRDM) and second, the computational complexity scales linearly with the number of the reference states. The extended multistate (XMS) treatment is further incorporated, giving suited treatment of the zeroth-order Hamiltonian despite the fact that the SS-SR based IC basis is not invariant with respect to the XMS rotation. In addition, the state-specific fourth-order reduced density matrix (RDM) is eliminated in an approximate fashion using the cumulant reconstruction formula, as also done in the previous state-specific DMRG-cu(4)-CASPT2 approach. The resultant method, referred to as DMRG-cu(4)-XMS-CASPT2, uses the RDMs and TRDMs of up to third-order provided by the DMRG calculation. The multistate potential energy curves of the photoisomerization of diarylethene derivatives with CAS(26e,24o) are presented to illustrate the applicability of our theoretical approach.

The density matrix renormalization group (DMRG) method is used in conjunction with the complete active space (CAS) procedure, the CAS configuration interaction (CASCI), and the CAS self-consistent field (CASSCF) to evaluate hyperfine coupling constants (HFCCs) for a series of diatomic (2)Σ radicals (BO, CO(+), CN, and AlO) and vinyl (C2H3) radical. The electron correlation effects on the computed HFCC values were systematically investigated using various levels of active space, which were increasingly extended from single valence space to large-size model space entailing double valence and at least single polarization shells. In addition, the core correlation was treated by including the core orbitals in active space. Reasonably accurate results were obtained by the DMRG-CASSCF method involving orbital optimization, while DMRG-CASCI calculations with Hartree-Fock orbitals provided poor agreement of the HFCCs with the experimental values. To achieve further insights into the accuracy of HFCC calculations, the orbital contributions to the total spin density were analyzed at a given nucleus, which is directly related to the FC term and is numerically sensitive to the level of correlation treatment and basis sets. The convergence of calculated HFCCs with an increasing number of renormalized states was also assessed. This work serves as the first study on the performance of the ab initio DMRG method for HFCC prediction.

The photochromic ring-opening reaction of spiropyran has been revisited at the multireference CASSCF and CASPT2 level with a CAS(22e,20o) active space, in combination with density matrix renormalization group (DMRG) methods. The accuracy of the DMRG-CASSCF and DMRG-CASPT2 calculations, with respect to the number of renormalized states, the number of roots in state-averaged wave functions, and the number basis functions, was examined. For the current system, chemically accurate results can be obtained with a relatively small number of renormalized states. The nature and vertical excitation energies of the excited (S1 and S2) states are consistent with conventional CAS(or RAS)PT2 with medium active spaces. The capability of the DMRG-CASSCF method in the optimization of molecular geometry is demonstrated for the first time. The computation costs (several hours per optimization cycle) are comparable with that of the conventional CASSCF geometry optimization with small active space. Finally, the DMRG-PT2 computed S1-MEP for the C-O and C-N bond-cleavage processes show good agreement with our previous calculations with a CAS(12e,10o) active space [Liu, F.; Morokuma, K. J. Am. Chem. Soc. 2013, 135, 10693-10702]. Especially, the role of the HOOP valleys in the S1 → S0 nonadiabatic decay has been confirmed.

Graphene nanoribbons (GNRs), also seen as rectangular polycyclic aromatic hydrocarbons, have been intensively studied to explore their potential applicability as superior organic semiconductors with high mobility. The difficulty arises in the synthesis or isolation of GNRs with increased conjugate length, GNRs being known to have radical electrons on their zigzag edges. Here, we use a most advanced ab initio theory based on density matrix renormalization group (DMRG) theory to show the emerging process of how GNRs develop electronic states from nonradical to radical characters with increasing ribbon length. We show the mesoscopic size effect that comes into play in quantum many-body interactions of π electrons, which is responsible for the polyradical nature. An analytic form is presented to model the size dependence of the number of radicals for arbitrary-length GNRs. These results and associated insights deepen the understanding of carbon-based chemistry and offer useful information for the synthesis and design of stable and functional GNRs.

The naphthalene molecule has two important lowest-lying singlet excited states, denoted (1)La and (1)Lb. Association of the excited and ground state monomers yields a metastable excited dimer (excimer), which emits characteristic fluorescence. Here, we report a first computational result based on ab initio theory to corroborate that the naphthalene excimer fluorescence is (1)La parentage, resulting from inversion of (1)La and (1)Lb-derived dimer states. This inversion was hypothesized by earlier experimental studies; however, it has not been confirmed rigorously. In this study, the advanced multireference (MR) theory based on the density matrix renormalization group that enables using unprecedented large-size active space for describing significant electron correlation effects is used to provide accurate potential energy curves (PECs) of the excited states. The results evidenced the inversion of the PECs and accurately predicted transition energies for excimer fluorescence and monomer absorption. Traditional MR calculations with smaller active spaces and single-reference theory calculations exhibit serious inconsistencies with experimental observations.