Taming the excited states of butadiene, hexatriene, and octatetraene using state specific multireference perturbation theory with density functional theory orbitals

Spinless formulation of linearized adiabatic connection approximation and its comparison with the second order N-electron valence state perturbation theory

The adiabatic connection (AC) approximation, along with its linearized variant AC0, was introduced as a method of obtaining dynamic correlation energy. When using a complete active space self-consistent field (CASSCF) wave function as a reference, the AC0 approximation is considered one of the most efficient multi-reference perturbation theories. It only involves the use of 1st- and 2nd-order reduced density matrices. However, some numerical results have indicated that the excitation energies predicted by AC0 are not as reliable as those from the second-order N-electron valence state perturbation theory (NEVPT2). In this study, we develop a spinless formulation of AC0 based on the Dyall Hamiltonian and provide a detailed comparison between AC0 and NEVPT2 approaches. We demonstrate the components within the correlation energy expressions that are common to both methods and those unique to either AC0 or NEVPT2. We investigate the role of the terms exclusive to NEVPT2 and explore the possibility of enhancing AC0's performance in this regard.

Ab initio extended Hubbard model of short polyenes for efficient quantum computing

We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited ¹Δ_g state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for ¹L_a and ¹L_b states in polyacenes and ¹A_u and ¹A_g states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

Theory, implementation, and disappointing results for two-photon absorption cross sections within the doubly electron-attached equation-of-motion coupled-cluster framework

The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels.

Block Effective Hamiltonian Theory and Its Application

Block effective Hamiltonian theory (BEHT) is presented in this work. Configuration interaction functions are divided into P, Q, and R spaces. Effective Hamiltonian is constructed with the partitioning technique within the P space. The eigenvalue problem of the effective Hamiltonian is then solved iteratively. It is demonstrated that the ground-state energies of N₂, HF, and F₂ calculated with BEHT converge to the multireference configuration interaction energies from below and the iteration number becomes smaller as BEHT energy becomes closer to the exact energy. The accuracy of BEHT is better than that of the second-order multireference perturbation theory, although the matrix elements in both methods are the same. The ionization potentials of the singlet state of HF, the doublet state of F, and the triplet state of NH and the potential energy curves of CH₄, C₂, and N₂ are calculated with BEHT and compared with experiments and results of CASSCF, CCSD, and CCSD(T) and the results of the full configuration interaction if available. The iteration numbers are all less than 10 in this study. These calculations show the good performances of BEHT in comparison with other theoretical approximation methods.

Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations

The Bethe-Salpeter equation (BSE) that results from the GW approximation to the self-energy is a frequency-dependent (nonlinear) eigenvalue problem due to the dynamically screened Coulomb interaction between electrons and holes. The computational time required for a numerically exact treatment of this frequency dependence is O(N6), where N is the system size. To avoid the common static screening approximation, we show that the full-frequency dynamical BSE can be exactly reformulated as a frequency-independent eigenvalue problem in an expanded space of single and double excitations. When combined with an iterative eigensolver and the density fitting approximation to the electron repulsion integrals, this reformulation yields a dynamical BSE algorithm whose computational time is O(N5), which we verify numerically. Furthermore, the reformulation provides direct access to excited states with dominant double excitation character, which are completely absent in the spectrum of the statically screened BSE. We study the 21Ag state of butadiene, hexatriene, and octatetraene and find that GW/BSE overestimates the excitation energy by about 1.5-2 eV and significantly underestimates the double excitation character.

Description of the Methylene Amidogene Radical and Its Anion with an Economical Treatment of Correlation Effects Using Density Functional Theory Orbitals

The ground and low-lying excited state electronic structural properties (such as equilibrium geometries, harmonic frequencies, excitation energies, barrier energy, and so on) of the methylene amidogene radical (H₂CN) and its anion (H₂CN^-) have been studied using the CASCI (complete active space configuration interaction) and SSMRPT (state-specific multireference Møller-Plesset perturbation theory) methods with density function theory (DFT) orbitals. Here, the span of the active orbitals have been obtained from Kohn-Sham DFT using B3LYP exchange-correlation functionals in the CASCI (DFT-CASCI) approximation to describe nondynamic correlation associated with electronic degeneracies. The DFT-SSMRPT protocol provides an attractive way to deal with both dynamical and nondynamical correlation effects in strongly correlated systems such as H₂CN and H₂CN^-. The present work clearly indicates that the electronic absorption band near 35,050 cm^-1 corresponds to the B̃²A₁ ← X̃²B₂ transition. DFT-SSMRPT findings are in close agreement with high-level theoretical estimates. It is concluded that the transition at 1725 cm^-1 could be due to the CN stretching of the trans-HCNH isomer which is originally assigned to the CN stretch of H₂CN in the experiment. The present results confirm most of the previous vibrational assignments. It is not possible to definitively assign a transition to the 35,600 cm^-1 band with the present estimations, suggesting further experiment is urgently called for.