Development of Xi'an-CI package – applying the hole–particle symmetry in multi-reference electronic correlation calculations

Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems

The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations

As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747-4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper(II) compound as well as Ln(III) and An(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets.

Nonadiabatic molecular dynamics simulations for ultrafast photo-induced ring-opening and isomerization reactions of 2,2-diphenyl-2H-chromene

Nonadiabatic molecular dynamics simulations with a global switching algorithm have been performed at the TD-CAM-B3LYP-D3/def2-SVP level of theory for ultrafast photo-induced ring-opening and isomerization reactions upon S1 excitation for 2,2-diphenyl-2H-chromene (DPC). Both DPC-T and DPC-C conformers undergo ring-opening relaxation and isomerization pathways accompanied with pyran conformation conserved and converted on the S1 or S0 states via competition and cooperation between C-O bond dissociation and pyran inversion motions. Upon S1 excitation, the DPC-T mainly relaxes to the T-type conical intersection region and thus yields a higher ring-opening efficiency with a faster S1 decay and intermediate formation than those of the DPC-C mainly relaxing to C-type conical intersection. The simulated ring-opening quantum yield for DPC-T (DPC-C) is 0.91 (0.76), which is in good agreement with the experimental value of 0.7-0.9, and the thermal weight averaged lifetimes are estimated as 182.0 fs, 228.6 fs, and 1262.4 fs for the excited-state decay, intermediate formation, and ring-opening product, respectively. These time constants are in good agreement with the experimentally measured τ1 time constant of 190-450 fs and τ2 time constant of 1000-1800 fs. The present work could be a valuable reference for understanding the nature of the photorelaxation mechanisms of DPC, and could help to develop DPC-based photoresponsive materials.

Unraveling the Spin-State Energetics of FeN4 Complexes with Ab Initio Methods

A systematic analysis was conducted to explore the spin-state energetics of a series of 19 FeN4 complexes. The performance of a large number of multireference methods was assessed, highlighting the significant challenges associated with accurately describing the spin-state energetics of FeN4 complexes. Most multireference methods were found to be susceptible to errors originating from the reference CASSCF wavefunction, leading to an overstabilization of high-spin states. Nonetheless, a few multireference methods, namely, CASPT2/CC, DSRG-MRPT3, and LDSRG(2), demonstrated promising performance compared to the benchmark CCSD(T) method. Furthermore, our study revealed that FeN4 complexes having a quintet ground state are exceedingly rare. Accordingly, only one specific model (Fe(L2)) and one synthesized complex (Fe(OTBP)) have the quintet ground state among the studied complexes. This scarcity of quintet FeN4 complexes highlights the unique nature of these systems and raises intriguing questions regarding the factors influencing spin states, such as the size of the macrocycle cavity, the introduction of substituents, or the induction of out-of-plane deformation.

Tuning Catalyst-Free Photocontrolled Polymerization by Substitution: A Quantitative and Qualitative Interpretation

Catalyst-free photocontrolled reversible addition-fragmentation chain transfer (RAFT) polymerization avoids the side effects of photocatalysts but has the accompanying slow kinetics, thereby warranting more efficient photolysis and faster chain transfer. To understand the underlying mechanisms, both quantitative and qualitative interpretations are needed. Such a goal can be achieved by the iCAS (imposed automatic selection and localization of complete active spaces) approach [J. Chem. Theory Comput. 2021, 17, 4846], which maintains the same CAS and meanwhile provides localized orbitals along the whole reaction. Taking dithiobenzoate as a representative of RAFT agents, it is found here that electron-donating substitution (by methoxy) clearly outperforms both electron-standing (by methyl) and electron-withdrawing (by cyano) substitutions in facilitating photo-RAFT polymerization, by narrowing the gap between the π* and σ* orbitals, so as to facilitate the π* → σ* charge transfer dominating both the photolysis and chain transfer processes. Such findings are of general values.

The Static-Dynamic-Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking

A series of methods (SDSCI, SDSPT2, iCI, iCIPT2, iCISCF(2), iVI, and iCAS) is introduced to accurately describe strongly correlated systems of electrons. Born from the (restricted) static-dynamic-static (SDS) framework for designing many-electron wave functions, SDSCI is a minimal multireference (MR) configuration interaction (CI) approach that constructs and diagonalizes a [Formula: see text] matrix for [Formula: see text] states, regardless of the numbers of orbitals and electrons to be correlated. If the full molecular Hamiltonian H in the QHQ block (which describes couplings between functions of the first-order interaction space Q) of the SDSCI CI matrix is replaced with a zeroth-order Hamiltonian [Formula: see text] before the diagonalization is taken, we obtain SDSPT2, a CI-like second-order perturbation theory (PT2). Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and is particularly advantageous in the presence of near degeneracy. On the other hand, if the SDSCI procedure is repeated until convergence, we will have iterative CI (iCI), which can converge quickly from the above to the exact solutions (full CI) even when starting with a poor guess. When further combined with the selection of important configurations followed by a PT2 treatment of dynamic correlation, iCI becomes iCIPT2, which is a near-exact theory for medium-sized systems. The microiterations of iCI for relaxing the coefficients of contracted many-electron functions can be generalized to an iterative vector interaction (iVI) approach for finding exterior or interior roots of a given matrix, in which the dimension of the search subspace is fixed by either the number of target roots or the user-specified energy window. Naturally, iCIPT2 can be employed as the active space solver of the complete active space (CAS) self-consistent field, leading to iCISCF(2), which can further be combined with iCAS for automated selection of active orbitals and assurance of the same CAS for all states and all geometries. The methods are calibrated by taking the Thiel set of benchmark systems as examples. Results for the corresponding cations, a new set of benchmark systems, are also reported.

iCAS: Imposed Automatic Selection and Localization of Complete Active Spaces

It is shown that in the spirit of "from fragments to molecule" for localizing molecular orbitals [J. Chem. Theory Comput. 2011, 7, 3643], a prechosen set of occupied/virtual valence/core atomic/fragmental orbitals can be transformed to an equivalent set of localized occupied/virtual pre-localized molecular orbitals (pre-LMO), which can then be taken as probes to select the same number of maximally matching localized occupied/virtual Hartree-Fock (HF) or restricted open-shell HF (ROHF) molecular orbitals as the initial local orbitals spanning the desired complete active space (CAS). In each cycle of the self-consistent field (SCF) calculation, the CASSCF orbitals can be localized by means of the noniterative "top-down least-change" algorithm for localizing ROHF orbitals [J. Chem. Phys. 2017, 146, 104104] such that the maximum matching between the orbitals of two adjacent iterations can readily be monitored, leading finally to converged localized CASSCF orbitals that overlap most the guess orbitals. Such an approach is to be dubbed as "imposed CASSCF" (iCASSCF or simply iCAS in short) for good reasons: (1) it has been assumed that only those electronic states that have largest projections onto the active space defined by the prechosen atomic/fragmental orbitals are to be targeted. This is certainly an imposed constraint but has wide applications in organic and transition metal chemistry where valence (or core) atomic/fragmental orbitals can readily be identified. (2) The selection of both initial and optimized local active orbitals is imposed from the very beginning by the pre-LMOs (which span the same space as the prechosen atomic/fragmental orbitals). Apart from the (imposed) automation and localization, iCAS has two additional merits: (a) the guess orbitals are guaranteed to be the same for all geometries, for the pre-LMOs do not change in character with geometry and (b) the use of localized orbitals facilitates the SCF convergence, particularly for large active spaces. Both organic molecules and transition-metal complexes are taken as showcases to reveal the efficacy of iCAS.

Photorelaxation Pathways of 4-(N,N-Dimethylamino)-4'-nitrostilbene Upon S1 Excitation Revealed by Conical Intersection and Intersystem Crossing Networks

Multi-state n-electron valence state second order perturbation theory (MS-NEVPT2) was utilized to reveal the photorelaxation pathways of 4-(N,N-dimethylamino)-4′-nitrostilbene (DANS) upon S₁ excitation. Within the interwoven networks of five S₁/S₀ and three T₂/T₁ conical intersections (CIs), and three S₁/T₂, one S₁/T₁ and one S₀/T₁ intersystem crossings (ISCs), those competing nonadiabatic decay pathways play different roles in trans-to-cis and cis-to-trans processes, respectively. After being excited to the Franck–Condon (FC) region of the S₁ state, trans-S₁-FC firstly encounters an ultrafast conversion to quinoid form. Subsequently, the relaxation mainly proceeds along the triplet pathway, trans-S₁-FC → ISC-S₁/T₂-trans → CI-T₂/T₁-trans → ISC-S₀/T₁-twist → trans- or cis-S₀. The singlet relaxation pathway mediated by CI-S₁/S₀-twist-c is hindered by the prominent energy barrier on S₁ surface and by the reason that CI-S₁/S₀-trans and CI-S₁/S₀-twist-t are both not energetically accessible upon S₁ excitation. On the other hand, the cis-S₁-FC lies at the top of steeply decreasing potential energy surfaces (PESs) towards the CI-S₁/S₀-twist-c and CI-S₁/S₀-DHP regions; therefore, the initial twisting directions of DN and DAP moieties determine the branching ratio between α_C=C twisting (cis-S₁-FC → CI-S₁/S₀-twist-c → trans- or cis-S₀) and DHP formation relaxation pathways (cis-S₁-FC → CI-S₁/S₀-DHP → DHP-S₀) on the S₁ surface. Moreover, the DHP formation could also take place via the triplet relaxation pathway, cis-S₁-FC → ISC-S₁/T₁-cis → DHP-T₁ → DHP-S₀, however, which may be hindered by insufficient spin-orbit coupling (SOC) strength. The other triplet pathways for cis-S₁-FC mediated by ISC-S₁/T₂-cis are negligible due to the energy or geometry incompatibility of possible consecutive stepwise S₁ → T₂ → T₁ or S₁ → T₂ → S₁ processes. The present study reveals photoisomerization dynamic pathways via conical intersection and intersystem crossing networks and provides nice physical insight into experimental investigation of DANS.