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

Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase

In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments (J. Chem. Phys. 2024, 160, 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 (J. Chem. Theory Comput. 2021, 17, 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.

Pushing the Limit of Photo-Controlled Polymerization: Hyperchromic and Bathochromic Effects

The photocatalyst (PC) zinc tetraphenylporphyrin (ZnTPP) is highly efficient for photoinduced electron/energy transfer reversible addition-fragmentation chain transfer (PET-RAFT) polymerization. However, ZnTPP suffers from poor absorbance of orange light by the so-called Q-band of the absorption spectrum (maximum absorption wavelength λmax = 600 nm, at which molar extinction coefficient εmax = 1.0×104 L/(mol·cm)), hindering photo-curing applications that entail long light penetration paths. Over the past decade, there has not been any competing candidate in terms of efficiency, despite a myriad of efforts in PC design. By theoretical evaluation, here we rationally introduce a peripheral benzo moiety on each of the pyrrole rings of ZnTPP, giving zinc tetraphenyl tetrabenzoporphyrin (ZnTPTBP). This modification not only enlarges the conjugation length of the system, but also alters the a1u occupied π molecular orbital energy level and breaks the accidental degeneracy between the a1u and a2u orbitals, which is responsible for the low absorption intensity of the Q-band. As a consequence, not only is there a pronounced hyperchromic and bathochromic effect (λmax = 655 nm and εmax = 5.2×104 L/(mol·cm)) of the Q-band, but the hyperchromic effect is achieved without increasing the intensity of the less useful, low wavelength absorption peaks of the PC. Remarkably, this strong 655 nm absorption takes advantage of deep-red (650-700 nm) light, a major component of solar light exhibiting good atmosphere penetration, exploited by the natural PC chlorophyll a as well. Compared with ZnTPP, ZnTPTBP displayed a 49% increase in PET-RAFT polymerization rate with good control, marking a significant leap in the area of photo-controlled polymerization.

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.

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.

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory

As the relativistic corrections become stronger for late-row elements, the fully perturbative treatment of spin-orbit coupling and dynamic correlation may become inadequate for accurate descriptions of chemical properties. In this work, we introduce a determinant-based Kramers-unrestricted exact-two-component multireference second-order perturbation (X2C-MRPT2) method which variationally includes relativistic corrections with a perturbative dynamic correlation. The restricted active space partitioning scheme is employed to provide an adjustable correlation space for the second-order perturbation treatment. The multistate perturbation theory is also developed to improve the descriptions of ground and excited states. Benchmark studies of atomic fine-structure splittings and spectroscopic constants of molecular monohydrides using X2C-MRPT2 are compared to the other perturbative and variational approaches. The results suggest that X2C-MRPT2 is a highly accurate alternative to the fully variational multireference configuration interaction method at only a small fraction of the computational cost.

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.

SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways

The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.