Phosphorescence parameters for platinum (II) organometallic chromophores: A study at the non-collinear four-component Kohn–Sham level of theory

Economical quasi-Newton unitary optimization of electronic orbitals

We present an efficient quasi-Newton orbital solver optimized to reduce the number of gradient evaluations and other computational steps of comparable cost. The solver optimizes orthogonal orbitals by sequences of unitary rotations generated by the (preconditioned) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm equipped with trust-region step restriction. The low-rank structure of the L-BFGS inverse Hessian is exploited when solving the trust-region problem. The efficiency of the proposed "Quasi-Newton Unitary Optimization with Trust-Region" (QUOTR) solver is compared to that of the standard Roothaan-Hall approach accelerated by the Direct Inversion of Iterative Subspace (DIIS), and other exact and approximate Newton solvers for mean-field (Hartree-Fock and Kohn-Sham) problems.

Meta-GGA Density Functional Calculations on Atoms with Spherically Symmetric Densities in the Finite Element Formalism

Density functional calculations on atoms are often used for determining accurate initial guesses as well as generating various types of pseudopotential approximations and efficient atomic-orbital basis sets for polyatomic calculations. To reach the best accuracy for these purposes, the atomic calculations should employ the same density functional as the polyatomic calculation. Atomic density functional calculations are typically carried out employing spherically symmetric densities, corresponding to the use of fractional orbital occupations. We have described their implementation for density functional approximations (DFAs) belonging to the local density approximation (LDA) and generalized gradient approximation (GGA) levels of theory as well as Hartree-Fock (HF) and range-separated exact exchange [Lehtola, S. Phys. Rev. A 2020, 101, 012516]. In this work, we describe the extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in which the energy is minimized with respect to the orbitals, which in turn are expanded in the finite element formalism with high-order numerical basis functions. Furnished with the new implementation, we continue our recent work on the numerical well-behavedness of recent meta-GGA functionals [Lehtola, S.; Marques, M. A. L. J. Chem. Phys. 2022, 157, 174114]. We pursue complete basis set (CBS) limit energies for recent density functionals and find many to be ill-behaved for the Li and Na atoms. We report basis set truncation errors (BSTEs) of some commonly used Gaussian basis sets for these density functionals and find the BSTEs to be strongly functional dependent. We also discuss the importance of density thresholding in DFAs and find that all of the functionals studied in this work yield total energies converged to 0.1 μEh when densities smaller than 10-11a0-3 are screened out.

Demystifying the Origin of Vibrational Coherence Transfer Between the S1 and T1 States of the Pt-pop Complex

We demonstrate that spin-vibronic coupling is the most significant mechanism in vibrational coherence transfer (VCT) from the singlet (S₁) to the triplet (T₁) state of the [Pt₂(P₂O₅H₂)₄]^4- complex. Our time-dependent correlation function-based study shows that the rate of intersystem crossing (k_ISC) through direct spin-orbit coupling is negligibly small, making VCT vanishingly small due to the ultrashort decoherence time (2.5 ps). However, the inclusion of the spin-vibronic contribution to the net k_ISC in selective normal modes along the Pt-Pt axis increases the k_ISC to such an extent that VCT becomes feasible. Our results suggest that k_ISC for the S₁ →T₂ (τ_ISC = 1.084 ps) is much faster than the S₁ → T₁ (τ_ISC = 763.4 ps) and S₁ → T₃ (τ_ISC = 13.38 ps) in CH₃CN solvent, indicating that VCT is possible from the low-lying excited singlet (S₁) to the triplet (T₁) state through the intermediate T₂ state. This is the first example where VCT occurs solely due to spin-vibronic interactions. This finding can pave the way for new types of photocatalysis.

Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Electronic structure calculations, such as in the Hartree-Fock or Kohn-Sham density functional approach, require an initial guess for the molecular orbitals. The quality of the initial guess has a significant impact on the speed of convergence of the self-consistent field (SCF) procedure. Popular choices for the initial guess include the one-electron guess from the core Hamiltonian, the extended Hückel method, and the superposition of atomic densities (SAD). Here, we discuss alternative guesses obtained from the superposition of atomic potentials (SAP), which is easily implementable even in real-space calculations. We also discuss a variant of SAD which produces guess orbitals by purification of the density matrix that could also be used in real-space calculations, as well as a parameter-free variant of the extended Hückel method, which resembles the SAP method and is easy to implement on top of existing SAD infrastructure. The performance of the core Hamiltonian, the SAD, and the SAP guesses as well as the extended Hückel variant is assessed in nonrelativistic calculations on a data set of 259 molecules ranging from the first to the fourth periods by projecting the guess orbitals onto precomputed, converged SCF solutions in single- to triple-ζ basis sets. It is shown that the proposed SAP guess is the best guess on average. The extended Hückel guess offers a good alternative, with less scatter in accuracy.