Changing aromatic properties through stacking: the face-to-face dimer of Ni(II) bis(pentafluorophenyl)norcorrole.

Nuclear magnetic resonance (NMR) shielding constants have been calculated for Ni(II) bis(pentafluorophenyl)norcorrole and its face-to-face stacked dimer at the Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), complete-active-space self-consistent-field (CASSCF) levels as well as at density functional theory (DFT) levels using several functionals. The calculated 1H NMR shielding constants agree rather well with the experimental ones. The shielding constants of N and Ni calculated at DFT, HF, and MP2 levels differ from those obtained in the CASSCF calculations due to near-degeneracy effects at the Ni atom. The calculated magnetically induced current densities show that the monomer is antiaromatic, sustaining a strong global paratropic ring current, and the dimer is aromatic, sustaining a strong diatropic ring current. Qualitatively the same current density is obtained at the employed levels of theory. The most accurate ring-current strengths are probably obtained at the MP2 level. The aromatic dimer has a short intermolecular distance of less than 3 Å. The intermolecular interaction changes the nature of the frontier orbitals leading to a formal double bond between the norcorrole macrocycles.

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions.

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

Cholesky Decomposition in Spin-Free Dirac-Coulomb Coupled-Cluster Calculations.

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their nonrelativistic counterparts. While for nonrelativistic CC calculations, atomic-orbital (AO)-based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost in that case. Here, molecular-orbital (MO)-based algorithms exploiting the CD of the two-electron integrals allow us to reduce disk-space requirements and lead to computational cost in the CC step that is more or less the same as in the nonrelativistic case. The only remaining overhead in a CD-SFDC-CC calculation is due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15% of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)4 molecules with X = Ni, Pd, Pt.

The OpenMMPol library for polarizable QM/MM calculations of properties and dynamics.

We present a new library designed to provide a simple and straightforward way to implement QM/AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) and other polarizable QM/MM (Molecular Mechanics) methods based on induced point dipoles. The library, herein referred to as OpenMMPol, is free and open-sourced and is engineered to address the increasing demand for accurate and efficient QM/MM simulations. OpenMMPol is specifically designed to allow polarizable QM/MM calculations of ground state energies and gradients and excitation properties. Key features of OpenMMPol include a modular architecture facilitating extensibility, parallel computing capabilities for enhanced performance on modern cluster architectures, a user-friendly interface for intuitive implementation, and a simple and flexible structure for providing input data. To show the capabilities offered by the library, we present an interface with PySCF to perform QM/AMOEBA molecular dynamics, geometry optimization, and excited-state calculation based on (time-dependent) density functional theory.

A novel coupled-cluster singles and doubles implementation that combines the exploitation of point-group symmetry and Cholesky decomposition of the two-electron integrals.

A novel implementation of the coupled-cluster singles and doubles (CCSD) approach is presented that is specifically tailored for the treatment of large symmetric systems. It fully exploits Abelian point-group symmetry and the use of the Cholesky decomposition of the two-electron repulsion integrals. In accordance with modern CCSD algorithms, we propose two alternative strategies for the computation of the so-called particle-particle ladder term. The code is driven toward the optimal choice depending on the available hardware resources. As a large-scale application, we computed the frozen-core correlation energy of buckminsterfullerene (C60) with a polarized valence triple-zeta basis set (240 correlated electrons in 1740 orbitals).

Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposition.

We present an implementation of coupled-perturbed complete active space self-consistent field (CP-CASSCF) theory for the computation of nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals and Cholesky decomposed two-electron integrals. The CP-CASSCF equations are solved using a direct algorithm where the magnetic Hessian matrix-vector product is expressed in terms of one-index transformed quantities. Numerical tests on systems with up to about 1300 basis functions provide information regarding both the computational efficiency and limitations of our implementation.

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces.

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

Linear Response Equations Revisited: A Simple and Efficient Iterative Algorithm.

We present an algorithm to solve the linear response equations for Hartree-Fock, Density Functional Theory, and the Multiconfigurational Self-Consistent Field method that is both simple and efficient. The algorithm makes use of the well-established symmetric and antisymmetric combinations of trial vectors but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Numerical tests showed that the algorithm is robust and stable.

Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals.

In this contribution, we present the implementation of a second-order complete active space-self-consistent field (CASSCF) algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called norm-extended optimization, guarantees convergence of the optimization, but it involves the full Hessian and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance of the new implementation is illustrated by means of benchmark calculations on molecules of increasing size, with up to about 3000 basis functions and 14 active orbitals.