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.

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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.

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A rigorous analysis is carried out concerning the use of Cholesky decomposition (CD) of two-electron integrals in the case of quantum-chemical calculations with finite or perturbative magnetic fields and gauge-including atomic orbitals. We investigate in particular how permutational symmetry can be accounted for in such calculations and how this symmetry can be exploited to reduce the computational requirements. A modified CD procedure is suggested for the finite-field case that roughly halves the memory demands for the storage of the Cholesky vectors. The resulting symmetry of the Cholesky vectors also enables savings in the computational costs. For the derivative two-electron integrals in case of a perturbative magnetic field we derive CD expressions by means of a first-order Taylor expansion of the corresponding finite magnetic-field formulas with the field-free case as reference point. The perturbed Cholesky vectors are shown to be antisymmetric (as already proposed by Burger et al. (J. Chem. Phys., 155, 074105 (2021))) and the corresponding expressions enable significant savings in the required integral evaluations (by a factor of about four) as well as in the actual construction of the Cholesky vectors (by means of a two-step procedure similar to the one presented by Folkestad et al. (J. Chem. Phys., 150, 194112 (2019)) and Zhang et al. (J. Phys. Chem. A, 125, 4258-4265 (2021))). Numerical examples with cases involving several hundred basis functions verify our suggestions concerning CD in case of finite and perturbative magnetic fields.