An approximation to the spin-flip extended configuration interaction singles method is developed using a second-order perturbation theory approach. In addition to providing significant efficiency advantages, the new framework is general for an arbitrary number of spin-flips, with the current implementation being applicable for up to around 4 spin-flips. Two new methods are introduced: one which is developed using non-degenerate perturbation theory, spin-flip complete active-space (SF-CAS(S)), and a second quasidegenerate perturbation theory method, SF-CAS(S)1. These two approaches take the SF-CAS wavefunction as the reference, and then perturbatively includes the effect of single excitations. For the quasidegenerate perturbation theory method, SF-CAS(S)1, the subscripted "1" in the acronym indicates that a truncated denominator expansion is used to obtain an energy-independent down-folded Hamiltonian. We also show how this can alternatively be formulated in terms of an extended Lagrangian, by introducing an orthonormality constraint on the first-order wavefunction. Several numerical examples are provided, which demonstrate the ability of SF-CAS(S) and SF-CAS(S)1 to describe bond dissociations, singlet-triplet gaps of organic molecules, and exchange coupling parameters for binuclear transition metal complexes.

We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited (and spin-flipped), from the single reference with maximum Ŝz, M, to the M - 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one β electron is required, together with only one α hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M - 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed.

We provide a simple procedure for using inexpensive ab initio calculations to compute exchange coupling constants, J(AB), for multiradical molecules containing both an arbitrary number of radical sites and an arbitrary number of unpaired electrons. For a system comprised of 2M unpaired electrons, one needs only to compute states having the Ŝ(z) quantum number M - 1. Conveniently, these are precisely the states that are accessed by the family of single spin-flip methods. Building an effective Hamiltonian with these states allows one to extract all of the J(AB) constants in the molecule. Unlike approaches based on density functional theory, this procedure relies on neither spin-contaminated states nor nonunique spin-projection formulas. A key benefit is that it is possible to obtain completely spin-pure exchange coupling constants with inexpensive ab initio calculations. A couple of examples are provided to illustrate the approach, including a 4-nickel cubane complex and a 6-chromium horseshoe complex with 18 entangled electrons.

We present a modification of the recently developed Restricted Active Space with n Spin Flips method (RAS-nSF), which provides significant efficiency advantages. In the RAS-nSF configuration interaction wave function, an arbitrary number of spin-flips are performed within an orbital active space (often simply the singly occupied orbitals), with state-specific orbital relaxation being described by single excitations into and out of the active space (termed hole and particle states, respectively). As the number of hole and particle states dominates the cost of the calculation, we present an attractive simplification in which the orbital relaxation effects (via hole and particle states) are treated perturbatively rather than variationally. The physical justification for this simplification stems from the spin-flip methodology itself, which suggests that the underlying molecular orbitals (high-spin ROHF) are capable of providing a decent description of the target (spin-flipped) electronic states. The current approach termed SF-CAS(h,p)n (Spin-Flip Complete Active-Space with perturbative Hole and Particle states) yields spin-pure energies and eigenfunctions due to the spin-free formulation. A description of the theory is presented, and a number of numerical examples are investigated to determine the accuracy of the approximation. Computational speedups of over 100 times were demonstrated on a 254 electron, 358 basis function calculation on a Cu(II) porphyrin derivatized with a verdazyl group.

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller-Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.