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.

We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 2 (3 n − 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a twoelectron problem, and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

We investigate the existence of holomorphic Hartree–Fock solutions using a revised SCF algorithm. We use this algorithm to study the Hartree–Fock solutions for H2 and H42+ and report the emergence of holomorphic solutions at points of symmetry breaking. Finally, we find these holomorphic solutions for H4 and use them as a basis for Non-Orthogonal Configuration Interaction at a range of rectangular geometries and show them to produce energies in good agreement with Full Configuration Interaction.

Orbital-optimised multiple self-consistent-eld (SCF) solutions are increasingly being interpreted as mean-eld approximations of diabatic or excited electronic states. However, surprisingly li le is known about the topology of the electronic energy landscape from which these multiple solutions emerge. In this contribution, we extend energy landscape methods, developed for investigating molecular potential energy surfaces, to investigate and understand the structure of the electronic SCF energy surface. Using analytic gradients and Hessians, we systematically identify every real SCF minimum for the prototypical H 4 molecule with the 3-21G basis set, and the index-1 saddles that connect these minima. e resulting SCF energy landscape has a double-funnel structure, with no high-energy local minima. e e ect of molecular symmetry on the pathways is analysed, and we demonstrate how the SCF energy landscape changes with the basis set, SCF potential, molecular structure, and spin state. ese results provide guiding principles for the future development of algorithms to systematically identify multiple SCF solutions from an orbital optimisation perspective.