Quantum chemistry and its “ages”
Authors: Nicolaides Cleanthes A. 
Published: February 2014

The popular methods of computational quantum chemistry (CQC) have acquired the status of “mainstream” quantum chemistry (QC), with countless useful applications to molecular science, especially for properties, potential energy surfaces, and reactions of the ground states. In earlier publications, four “ages of QC” have been defined, the classification having been based exclusively on the progress of QC in the direction of CQC.The core of the present article has a dual character: On the one hand, it is a commentary on the nature of QC, whereby it is argued that modern QC, while keeping its focus on the many‐electron problem, (MEP), and on the consequences of Electron Correlations on observable quantities, has a domain and a scope that are larger than those determined, more or less, by CQC. Hence, additional “ages” are singled out and proposed, which are connected to “time‐independent” and “time‐dependent” theoretical “many‐electron” formulations and calculations in which the “continuous spectrum” is involved explicitly. They are connected to experimental directions, which challenge theory to provide not only phenomenology but also quantitative answers and predictions for properties and phenomena involving various types of “unstable (nonstationary) states,” which decay irreversibly into the continuous spectrum either via interactions within the atomic (molecular) Hamiltonian (e.g., autoionizing states) or via the interaction with external electromagnetic fields.On the other hand, the article presents, in the form of brief reviews and retrospective accounts, a gleaning from our contributions to the theory and to methods of calculation for the quantitative treatment of such MEPs. Specifically, in the context of the previous paragraphs, I comment briefly on basic concepts, I point to early theoretical work, and, in support of the arguments, I refer to practical theoretical constructions and sample results regarding the following two themes: “resonances in many‐electron systems” and “theoretical time‐resolved many‐electron physics.”Both the themes are connected to the recent developments on the experimental front of the interaction of atoms and molecules with ultrashort radiation pulses (weak or strong) in the femtosecond and attosecond regimes. The first theme is treatable within energy‐dependent or time‐dependent frameworks. The second one requires the computation of a physically transparent Ψ(t), which solves to a very good approximation the many‐electron time‐dependent Schrödinger equation (METDSE) for given characteristics of the pulses.Our approaches to related problems have been developed and implemented within state‐ and property‐specific formulations. These are constructed in terms of energy‐dependent Hermitian and non‐Hermitian formalisms, as well as in terms of time‐dependent ones, whose essential elements are explained here. In either case, in line with the main tenet of QC, the focus is on the understanding and efficient solution of the corresponding MEPs, especially in terms of nonperturbative methods. For time‐dependent problems involving the interaction with strong fields, the solution of the relevant METDSE is carried out by applying the “state‐specific expansion approach.” This type of calculation entails the solution of many thousands of coupled equations, where the input consists of bound–bound, bound–free, and free–free coupling matrix elements, on‐ and off‐resonance with respect to the frequency of the pulse.As an example of a solution of a time‐resolved many‐electron process, I present snapshots of the time‐dependent formation of the asymmetric profile of the He 2s2p 1P0 resonance state excited by a femtosecond pulse. This profile is formed within about 180 fs and is the same as the one which is well‐known from theory and experiment on the energy axis.The domain and horizon of modern Quantum Chemistry are broader than those of its original component, namely, Computational Quantum Chemistry of the ground state. Hamiltonians can create energy‐ or time‐dependent unstable states whose effects are measured inside the continuous spectrum. The understanding and practical solution of the corresponding many‐electron problems can be carried out reliably, using state‐specific, nonperturbative methodologies that solve the Schrödinger equation efficiently as a function of real or complex energies, or of time. © 2014 Wiley Periodicals, Inc.