Initial Maximum Overlap Method for Large Systems by the Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Technique

Abstract

Quantum chemistry offers a large variety of methods to treat excited states. Many of them are based on a multireference wave function ansatz and are therefore characterized by an intrinsic complexity and high computational costs. To overcome these drawbacks and also some limitations of simpler single-reference approaches (e.g., configuration interaction singles and time-dependent density functional theory), the singledeterminant Δself-consistent field-initial maximum overlap method (ΔSCF-IMOM) has been proposed. This strategy substitutes the aufbau principle with a criterion that occupies molecular orbitals at successive SCF iterations on the basis of their maximum overlap with a proper set of guess orbitals for the target excited state. In this way, it prevents the SCF process to collapse to the ground state wave function and provides excited state single Slater determinant solutions to the SCF equations. Here, we propose to extend the applicability of the IMOM to the treatment of localized excited states of large systems. To accomplish this task, we coupled it with the QM/ELMO (quantum mechanics/extremely localized molecular orbitals) strategy, a quantum mechanical embedding method in which the most chemically relevant part of the system is treated with traditional quantum chemical approaches, while the rest is described by extremely localized molecular orbitals transferred from recently constructed libraries or proper model molecules. After presenting the theoretical foundations of the new IMOM/ELMO technique, in this paper, we will show and discuss the results of preliminary test calculations carried out on both model systems (i.e., decanoic acid, decene, decapentaene, and solvated acrolein) and a system of biological interest (flavin mononucleotide in the flavodoxin protein). We observed that, for localized excited states, the new IMOM/ELMO method provides reliable results, and it reproduces the outcomes of fully IMOM calculations within the chemical accuracy threshold (i.e., 0.043 eV) by including only a limited number of atoms in the QM region. Furthermore, the first application of our embedding technique to a larger biological system gave completely plausible results in line with those obtained through more traditional quantum mechanical methods, thus opening the possibility of using the new approach in future investigations of photobiology problems.

Fast Method for Excited-State Dynamics in Complex Systems and Its Application to the Photoactivation of a Blue Light Using Flavin Photoreceptor

“…An interesting strategy to enhance the applicability of these calculations is to exploit GPU-accelerated routines. , However, until now, the most effective speed up has been obtained by introducing semiempirical QM methods in their wave function basis or as DFT formulations as shown by recent studies on photoreceptors and pigment–protein complexes. − In both cases, however, a proper parametrization is needed, which largely limits the ease of use and generalizability of the selected semiempirical method. An interesting ab initio alternative is represented by the excited-state self-consistent field methods (also known as ΔSCF). − These methodologies are thought to be less computational demanding than TD-DFT while maintaining a high accuracy of the description, especially in the case of conical intersections and charge-transfer (CT) states. ΔSCF proposes to treat the excited state as a single determinant and to optimize molecular orbitals (MOs) at the excited-state level.…”

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

“…The latter can be achieved, e.g., by applying the Initial Maximum Overlap Method. 36,59 For closed-shell systems, which have an even number of electrons, the two lowest energy excited state multiplicities are in general the singlet (S) and triplet (T) electronic states, the latter being triply degenerate, whose degenerate states differ in the projection of the total spin. In the wave function formulation, these states are eigenfunctions of the total and projection spin operators, but within DFT, the singlet and the triplet state with spin projection S tot.,z = 0 cannot be distinguished based on their corresponding spin densities.…”

“…Due to this, the KS equations () together with () are solved self-consistently so that they minimize the i -th electronic state energy while simultaneously assuring that electronic densities resemble those of an excited state with defined spin multiplicity by appropriately keeping adequate occupation numbers associated with the selected KS-MOs through eq . The latter can be achieved, e.g., by applying the Initial Maximum Overlap Method. , …”

Extracting Quantitative Information at Quantum Mechanical Level from Noncovalent Interaction Index Analyses

“…To improve the quantitative description of the NCI strategy, the only possibility is to resort to localized QM methods that still enable a clear partitioning of the global electron density into distinct fragment contributions. With this purpose in mind, in this work, we propose the coupling of the NCI integral approach (i) with the transfer of the abovementioned ELMOs and (ii) with the QM/ELMO embedding method. − In the former case, the overall electron distribution can always be seen as given by the sum of terms (i.e., the square moduli of the molecular orbitals) that can be directly associated with well-defined subunits. In the latter situation, we will consider a recently developed embedding technique in which a region of the system under examination is treated at a fully QM level, while the rest is described by means of frozen ELMOs previously transferred from the available ELMO databanks or from tailor-made model molecules.…”