Explicitly Correlated R12/F12 Methods for Electronic Structure

This chapter is devoted to unravel the relaxation processes taking place after photoexcitation of isolated DNA/RNA nucleobases in gas phase from a time-dependent perspective. To this aim, several methods are at hand, ranging from full quantum dynamics to various flavours of semiclassical or ab initio molecular dynamics, each with its advantages and its limitations. As this contribution shows, the most common approach employed up to date to learn about the deactivation of nucleobases in gas phase is a combination of the Tully surface hopping algorithm with on-the-fly CASSCF calculations. Different dynamics methods or, even more dramatically, different electronic structure methods can provide different dynamics. A comprehensive review of the different mechanisms suggested for each nucleobase is provided and compared to available experimental time scales. The results are discussed in a general context involving the effects of the different applied electronic structure and dynamics methods. Mechanistic similarities and differences between the two groups of nucleobases - the purine derivatives (adenine and guanine) and the pyrimidine derivatives (thymine, uracil, and cytosine) - are elucidated. Finally, a perspective on the future of dynamics simulations in the context of nucleobase relaxation is given.

Review: 119 refs.

The simulation of excited states at low computational cost remains an open challenge for electronic structure (ES) methods. While much attention has been given to orthogonal ES methods, relatively little work has been done to develop nonorthogonal ES methods for excited states, particularly those involving nonorthogonal orbital optimization. We present here a numerically stable formulation of the Resonating Hartree-Fock (ResHF) method that uses the matrix adjugate to remove numerical instabilities arising from nearly orthogonal orbitals, and as a result, we demonstrate improvements to ResHF wavefunction optimization. We then benchmark the performance of ResHF against complete active space self-consistent field in the avoided crossing of LiF, the torsional rotation of ethene, and the singlet-triplet energy gaps of a selection of small molecules. ResHF is a promising excited state method because it incorporates the orbital relaxation of state-specific methods, while retaining the correct state crossings of state-averaged approaches. Our open-source ResHF implementation, yucca, is available on GitLab.

The main goal of electronic structure methods is to solve the Schroedinger equation for the electrons in a molecule or solid, to evaluate the resulting total energies, forces, response functions and other quantities of interest. In this paper we describe the basic ideas behind the main electronic structure methods such as the pseudopotential and the augmented wave methods and provide selected pointers to contributions that are relevant for a beginner. We give particular emphasis to the Projector Augmented Wave (PAW) method developed by one of us, an electronic structure method for ab-initio molecular dynamics with full wavefunctions. We feel that it allows best to show the common conceptional basis of the most widespread electronic structure methods in materials science.

The main goal of electronic structure methods is to solve the Schrodinger equation for the electrons in a molecule or solid, to evaluate the resulting total energies, forces, response functions and other quantities of interest. In this paper we describe the basic ideas behind the main electronic structure methods such as the pseudopotential and the augmented wave methods and provide selected pointers to contributions that are relevant for a beginner. We give particular emphasis to the projector augmented wave (PAW) method developed by one of us, an electronic structure method for ab initio molecular dynamics with full wavefunctions. We feel that it allows best to show the common conceptional basis of the most widespread electronic structure methods in materials science.

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Pythonic Black-box Electronic Structure Tool (PyBEST). An open-source Python platform for electronic structure calculations at the interface between chemistry and physics

The numerical atomic orbital (NAO) basis sets offer a computationally efficient option for electronic structure calculations, as they require fewer basis functions compared with other types of basis sets. Moreover, their strict localization allows for easy combination with current linear scaling methods, enabling efficient calculation of large physical systems. In recent years, NAO bases have become increasingly popular in modern electronic structure codes. This article provides a review of the ab initio electronic structure calculations using NAO bases. We begin by introducing basic formalisms of the NAO‐based electronic structure method, including NAO base set generation, self‐consistent calculations, force, and stress calculations. We will then discuss some recent advances in the methods based on the NAO bases, such as real‐time dependent density functional theory (rt‐TDDFT), efficient implementation of hybrid functionals, and other advanced electronic structure methods. Finally, we introduce the ab initio tight‐binding model, which can be generated directly after the self‐consistent calculations. The model allows for efficient calculation of electronic structures, and the associated topological, and optical properties of the systems.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory Structure and Mechanism > Computational Materials Science

R. B. Gerber, B. Brauer, S. K. Gregurick and G. M. Chaban, PhysChemComm, 2002, 5, 142 DOI: 10.1039/B208000A

Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient calculations is necessary to optimize the instanton tunneling path, and second derivatives of the potential energy along the tunneling path have to be evaluated, restricting the range of suitable electronic structure methods. To enhance the applicability of instanton theory, we present a dual-level approach in which instanton optimizations and Hessian calculations are performed using an efficient but approximate electronic structure method, and the potential energy along the tunneling path is recalculated using a more accurate method. This procedure extends the applicability of instanton theory to high-level electronic structure methods for which analytic gradients may not be available, like local linear-scaling approaches. We demonstrate for the analytical Eckart barrier and three molecular systems how the dual-level instanton approach corrects for the largest part of the error caused by the inaccuracy of the efficient electronic structure method. This reduces the error of the calculated rate constants significantly.

Over the past decade, there has been a significant growth in the development and application of methods for performing global optimization (GO) of cluster and nanoparticle structures using first‐principles electronic structure methods coupled to sophisticated search algorithms. This has in part been driven by the desire to avoid the use of empirical potentials (EPs), especially in cases where no reliable potentials exist to guide the search toward reasonable regions of configuration space. This has been facilitated by improvements in the reliability of the search algorithms, increased efficiency of the electronic structure methods, and the development of faster, multiprocessor high‐performance computing architectures. In this review, we give a brief overview of GO algorithms, though concentrating mainly on genetic algorithm and basin hopping techniques, first in combination with EPs. The major part of the review then deals with details of the implementation and application of these search methods to allow exploration for global minimum cluster structures directly using electronic structure methods and, in particular, density functional theory. Example applications are presented, ranging from isolated monometallic and bimetallic clusters to molecular clusters and ligated and surface supported metal clusters. Finally, some possible future developments are highlighted. © 2013 Wiley Periodicals, Inc.

Preface: phys. stat. sol. (b) 243/5

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

The techniques of computational photodynamics are increasingly employed to unravel reaction mechanisms and interpret experiments. However, misinterpretations in nonadiabatic dynamics caused by inaccurate underlying potentials are often difficult to foresee. This work focuses on revealing the systematic errors in the nonadiabatic simulations due to the underlying potentials and suggests a thrifty approach to evaluate the sensitivity of the simulations to the potential. This issue is exemplified in the photochemistry of cis-stilbene, where similar experimental outcomes have been differently interpreted based on the electronic structure methods supporting nonadiabatic dynamics. We examine the predictions of cis-stilbene photochemistry using trajectory surface hopping methods coupled with various electronic structure methods (OM3-MRCISD, SA2-CASSCF, XMS-SA2-CASPT2, and XMS-SA3-CASPT2) and assess their ability to interpret experimental observations. While the excited-state lifetimes and calculated photoelectron spectra show consistency with experiments, the reaction quantum yields vary significantly: either completely suppressing cyclization or isomerization. Intriguingly, analyzing stationary points on the potential energy surface does not hint at any major discrepancy, making the electronic structure methods seemingly reliable when treated separately. We show that performing an ensemble of simulations with different potentials provides an estimate of the electronic structure sensitivity. However, this ensemble approach is costly. Thus, we propose running nonadiabatic simulations with an external bias at a resource-efficient underlying potential (semiempirical or machine-learned) for the sensitivity analysis. We demonstrate this approach using a semiempirical OM3-MRCISD method with a harmonic bias toward cyclization.

The molecular and crystal structure of 3-(trifluoromethyl)phenanthrene has been determined by X-ray diffraction. The structure of the isolated molecule has been calculated using electronic structure methods at the HF/3-21G, HF/6-31G, MP2/6-31G and B3LYP/6-31G levels. The potential energy surfaces for the rotation of the CF3 group in both the isolated molecule and cluster models for the crystal were computed using electronic structure methods. The barrier height for CF3 rotation in the isolated molecule was calculated to be 0.40 kcal mol(-1) at B3LYP/6-311+G//B3LYP/6-311+G. The B3LYP/6-31G calculated CF3 rotational barrier in a 13-molecule cluster based on the X-ray data was found to be 2.6 kcal mol(-1). The latter is in excellent agreement with experimental results from the NMR relaxation experiments reported in the companion paper (Beckmann, P. A.; Rosenberg, J.; Nordstrom, K.; Mallory, C. W.; Mallory, F. B. J. Phys. Chem. A 2006, 110, 3947). The computational results on the models for the solid state suggest that the intermolecular interaction between nearest neighbor pairs of CF3 groups in the crystal accounts for roughly 75% of the barrier to rotation in the solid state. This pair is found to undergo cooperative reorientation. We attribute the CF3 reorientational disorder in the crystal as observed by X-ray diffraction to the presence of a pair of minima on the potential energy surface and the effects of librational motion.