How delocalized are the polyacenes?

In an attempt to quantify electron delocalization in polyacenes with up to 50 carbon atoms, we have performed self-consistent field calculations in which the π electrons are constrained to occupy highly localized molecular orbitals (HILOs) centered on a maximum of two, six or ten adjacent carbon atoms. We have also performed similar calculations on simple polyacene analogs consisting only of hydrogen atoms and exhibiting electron delocalization in the σ framework. We find that the energetic cost of localizing the π electrons in the polyacenes is roughly 60, 5 or 0.1 kJ/mol per ring atom for the two-, six- and ten-atom HILOs, respectively, and the use of these localized models overestimates the predicted hydrogenation energies of the acenes by roughly 50%, 4% and 0.1%, respectively. We conclude that the chemistry of polyacenes can be modeled well using highly localized descriptions of the π electrons.

Economical Models for Electron Densities

We discuss a new theoretical framework for modeling molecular electron densities. Our approach decomposes the total density into contributions from basis function products and then approximates each product using constrained least-squares approximation in a tailored local basis of functions with adjustable non-linear parameters. We show how to solve directly for the expansion coefficients and Lagrange multipliers and present an iterative method to optimize the non-linear parameters. Example products from the Dunning cc-pVTZ basis set are discussed.

Avoiding Negligible Shell Pairs and Quartets in Electronic Structure Calculations

We define a significant shell pair in an electronic structure calculation as one that generates at least one two-electron integral larger than a preset threshold. We define a significant shell quartet similarly. We then explore several methods for identifying nonsignificant pairs and quartets so that they can be avoided and computational efficiency improved. We find that the widely used Cauchy-Schwarz bound identifies most nonsignificant quartets but that the Hölder bound is slightly more powerful for identifying nonsignificant pairs.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

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.

Q-MP2-OS: Møller-Plesset Correlation Energy by Quadrature

We present a quadrature-based algorithm for computing the opposite-spin component of the MP2 correlation energy which scales quadratically with basis set size and is well-suited to large-scale parallelization. The key ideas, which are rooted in the earlier work of Hirata and co-workers, are to abandon all two-electron integrals, recast the energy as a seven-dimensional integral, approximate that integral by quadrature, and employ a cutoff strategy to minimize the number of intermediate quantities. We discuss our implementation in detail and show that it parallelizes almost perfectly on 840 cores for cyclosporine (a molecule with roughly 200 atoms), exhibits [Formula: see text] scaling for a sequence of polyglycines, and is principally limited by the accuracy of its quadrature.

Assessment of DFT Methods for Transition Metals with the TMC151 Compilation of Data Sets and Comparison with Accuracies for Main-Group Chemistry

In the present study, we have gathered a collection (that we term TMC151) of accurate reference data for transition-metal reactions for the assessment of quantum chemistry methods. It comprises diatomic dissociation energies and reaction energies and barriers for prototypical transition-metal reactions. Our assessment of a diverse range of different types of DFT methods shows that the most accurate functionals include ωB97M-V, ωB97X-V, MN15, and B97M-rV. Notably, they have also been previously validated to be highly robust for main-group chemistry. Nevertheless, even these methods show substantially worse accuracies for transition metals than for main-group chemistry. For less accurate methods, there is not a good correlation between their accuracies for main-group and transition-metal chemistries. Thus, in the development of new DFT, it is important to assess the accuracies for both types of data. In this regard, we have formulated the TMC34 model for efficient assessment of the performance for transition metals, which complements our previously developed MG8 model for main-group chemistry. Together, they provide a cost-effective means for initial assessment of new methodologies.

Efficient Method for Calculating Effective Core Potential Integrals

Effective core potential (ECP) integrals are among the most difficult one-electron integrals to calculate due to the projection operators. The radial part of these operators may include r⁰, r^-1, and r^-2 terms. For the r⁰ terms, we exploit a simple analytic expression for the fundamental projected integral to derive new recurrence relations and upper bounds for ECP integrals. For the r^-1 and r^-2 terms, we present a reconstruction method that replaces these terms by a sum of r⁰ terms and show that the resulting errors are chemically insignificant for a range of molecular properties. The new algorithm is available in Q-Chem 5.0 and is significantly faster than the ECP implementations in Q-Chem 4.4, GAMESS (US) and Dalton 2016.

Molecular electronic structure in one-dimensional Coulomb systems

Following two recent papers [Phys. Chem. Chem. Phys., 2015, 17, 3196; Mol. Phys., 2015, 113, 1843], we perform a larger-scale study of chemical structure in one dimension (1D). We identify a wide, and occasionally surprising, variety of stable 1D compounds (from diatomics to tetra-atomics) as well as a small collection of stable polymeric structures. We define the exclusion potential, a 1D analogue of the electrostatic potential, and show that it can be used to rationalise the nature of bonding within molecules. This allows us to construct a small set of simple rules which can predict whether a putative 1D molecule should be stable.

Chemistry in one dimension

Orbital basis functions in a one-dimensional triatomic molecule ABC.

Mixed Ramp-Gaussian Basis Sets

We discuss molecular orbital basis sets that contain both Gaussian and polynomial (ramp) functions. We show that, by modeling ramp-Gaussian products as sums of ramps, all of the required one- and two-electron integrals can be computed quickly and accurately. To illustrate our approach, we construct R-31+G, a mixed ramp-Gaussian basis in which the core basis functions of the 6-31+G basis are replaced by ramps. By performing self-consistent Hartree-Fock calculations, we show that the thermochemical predictions of R-31+G and 6-31+G are similar but the former has the potential to be significantly faster.

Resolutions of the Coulomb Operator: VII. Evaluation of Long-Range Coulomb and Exchange Matrices

Use of the resolution of Ewald operator method for computing long-range Coulomb and exchange interactions is presented. We show that the accuracy of this method can be controlled by a single parameter in a manner similar to that used by conventional algorithms that compute two-electron integrals. Significant performance advantages over conventional algorithms are observed, particularly for high quality basis sets and globular systems. The approach is directly applicable to hybrid density functional theory.

Distributions of r1·r2 and p1·p2 in Atoms

We consider the two-electron position and momentum dot products, α = r1·r2 and β = p1·p2, and present a method for extracting their distributions, A(α) and B(β), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree-Fock AHF(α) and BHF(β) for He and the first-row atoms are investigated, with particular attention to the effects of Pauli exchange. The effects of electron correlation are studied via the holes, ΔA(α) ≡ A(α) - AHF(α) and ΔB(β) ≡ B(β) - BHF(β), and the hole structures are rationalized in terms of radial and angular correlation effects. Correlation effects are also examined through an analysis of the first moments of A(α), AHF(α), B(β), and BHF(β).

A remarkable identity involving Bessel functions

We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and the integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical examples of the identity are discussed.

Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.

Exact wave functions of two-electron quantum rings

We demonstrate that the Schrödinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states.

Resolutions of the Coulomb Operator: V. The Long-Range Ewald Operator

We show that the long-range Ewald operator can be resolved as erf(ωr12)/r12 = ∑k ϕk*(r1) ϕk(r2), where ϕk is proportional to the product of a spherical Bessel function and a spherical harmonic. We demonstrate the use of this new resolution by calculating the long-range Coulomb energy of the nanodiamond crystallite C84H64 and the long-range exchange energy of the graphene C96H24. The resolution appears particularly effective for long-range exchange calculations.

Distribution of r·p in atomic systems

We present formulas for computing the probability distribution of the posmom s = r · p in atoms, when the electronic wave function is expanded in a single particle Gaussian basis. We study the posmom density, S(s), for the electrons in the ground states of 36 lightest atoms (H-Kr) and construct an empirical model for the contribution of each atomic orbital to the total S(s). The posmom density provides unique insight into types of trajectories electrons may follow, complementing existing spectroscopic techniques that provide information about where electrons are (X-ray crystallography) or where they go (Compton spectroscopy). These, a priori, predictions of the quantum mechanically observable posmom density provide an challenging target for future experimental work.

Invariance of the correlation energy at high density and large dimension in two-electron systems

We prove that, in the large-dimension limit, the high-density correlation energy Ec of two opposite-spin electrons confined in a D-dimensional space and interacting via a Coulomb potential is given by Ec∼-1/(8D2) for any radial confining potential V(r). This result explains the observed similarity of Ec in a variety of two-electron systems in three-dimensional space.

Two electrons on a hypersphere: a quasiexactly solvable model

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a D-sphere (D >or= 1), is a polynomial in the interelectronic distance u for a countably infinite set of values of the radius R. A selection of these radii and the associated energies are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the D = 3 model bears the greatest similarity to normal physical systems.