A software implementation of analytic geometric derivatives of electron-repulsion integrals up to second order is presented for the modeling of vibrational spectroscopies at the level of first-principles Kohn–Sham density functional theory (DFT). In line with the general goals of the VeloxChem program, it targets efficient execution in high-performance computing environments with a hybrid MPI/OpenMP parallelization model and is based on the technique of automatic C++ code generation for high versatility. Gradient calculations scale identically with conventional Fock matrix constructions, and also with the prefactor taken into account, the computational cost of the gradient is significantly lower than that of the self-consistent field (SCF) optimization of the reference state. The Hessian calculation shows a scaling of N3.5 with N being the number of contracted Gaussian basis functions. The computational bottleneck in the Hessian calculation is the solving of the coupled-perturbed Kohn–Sham equations that with VeloxChem can be offloaded to GPU-accelerated nodes. The large-scale virtues of the presented software module are demonstrated by the DFT/B3LYP calculation of the IR spectrum of the entire ubiquitin protein with 1,152 atoms in the quantum mechanical (QM) region and TIP3P water in the molecular mechanics (MM) region. The simulated amide I band shows to be in excellent agreement with experiment.

The eChem project has been previously presented as an interactive platform for quantum and computational chemistry education [J. Chem. Educ. 100, 1664-1671]. However, education is only one side of the eChem project. Another aspect is that it highly accelerates method development by means of code prototyping in notebooks. Complex equations can be understood, and algorithms are examined before the actual software programming step is carried out. Here, the benefits of notebooks for code prototyping are illustrated using the example of vibrational spectroscopy-a type of spectroscopy which involves complex equations with a large number of terms.

A scheme for the calculation of electron-attachment (EA) processes within the framework of unitary coupled-cluster (UCC) theory is presented. Analogous to the description of electron-detachment, the intermediate state representation (ISR) approach is used for the formulation and its relation to the algebraic-diagrammatic construction scheme is pointed out. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions, but need to be approximated. Explicit working equations for two computational schemes referred to as EA-UCC2 and EA-UCC3 are given, providing electron-attachment energies and spectroscopic amplitudes of electron-attached states dominated by one-particle excitations correct through second and third order in perturbation theory, respectively. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is employed. In a benchmark against full configuration interaction (FCI) results including 50 states of 21 different species, both neutral and charged, closed- and open-shell, the novel methods are characterized by mean absolute errors of 0.15 eV (EA-UCC2) and 0.10 eV (EA-UCC3). Furthermore, an approach for the computation of physical properties of electron-attached as well as electron-detached states within the UCC framework is presented. It also builds upon the ISR approach, featuring an expectation value-like formulation similar to that of the equation-of-motion coupled-cluster (EOM-CC) method or the ISR approach of the algebraic-diagrammatic construction (ADC) method. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory are given and shown to be equivalent to those of the second-order ADC/ISR procedure.

The eChem project features an e-book published as a web page (10.30746/978-91-988114-0-7), collecting a repository of Jupyter notebooks developed for the dual purpose of explaining and exploring the theory underlying computational chemistry in a highly interactive manner as well as providing a tutorial-based presentation of the complex workflows needed to simulate embedded molecular systems of real biochemical and/or technical interest. For students ranging from beginners to advanced users, the eChem book is well suited for self-directed learning, but workshops led by experienced instructors and targeting student bodies with specific needs and interests can readily be formed from its components. This has been done by using eChem as the base for a workshop directed toward graduate students learning the theory and practices of quantum chemistry, resulting in very positive assessment of the interactive nature of this framework. The members of the eChem team are engaged in both education and research, and as a mirroring activity, we develop the open-source software upon which this e-book is predominantly based. The overarching vision and goal of our work is to provide a science- and education-enabling software platform for quantum molecular modeling on contemporary and future high-performance computing systems, and to document the resulting development and workflows in the eChem book.

Quantum chemistry is a powerful tool. It is now possible to model complex chemical processes even on a laptop getting insights into matter at its fundamental scale.

But quantum chemistry is also very complex. Answering a chemical question requires selecting parameters among a wide variety of choices. Choosing a model system, an electronic structure method, a basis set, a set of properties, and a wide array of parameters which can affect the results in small but sometimes meaningful way… It can be a very daunting task, even for veterans of the field.

Similarly, for those who wish to get a deeper understanding of a method, going through the pages of equation often riddled with inconsistent notations and formulations is very challenging. And at the end, the link between the equation and the computer implementation found in existing softwares can be vague at best.

We believe that a core issue is that humans are not good at learning in abstract terms. We can get very far with a lecture or a textbook, but we will never build as much intuition about how a clock work as by simply breaking one apart and rebuilding it from scratch.

This is exactly the aim of this page, allowing a hands-on approach to computational chemistry. Together we will dismantle the black box that a computational chemistry code often seems to be, go through all the cogs and gears, and build back together some of the main computational methods of modern computational chemistry. We will do this by presenting the underlying equations, all expressed with consistent notations, as well as by suggesting a simple python implementation, to really display in action how the theory is implemented into a practical tool. Additionally, we will put these methods in context by showing how they can be used to address concrete chemical questions, discussing the strengths and weaknesses of each method and how to best use them to solve practical problems.

This article describes a novel approach for the calculation of ionization potentials (IPs), or, more generally, electron-detachment energies, based on a unitary coupled-cluster (UCC) parameterization of the ground-state wave function. Explicit working equations for a scheme referred to as IP-UCC3 are given, providing electron-detachment energies and spectroscopic amplitudes of electron-detached states dominated by one-hole excitations correct through third order. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is employed. Both the secular matrix and the effective transition moments are shown to be essentially equivalent to the strict third-order algebraic-diagrammatic construction scheme for the electron propagator (IP-ADC). Interestingly, due to the Bernoulli expansion, neglecting triple substitutions in the UCC expansion manifold does not affect the third-order consistency of the IP-UCC effective transition moments. Finally, the equivalence between ADC and UCC excited-state schemes is shown to not hold in fourth or higher order due to a different treatment of the correlated excited-state basis.

The performance of several methods for the calculation of vertical ionization potentials (IPs) or, more generally, electron-detachment energies based on unitary coupled-cluster (UCC) theory and the algebraic-diagrammatic construction (ADC) scheme is evaluated with respect to benchmark data computed at the level of equation-of-motion coupled-cluster theory, including single, double, and triple excitations (IP-EOM-CCSDT). Based on a statistical evaluation of about 200 electron-detached states of 41 molecules, the second-order methods IP-ADC(2) and IP-UCC2 show modest accuracies with IP-EOM-CCSDT as reference, exposing a mean signed error and a standard deviation of the error of -0.54 & PLUSMN; 0.50 and -0.49 & PLUSMN; 0.54 eV, respectively, accompanied by a mean absolute error (MAE) of 0.61 and 0.58 eV, respectively. The strict third-order IP-ADC method demonstrates an accuracy of 0.26 & PLUSMN; 0.35 eV (MAE = 0.35 eV), while the IP-UCC3 method is slightly more accurate with 0.24 & PLUSMN; 0.26 eV (MAE = 0.29 eV). Employing the static self-energy computed using the Dyson expansion method (DEM) improves the IP-ADC(3) performance to 0.27 & PLUSMN; 0.28 eV, with the mean absolute error of this method being 0.32 eV. However, employing the simpler improved fourth-order scheme sigma(4+) for the static self-energy provides almost identical results as the DEM. Based on the quality of the present benchmark results, it therefore appears not necessary to use the computationally more demanding DEM.

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.

In this work, we present the core-valence separation (CVS) approximation applied to unitary coupled-cluster (UCC) theory for the calculation of core-excited states and the simulation of x-ray absorption spectroscopy (XAS). Excitation energies and oscillator strengths of small- to medium-sized organic molecules have been computed using the second-order and extended second-order UCC schemes (CVS-UCC2 and CVS-UCC2-x) as well as the third-order scheme (CVS-UCC3). All results are compared to the corresponding algebraic-diagrammatic construction methods and experimental data. The agreement between CVS-UCC and experimental data demonstrates its potential as a new approach for the calculation of XAS.

A scheme for the calculation of molecular properties within the framework of unitary coupled-cluster (UCC) theory in both the electronic ground and excited states is presented. The scheme is based on an expectation-value ansatz, similar to the equation-of-motion coupled-cluster method or the intermediate state representation (ISR) approach of the algebraic-diagrammatic construction (ADC) scheme. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions but need to be approximated. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory have been derived and coded for the electronic ground state as well as for excited states of predominant single-excitation character. The resulting equations are shown to be equivalent to those of the second-order ADC/ISR procedure. As first computational tests, the second-order UCC method (UCC2) and the one employing third-order amplitudes (also eigenvectors) together with the second-order density matrix, denoted as UCC3(2), are applied to the calculation of dipole moments for a series of small closed- and open-shell systems as well as 4-cyanoindole and 2,3-benzofuran and compared to full configuration interaction or experimental results. For the aromatic organic molecules, the UCC2 method is shown to be sufficient for the ground-state dipole moment, whereas the UCC3(2) scheme is superior for excited-state dipole moments.