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.

An automatic code generated C++/HIP/CUDA implementation of the (auxiliary) Fock, or Kohn-Sham, matrix construction for execution in GPU-accelerated hardware environments is presented. The module is developed as part of the quantum chemistry software package VeloxChem, employing localized Gaussian atomic orbitals. The performance and scaling characteristics are analyzed in view of the specific requirements for self-consistent field optimization and response theory calculations. As an example, the electronic circular dichroism spectrum of a G-quadruplex is calculated at the level of time-dependent density functional theory in conjunction with the range-separated CAM-B3LYP exchange-correlation functional. Computational issues due to the high-density of states following the adoption of large-scale model systems are here bypassed with use of the complex polarization propagator approach. The origin of the negative Cotton effect in the long-wavelength onset of the experimental spectrum is elucidated in large-scale modeling and shown to be associated with the TTA nucleobase linkers in the G-quadruplex.

Being a program written primarily in Python that strictly adheres to modern object-oriented software engineering and parallel programming practices, VeloxChem is shown to be suitable for the development of (semi)automatized workflows that extend its scope from first-principles quantum chemical purism to hybrid quantum-classical interoperability and some degree of semiempiricism. Methods are presented for building complex systems such as metal-organic frameworks, constructing molecular mechanics and interpolation mechanics force fields, conformer searches, system solvation, determining free energies of solvation, and determining free energy profiles of reaction pathways using the empirical valence bond method. The implementations are made intuitive with opportunities for interactive plotting and 3D molecular structure illustrations through the use of Jupyter notebooks.

Spin-casting of molecularly doped polymer solution mixtures is one of the commonly used methods to obtain conductive organic semiconductor films. In spin-casted films, electronic interaction between the dopant and polymer is one of the crucial factors that dictates the doping efficiency. Here, we investigate excitonic couplings using ultrafast two-dimensional electronic spectroscopy to examine the different types of electronic interactions in ion pairs of the prototype F4TCNQ-doped P3HT polymer system in a precursor solution mixture for spin-casting. Off-diagonal peaks in the 2D spectra clearly establish the excitonic coupling between P3HT+ and F4TCNQ– ions in solution. The observed excitonic coupling is the direct manifestation of a Coulombic interaction between the ion pair. The excited-state lifetime of F4TCNQ– in ion pairs shows biexponential decay at 30 and 200 fs, which hints toward the presence of a heterogeneous population with different interaction strengths. To examine the nature of these different types of interactions in solution mixtures, we study the system using molecular dynamics simulations on a fully solvated model employing the generalized Amber force field. We retrieve three dominant interaction modes of F4TCNQ anions with P3HT: side chain, π-stack, and slipped stack. To quantify these interactions, we complement our studies with electronic structure calculations, which reveal the excitonic coupling strengths of ∼ 75 cm–1 for side chain, ∼ 150 cm–1 for π–π-stack, and ∼69 cm–1 for slipped stack. These various interaction modes provide information about the key geometries of the seed structures in precursor solution mixtures, which may determine the final structures in spin-casted films. The insights gained from our study may guide new strategies to control and ultimately tune Coulomb interactions in polymer-dopant solutions. 

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT’s standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12 000 basis functions.

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.

We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

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.

For general exchange-correlation functionals with a dependence on the local spin densities and spin-density gradients, we provide computationally tractable expressions for the tensor-averaged quadratic response functions pertinent to the experimental observables in second-harmonic generation (SHG). We demonstrate how the tensor-averaged quantities can be implemented with reference to a derived minimal number of first- and second-order perturbed Fock matrices. Our consideration has the capability of treating a situation of resonance enhancement as it is based on damped response theory and allows for the evaluation of tensor-averaged resonant-convergent quadratic response functions using only similar to 25% (one-photon off-resonance regions) and similar to 50% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of SHG intensities in the one-photon off-resonance region are provided for a sample of makaluvamine derivatives recognized for their large nonlinear optical responses as well as a benchmark set of small- and medium-sized organic molecules.