Analytic second derivatives from auxiliary density perturbation theory

Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory

CONTEXT

Analytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses.

METHOD

All calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.

Pd8 Cluster: Too Small to Melt? A BOMD Study

The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.

Chlorophyll and pheophytin protonated and deprotonated ions: Observation and theory

Pheophytin a and chlorophyll a have been investigated by electrospray mass spectrometry in the positive and negative modes, in view of the importance of the knowledge of their properties in photosynthesis. Pheophytin and chlorophyll are both observed intensely in the protonated mode, and their main fragmentation route is the loss of their phytyl chain. Pheophytin is observed intact in the negative mode, while under collisions, it is primarily cleaved beyond the phytyl chain and loses the attaching propionate group. Chlorophyll is not detected in normal conditions in the negative mode, but addition of methanol solvent molecule is detected. Fragmentation of this adduct primarily forms a product (-30 amu) that dissociates into dephytyllated deprotonated chlorophyll. Semi-empirical molecular dynamics calculations show that the phytyl chain is unfolded from the chlorin cycle in pheophytin a and folded in chlorophyll a. Density functional theory calculations have been conducted to locate the charges on protonated and deprotonated pheophytin a and chlorophyll a and have found the major location sites that are notably more stable in energy by more than 0.5 eV than the others. The deprotonation site is found identical for pheophytin a and the chlorophyll a-methanol adduct. This is in line with experiment and calculation locating the addition of methanol on a double bond of deprotonated chlorophyll a.

NWChem: Recent and Ongoing Developments

This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

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.

In-depth theoretical understanding of the chemical interaction of aromatic compounds with a gold nanoparticle

The orientations of aromatic molecules at the surface of gold nanoparticles are probed and characterized by a combination of several topological analyses, energy decomposition analyses, and infrared spectroscopy.

Analytic Alchemical Derivatives for the Analysis of Differential Acidity Assisted by the h Function

Analytical calculation of alchemical derivatives based on auxiliary density perturbation theory is described, coded, and validated. For the case where the nucleus is a hydrogen atom and the nuclear charge is changed from 1 to 0, it turns out that a good estimate of the proton binding energies can be obtained very efficiently. First-order results correspond exactly to the molecular electrostatic potential evaluated at the hydrogen nucleus location (removing self-repulsion), in agreement with previously reported extensive studies. Therefore, the second-order results reported here are refinements in accuracy that finally allow a quantitative exploration of differential acidity. Furthermore, the recently reported h function is produced in its analytical form as a byproduct and local descriptor associated with the proton binding energy values found with this approach. In an example application, proton binding energies are computed for a family of imidazolium derivatives to demonstrate the capabilities and the stability of the method with respect to changes in basis set or exchange-correlation functional.

First-principle study of the structures, growth pattern, and properties of (Pt3Cu)n, n = 1-9, clusters

In this work, a first-principles systematic study of (Pt₃Cu)_n, n = 1-9, clusters was performed employing the linear combination of Gaussian-type orbital auxiliary density functional theory approach. The growth of the clusters has been achieved by increasing the previous cluster by one Pt₃Cu unit at a time. To explore in detail the potential energy surface of these clusters, initial structures were obtained from Born-Oppenheimer molecular dynamics trajectories generated at different temperatures and spin multiplicities. For each cluster size, several dozens of structures were optimized without any constraints. The most stable structures were characterized by frequency analysis calculations. This study demonstrates that the obtained most stable structures prefer low spin multiplicities. To gain insight into the growing pattern of these systems, average bond lengths were calculated for the lowest stable structures. This work reveals that the Cu atoms prefer to be together and to localize inside the cluster structures. Moreover, these systems tend to form octahedra moieties in the size range of n going from 4 to 9 Pt₃Cu units. Magnetic moment per atom and spin density plots were obtained for the neutral, cationic, and anionic ground state structures. Dissociation energies, ionization potential, and electron affinity were calculated, too. The dissociation energy and the electron affinity increase as the number of Pt₃Cu units grows, whereas the ionization potential decreases.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.

Hybrid ADFT Study of the C104 and C106 IPR Isomers

This work presents a hybrid auxiliary density functional theory (ADFT) study of the neutral and hexaanionic C₁₀₄ and C₁₀₆ fullerenes with the aim to determine their ground state structures. To this end, all C₁₀₄ and C₁₀₆ fullerene structures that obey the isolated pentagon rule (IPR) were optimized with the Perdew-Burke-Ernzerhof generalized gradient approximation followed by a single-point energy calculation with the PBE0 hybrid functional. Our studies show that this composite approach yields relative energies of giant fullerenes that are accurate to around 1 kcal/mol. As a result, the ground states of C₁₀₄, C₁₀₄^6-, and C₁₀₆^6- can be assigned to the isomers 234:C_s, 821:D₂, and 891:C_s, respectively. On the other hand, the energetically lowest lying IPR isomers of C₁₀₆, 331:C_s, 1194:C₂, 534:C₁ are separated by less than 1 kcal/mol which makes an unequivocal ground state assignment by hybrid DFT methods impossible. To guide future experiments, we also report the simulated IR and Raman spectra of the most stable neutral and hexaanionic C₁₀₄ and C₁₀₆ fullerenes.

When finite becomes infinite: convergence properties of vibrational spectra of oligomer chains

We present a computational study of convergence properties of vibrational IR and Raman spectra for a series of increasingly long units of polyethylene, cis- and trans-polyacetylenes, and polyynes. Convergent behavior to the spectra of infinitely long polymers was observed in all cases when chains reached lengths of approximately 60 carbon atoms, both with respect to the positions of the bands and to their intensities. The vibrational spectra of longer chains are practically indistinguishable. The convergence rate depends on the degree of the π conjugation in a studied system: Vibrational spectra for oligoethylenes converge noticeably faster than the spectra for the conjugated systems. The slowest convergence is observed for skeletal motions of the oligomer chains, which may require more than a hundred carbon atoms in the chain to show deviations smaller than 1 cm^-1 to the corresponding solid-state calculations. The results suggest that the boundary between the properties of finite and infinite molecular systems fades away for a surprisingly small number of atoms.

Accuracy of auxiliary density functional theory hybrid calculations for activation and reaction enthalpies of pericyclic reactions

Auxiliary density functional theory (ADFT) hybrid calculations are based on the variational fitting of the Coulomb and Fock potential and, therefore, are free of four-center electron repulsion integrals. So far, ADFT hybrid calculations have been validated successfully for standard enthalpies of formation. In this work the accuracy of ADFT hybrid calculations for the description of pericyclic reactions was quantitatively validated at the B3LYP/6-31G*/GEN-A2* level of theory. Our comparison with conventional Kohn-Sham density functional theory (DFT) results shows that the DFT and ADFT activation and reaction enthalpies are practically indistinguishable. A systematic study of various functionals (PBE, B3LYP, PBE0, CAMB3LYP, CAMPBE0 and HSE06) and basis sets (6-31G*, DZVP-GGA and aug-cc-pVXZ; X = D, T and Q) revealed that the ADFT HSE06/aug-cc-pVTZ/GEN-A2* level of theory yields best balanced accuracy for the activation and reaction enthalpies of the studied pericyclic reactions. With the successfully validate ADFT composite approach consisting of PBE/DZVP-GGA/GEN-A2* structure and transition state optimizations and single-point HSE06/aug-cc-pVTZ/GEN-A2* energy calculations, an accurate, reliable and efficient computational approach for the study of pericyclic reactions in systems at the nanometer scale is proposed.