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, {\omega}B97X-V and the hybrid mGGA, {\omega}B97M-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, {\omega}B97M-V, and {\omega}B97X-V perform very well. The convergence of frequencies with respect to grid size and atomic orbital basis set size is studied and recommendations 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, {\omega}B97X-V, M06-SX, and {\omega}B97M-V).Comment: 30 pages, 5 figures, 4 table

Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids Near the Basis Set Limit

In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well-suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with a large uncontracted basis set to assess their performance on band gaps of 26 simple solids near the basis set limit. The largest calculation performed in this work involves 3456 electrons and 75600 basis functions utilizing a 6$\times$6$\times$6 k-mesh. With 20-27% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square-deviation (RMSD) of 0.60-0.76 eV while other global hybrid functionals such as M06-2X (1.98 eV) and MN15 (1.03 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.74 eV) but shows a noticeable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, $\omega$B97X-rV (3.86 eV) and $\omega$B97M-rV (3.34 eV), and the two other range separated hybrid functionals, CAM-B3LYP (2.36 eV) and CAM-QTP01 (4.08 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of $\omega$B97X-rV and $\omega$B97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone towards developing more accurate hybrid functionals and applying them to practical applications

Analytic evaluation of non-adiabatic couplings within the complex absorbing potential equation-of-motion coupled-cluster method

We present the theory for the evaluation of non-adiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motions can facilitate transitions between different resonances and between resonances and bound states. These non-adiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the non-adiabatic coupling between bound states and pseudocontinuum states, between bound states and resonances and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate

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

Normative Analysis of Individual Brain Differences Based on a Population MRI-Based Atlas of Cynomolgus Macaques

The developmental trajectory of the primate brain varies substantially with aging across subjects. However, this ubiquitous variability between individuals in brain structure is difficult to quantify and has thus essentially been ignored. Based on a large-scale structural magnetic resonance imaging dataset acquired from 162 cynomolgus macaques, we create a species-specific 3D template atlas of the macaque brain, and deploy normative modeling to characterize individual variations of cortical thickness (CT) and regional gray matter volume (GMV). We observed an overall decrease in total GMV and mean CT, and an increase in white matter volume from juvenile to early adult. Specifically, CT and regional GMV were greater in prefrontal and temporal cortices relative to early unimodal areas. Age-dependent trajectories of thickness and volume for each cortical region revealed an increase in the medial temporal lobe, and decreases in all other regions. A low percentage of highly individualized deviations of CT and GMV were identified (0.0021%, 0.0043%, respectively, P \u3c 0.05, false discovery rate [FDR]-corrected). Our approach provides a natural framework to parse individual neuroanatomical differences for use as a reference standard in macaque brain research, potentially enabling inferences regarding the degree to which behavioral or symptomatic variables map onto brain structure in future disease studies

Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube

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

Research on Functional Value Estimation and Development Mode of Green Infrastructure Based on Multi-Dimensional Evaluation Model: A Case Study of China

With the rapid development of urbanization and industrial economy, urban green space and land resources have been squeezed. The problem of urban ecological environment pollution is becoming increasingly serious. With the concept of sustainable development, green infrastructure construction can not only improve the adverse effects of human activities on the urban ecological environment, it can also deal with the relationship between survival and development, economy and the environment, society, and resources. This paper used different provinces and regions of China as an example to construct a multi-dimensional evaluation model. The multi-function green infrastructure was evaluated quantitatively from three dimensions: economy, society, and ecology. The study results showed that the multifunctional development level of green infrastructure varies among different regions in China due to regional location, economic development, and natural resources. The development mode of green infrastructure in North China, South China, and Northwest China has changed from multi-functional weak and basic coordination to strong and coordinated development. Therefore, the multi-dimensional analysis of green infrastructure is helpful for systematically studying and evaluating the functional value of green infrastructure. It can be used to investigate the development models of green infrastructure in different regions, formulate green infrastructure development strategies, and provide countermeasures and suggestions for relevant government departments

Research on Functional Value Estimation and Development Mode of Green Infrastructure Based on Multi-Dimensional Evaluation Model: A Case Study of China

With the rapid development of urbanization and industrial economy, urban green space and land resources have been squeezed. The problem of urban ecological environment pollution is becoming increasingly serious. With the concept of sustainable development, green infrastructure construction can not only improve the adverse effects of human activities on the urban ecological environment, it can also deal with the relationship between survival and development, economy and the environment, society, and resources. This paper used different provinces and regions of China as an example to construct a multi-dimensional evaluation model. The multi-function green infrastructure was evaluated quantitatively from three dimensions: economy, society, and ecology. The study results showed that the multifunctional development level of green infrastructure varies among different regions in China due to regional location, economic development, and natural resources. The development mode of green infrastructure in North China, South China, and Northwest China has changed from multi-functional weak and basic coordination to strong and coordinated development. Therefore, the multi-dimensional analysis of green infrastructure is helpful for systematically studying and evaluating the functional value of green infrastructure. It can be used to investigate the development models of green infrastructure in different regions, formulate green infrastructure development strategies, and provide countermeasures and suggestions for relevant government departments

Revisiting the performance of time-dependent density functional theory for electronic excitations: Assessment of 43 popular and recently developed functionals from rungs one to four

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between performance and accuracy. The functionals $\omega$B97X-D and BMK are found to offer the best performance overall with a Root-Mean Square Error (RMSE) of 0.28 eV, better than the computationally more demanding CIS(D) wavefunction method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for TDDFT excitation energies, though hybrid meta-GGAs are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.Comment: 12 pages, 8 figures; 8 pages, 7 figures for supporting inf