Infinite Basis Set Extrapolation for Double Hybrid Density Functional Theory 2: Effect of Adding Diffuse Basis Functions

We applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the electron affinities, reaction barrier heights, proton affinities, non‐covalent interactions, atomization, ionization, and alkyl bond dissociation energies. We previously found that the mean unsigned error of the B2KPLYP‐IB calculation with the combination of cc‐pVTZ and cc‐pVQZ reach the chemical accuracy limit (～2 kcal/mol) where the largest deviation occurred in the electron affinity calculations and the weak interactions between noble gases and nonpolar molecules. Here, we investigated the basis set effect using the B2KPLYP‐IB extrapolation scheme that involves (1) the addition of extra tight d basis functions to the second row elements (i.e. cc‐pV(L+d)Z), (2) the addition of extra s, p, and d diffuse basis functions, and (3) a comparison between Dunning's Correlation Consistent and Jensen's Polarization Consistent (pc‐L) basis sets. We found that the addition of extra s and p diffuse basis functions formed the minimal augmented basis sets proposed by Truhlar. This addition permitted the B2KPLYP‐IB to reach the chemical accuracy limit with the combination of the double ζ and triple ζ basis sets. Adding extra s, p diffuse functions to the pc‐L series permitted only a small improvement. This small improvement is due to the fact that the pc‐L basis sets already contain a large number of functions for the p block elements. Taken together, the results suggest that this minimal augmented basis sets is useful for due to its accuracy and affordable computational cost.     

A comment on “Accurate ab initio determination of binding energies for rare-gas dimers by basis set extrapolation”

In this work we comment on an extrapolation scheme presented by Lee in Theoretical Chemistry Accounts, which is based on an extrapolation of energy differences instead of actual energies. In particular, we show that a very similar scheme had been introduced already in 1999, and used to estimate the MP5, CCSDT and FCI complete basis set limits of He₂. Comment to the article “Accurate ab initio determination of binding energies for rare-gas dimers by basis set extrapolation” by J.S. Lee, Theor Chem Acc (2005) 113: 87–94     

On the validity of complete basis set extrapolation formula optimized for the equilibrium distance applied to the potential energy surface for the correlation energy of the helium dimer

Full configuration interaction calculations are performed for He₂ using various orbital basis sets of the aug‐cc‐pVXZ type, with the correlation energies being extrapolated to the complete basis set (CBS) limit. A two‐point CBS extrapolation formula has been utilized for such a purpose. It is shown that the extrapolation formula with the offset parameter k(R) optimized for the equilibrium distance is not uniformly applicable to He He distances in the very short region of the potential energy curve. The offset parameter k(R) in the repulsive region of the potential energy curve can be largely different with the one in the long‐range distances especially in the cases of basis‐sets with large cardinality number. It is also noticed that the accuracy of this extrapolation scheme may not be improved with the increasing of the cardinality number.     

Accurate ab intio determination of binding energies for rare-gas dimers by basis set extrapolation

To investigate the electron correlation effect on the binding energies of very weakly bound complexes at highly correlated levels, an extrapolation scheme exploiting the convergent behavior of the binding energy differences between two correlation levels with the correlation-consistent basis set aug-cc-pVXZ was explored. The scheme is based on extrapolating the binding energy differences between the lower and higher correlation levels (such as second-order Møller–Plesset perturbation theory and the single and double coupled-cluster method with perturbative triple correction level), CCSD(T), by X^–3 for relatively small basis set calculations to estimate the corresponding basis set limit, which is then added to the complete basis set(CBS) limit binding energy at the lower correlation level to derive the CBS limit binding energy at the higher level. Test results on rare-gas dimers Rg₂ (Rg is He, Ne, Ar) show that the CCSD(T) CBS limit binding energies estimated by this scheme with aug-cc-pVXZ and aug-cc-pV(X+1)Z basis sets are more accurate than the CBS limit estimated by direct extrapolation of correlation energies by X^–3 with aug-cc-pV(X+1)Z and aug-cc-pV(X+2)Z basis sets in most cases, which signifies the utility of the proposed extrapolation scheme as the level of electron correlation treatment increases. The nonnegligible discrepancy in the well depth near equilibrium between the experimental and the full connected single, double, and triple coupled-cluster method CBS limit estimate obtained by this procedure in the case of Ar₂ suggests that the previous semiempirical potential may be too attractive near equilibrium compared with the actual one.Acknowledgement The major portion of this work was carried out while the author was visiting the Quantum Theory Project (QTP) at the University of Florida. The author is thankful to Rodney Bartlett for hospitality and support during the visit. The author is also thankful to Ajith Perera for assistance in using the ACESII program package. Computational support from the QTP at the University of Florida and the Institute for Basic Science at Ajou University is gratefully acknowledged.     

A Density Functional Theory Study on Nonlinear Optical Properties of Double Cage Excess Electron Compounds: Theoretically Design M[Cu(Ag)@(NH3)n](M = Be,Mg and Ca; n = 1–3)

In this work, we investigated the nonlinear optical (NLO) properties of excess electron electride molecules of M[Cu(Ag)@(NH₃)_n](M = Be, Mg and Ca; n = 1–3) using density functional theory (DFT). This electride molecules consist of an alkaline-earth (Be, Mg and Ca) together with transition metal (Cu and Ag) doped in NH₃ cluster. The natural population analysis of charge and their highest occupied molecular orbital suggests that the M[Cu(Ag)@(NH₃)_n] compound has excess electron like alkaline-earth metal form double cage electrides molecules, which exhibit a large static first hyperpolarizability () (electron contribution part) and one of which owns a peak value of 216,938 (a.u.) for Be[Ag@(NH₃)₂] and vibrational harmonic first hyperpolarizability () (nuclear contribution part) values and the ratio of /, namely, η values from 0.02 for Be[Ag@(NH₃)] to 0.757 for Mg[Ag@(NH₃)₃]. The electron density contribution in different regions on values mainly come from alkaline-earth and transition metal atoms by first hyperpolarizability density analysis, and also explains the reason why values are positive and negative. Moreover, the frequency-dependent values β(−2ω,ω,ω) are also estimated to make a comparison with experimental measures. © 2018 Wiley Periodicals, Inc.     

Functional and Basis Set Dependence for Time-Dependent Density Functional Theory Trajectory Surface Hopping Molecular Dynamics: Cis-Azobenzene Photoisomerization

Within three functionals (TD-B3LYP, TD-BHandHLYP, and TD-CAM-B3LYP) in combination with four basis sets (3-21g, 6-31g, 6-31g(d), and cc-pvdz), global switching (GS) trajectory surface hopping molecular dynamics has been performed for cis-to-trans azobenzene photoisomerization up to the S₁(nπ*) excitation. Although all the combinations show artificial double-cone structure of conical intersection between ground and first excited states, simulated quantum yields and lifetimes are in good agreement with one another; 0.6 (±5%) and 40.5 fs (±10%) by TD-B3LYP, 0.5 (±10%) and 35.5 fs (±4%) by TD-BHandHLYP, and 0.44 (±9%) and 35.2 fs (±10%) by TD-CAM-B3LYP. By analyzing distributions of excited-state population decays, hopping spots, and typical trajectories with performance of 12 functional/basis set combinations, it has been concluded that functional dependence for given basis set is slightly more sensitive than basis set dependence for given functional. The present GS on-the-fly time-dependent density functional theory (TDDFT) trajectory surface hopping simulation can provide practical benchmark guidelines for conical intersection driven excited-state molecular dynamics simulation involving in large complex system within ordinary TDDFT framework. © 2019 Wiley Periodicals, Inc.     

Hydricity of 3d Transition Metal Complexes from Density Functional Theory: A Benchmarking Study

A range of modern density functional theory (DFT) functionals have been benchmarked against experimentally determined metal hydride bond strengths for three first-row TM hydride complexes. Geometries were found to be produced sufficiently accurately with RI-BP86-D3(PCM)/def2-SVP and further single-point calculations with PBE0-D3(PCM)/def2-TZVP were found to reproduce the experimental hydricity accurately, with a mean absolute deviation of 1.4 kcal/mol for the complexes studied.     

On the Structure of the Arginine-carboxylate Salt Bridge: A Density Functional Theory Study

The arginine-carboxylate salt bridge, which represents about 40% of the pairs of ionic groups within proteins, plays a crucial role in determining the structures and functions of proteins1. Numerous experimental evidences have indicated that this type of salt bridge, which usually includes the arginine-glutamate pair and the arginine-aspartate pair, should stay in a zwitterionic state rather than in a neutral one2. This viewpoint has been widely accepted and in usual it is directly used in the…     

Assessment of Various Density Functional Theory Methods for Finding Accurate Structures of Actinide Complexes

Density functional theory (DFT) is a widely used computational method for predicting the physical and chemical properties of metals and organometals. As the number of electrons and orbitals in an atom increases, DFT calculations for actinide complexes become more demanding due to increased complexity. Moreover, reasonable levels of theory for calculating the structures of actinide complexes are not extensively studied. In this study, 38 calculations, based on various combinations, were performed on molecules containing two representative actinides to determine the optimal combination for predicting the geometries of actinide complexes. Among the 38 calculations, four optimal combinations were identified and compared with experimental data. The optimal combinations were applied to a more complicated and practical actinide compound, the uranyl complex (UO₂(2,2′-(1E,1′E)-(2,2-dimethylpropane-1,3-dyl)bis(azanylylidene)(CH₃OH)), for further confirmation. The corresponding optimal calculation combination provides a reasonable level of theory for accurately optimizing the structure of actinide complexes using DFT.     

Dimensional Reduction of Cs2AgBiBr6: A 2D Hybrid Double Perovskite with Strong Polarization Sensitivity

By dimensional reduction of the 3D motif of Cs₂AgBiBr₆, a lead‐free 2D hybrid double perovskite, (i‐PA)₂CsAgBiBr₇ ( 1, i‐PA=isopentylammonium), was successfully designed. It adopts a quantum‐confined bilayered structure with alternating organic and inorganic sheets. Strikingly, the unique 2D architecture endows it highly anisotropic nature of physical properties, including electric conductivity and optical absorption (the ratio α_b/α_c=1.9 at 405 nm). Such anisotropy attributes result in the strong polarization‐sensitive responses with large dichroic ratios up to 1.35, being comparable to some 2D inorganic materials. This is the first study on the hybrid double perovskites with strong polarization sensitivity. A crystal device of 1 also exhibits rapid response speed (ca. 200 μs) and excellent stabilities. The family of 2D hybrid double perovskites are promising optoelectronic candidates, and this work paves a new pathway for exploring new green polarization‐sensitive materials.     

Studies of Structural and Thermodynamic Properties for Polychlorinated Thianthrenes by Density Functional Theory

The structural and thermodynamic （PCTAs） in the ideal gas state at 298.15 K and 1.013 properties of 75 polychlorinated thianthrenes ×10^5 Pa have been calculated at the B3LYP/6- 31G＊ level using Gaussian 98 program. Based on the output data of Gaussian, the isodesmic reactions were designed to calculate standard enthalpy of formation （△fH^θ） and standard free energy of formation （△fH^θ） of PCTAs congeners. The relations of these thermodynamic parameters with the number and position of C1 atom substitution （Npcs） were discussed, and it was found that there exists high correlation between thermodynamic parameters （total energy （TE）, zero-point vibrational energy （ZPE）, thermal correction to energy （Eth）, heat capacity at constant volume （Cv^θ）, entropy （S^θ）, enthalpy （H^θ）, free energy （G^θ）, standard enthalpies of formation （△fH^θ） and standard Gibbs energies of formation （△fG^θ）） and Npcs. On the basis of the relative magnitude of their △fG^θ, the order of relative stability of PCTA congeners was theoretically proposed. In addition, the correlations between structural parameters and Npcs were also discussed. The good correlations were found between molecular average polarizability （α）, energy of the highest occupied molecular orbital （EHOMO）, molecular volume （Vm） and Npcs, and all R^2 values are larger than 0.95. Moreover, it was supposed that the isomer groups with higher toxicity should be Tri-CTA and TCTA.     

芳构化法合成2,5-二羟基对苯二甲酸反应机理的密度泛函理论研究

采用密度泛函理论（DFT）计算,研究了由1,4-环己二酮-2,5-二甲酸二甲酯（DMSS）制备2,5-二羟基对苯二甲酸（DHTA）的反应机理。其中,采用IEFPCM溶剂模型着重计算了DMSS由酮式互变异构为烯醇式的溶剂效应,并探究了碘在催化DMSS烯醇式氧化芳构化过程中的作用机制。计算结果表明,在溶剂分子的辅助下,DMSS酮-烯醇式互变异构反应的能垒显著降低;芳构化过程中,碘首先与过氧化氢反应生成活性物质次碘酸,其催化DMSS烯醇式发生碘代反应,并经过后续的消去和互变异构生成2,5-二羟基对苯二甲酸二甲酯（DMDHT）,DMDHT进一步水解生成DHTA。同时,通过核磁共振氢谱测试验证了DMSS酮-烯醇式互变异构的溶剂效应;反应性能考评实验结果表明,相较于无催化剂,在碘的催化作用下,DMDHT产品的纯度和收率更高。     

Density Functional Theory studies on interactions of phosphoryl ligands with the Ca cation: Affinity and associated parameters

DFT (B3LYP/6-31G(d)) and semi-empirical (PM6) calculations of Ca²⁺ affinities on a set of substituted phosphoryl ligands were performed with complete geometry optimization. Two types of ligands were calculated: a set of trivalent [OP(R)] and a set of pentavalent [OP(R)₃] ones (R = H, F, Cl, Br, OH, OCH₃, CH₃, CN, NH₂ and NO₂), with R either directly bound to the phosphorus atom or to the para position of a phenyl ring. The affinity of the Ca²⁺ cation for the ligands was quantified in terms of interaction energy. Additionally, geometric and electronic parameters were correlated with the intensity of that interaction. Our results show that the electronic nature of the substituent mainly affects the interaction energy. Donor groups are associated with more negative interaction energies, while acceptor groups are associated with less negative interaction energies.     

A comparison of quantum chemical models for calculating NMR shielding parameters in peptides: mixed basis set and ONIOM methods combined with a complete basis set extrapolation

This article compares several quantum mechanical approaches to the computation of chemical shielding tensors in peptide fragments. First, we describe the effects of basis set quality up to the complete basis set (CBS) limit and level of theory (HF, MP2, and DFT) for four different atoms in trans N-methylacetamide. For both isotropic shielding and shielding anisotropy, the MP2 results in the CBS limit show the best agreement with experiment. The HF values show quite a different tendency to MP2, and even in the CBS limit they are far from experiment for not only the isotropic shielding of carbonyl carbon but also most shielding anisotropies. In most cases, the DFT values differ systematically from MP2, and small basis-set (double- or triple-zeta) results are often fortuitously in better agreement with the experiment than the CBS ones. Second, we compare the mixed basis set and ONIOM methods, combined with CBS extrapolation, for chemical shielding calculations at a DFT level using various model peptides. From the results, it is shown that the mixed basis set method provides better results than ONIOM, compared to CBS calculations using the nonpartitioned full systems. The information studied here will be useful in guiding the selection of proper quantum chemical models, which are in a tradeoff between accuracy and cost, for shielding studies of peptides and proteins.     

KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set?

KSSOLV (Kohn-Sham Solver) is a MATLAB (Matrix Laboratory) toolbox for solving the Kohn-Sham density functional theory (KS-DFT) with the plane-wave basis set. In the KS-DFT calculations, the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field (SCF) scheme. To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms, we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox. We compare the performance of KSSOLV-GPU on three types of GPU, including RTX3090, V100, and A100, with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.     

5-硝基-1-氢-四唑分子热分解反应机理的密度泛函理论研究

利用密度泛函理论研究了5-硝基-1-氢-四唑分子热分解的反应机理。首先用 B3LYP/6-31G（d）方法优化反应中反应物、过渡态、中间体以及产物的几何构型， 通过振动分析得到零点能校正值并确认反应的过渡态。此外，对各个构型作了 CCSD（T）/6-31G（d,p）水平下的单点计算。报道了三条可能的反应途径，即直接 开环途径和质子转移途径；其中N（1）-N（2）键断裂直接开环的机理与文献报道 一致；而涉及质子转移的反应途径则是一个新的发现；另一条关于N（4）-C（5） 键断裂直接开环的途径由于能垒较高，因此发生的几率较小。