Predicting adsorption enthalpies on silicalite and HZSM‐5: A benchmark study on DFT strategies addressing dispersion interactions

We evaluated the accuracy of periodic density functional calculations for adsorption enthalpies of water, alkanes, and alcohols in silicalite and HZSM‐5 zeolites using a gradient‐corrected density functional with empirical dispersion corrections (PBE‐D) as well as a nonlocal correlation functional (vdW‐DF2). Results of both approaches agree in acceptable fashion with experimental adsorption energies of alcohols in silicalite, but the adsorption energies for n‐alkanes in both zeolite models are overestimated, by 21?46 kJ mol^?1. For PBE‐D calculations, the adsorption of alkanes is exclusively determined by the empirical dispersion term, while the generalized gradient approximation‐DFT part is purely repulsive, preventing the molecule to come too close to the zeolite walls. The vdW‐DF2 results are comparable to those of PBE‐D calculations, but the latter values are slightly closer to the experiment in most cases. Thus, both computational approaches are unable to reproduce available experimental adsorption energies of alkanes in silicalite and HZSM‐5 zeolite with chemical accuracy. © 2014 Wiley Periodicals, Inc.     

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

We study the orbital‐dependence of three (parameter‐free) double‐hybrid density functionals, namely the PBE0‐DH, the PBE‐QIDH models, and the SOS1‐PBE‐QIDH spin‐opposite‐scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self‐consistent density functional theory calculations using several exchange‐correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF‐PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self‐interaction errors. We find that the PBE‐QIDH double‐hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.     

Analytic energy gradients for orbital‐optimized MP3 and MP2.5 with the density‐fitting approximation: An efficient implementation

Efficient implementations of analytic gradients for the orbital‐optimized MP3 and MP2.5 and their standard versions with the density‐fitting approximation, which are denoted as DF‐MP3, DF‐MP2.5, DF‐OMP3, and DF‐OMP2.5, are presented. The DF‐MP3, DF‐MP2.5, DF‐OMP3, and DF‐OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density‐fitted perturbation theory (DF‐MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF‐MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z‐vector equation, back‐transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc‐pCVQZ basis set, is 0.0001–0.0002 Å. © 2017 Wiley Periodicals, Inc.     

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

We present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Theoretical study of the vibrational frequencies of carbon disulfide

A benchmark comparison for different computational methods and basis sets has been presented. In this study, five computational methods (Hartree–Fock (HF), MP2, B3LYP, MPW1MP91, and PBE1PBE) along with 18 basis sets have been applied to optimize the geometry of carbon disulfide (CS₂), and further calculate the vibrational frequencies of the optimized geometries. The differences between the calculated frequencies and corresponding experimental data are used to evaluate the efficiency of each combination of computational method and basis set. The comparison of frequency difference indicates that B3LYP generally gives the best prediction of frequencies for CS₂, whereas the other two density functional theory (DFT) methods, i.e., MPW1PW91 and PBE1PBE, often give parallel results. Although MP2 predicts the frequencies with accuracy almost as good as those from DFT methods, in a particular case, HF calculation outperforms MP2 as well as MPW1PW91 and PBE1PBE for prediction of the frequency of asymmetrical stretching for CS₂. © 2013 Wiley Periodicals, Inc.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.     

Theoretical exploration of the cooperative effect in NMF-NMF-amino acid residue hydrogen bonding system

This paper presents a theoretical study of the cooperative effect in sixteen linearly-arranged trimer systems consisting of N-methylformamide dimer and an extra amino acid residue. These trimer systems, NMF-NMF-AAR, in short, have been systematically investigated by full optimization at B3LYP/cc-pVTZ level and subsequent electronic energy calculations at PBE1PBE/cc-pVTZ, HF/cc-pVTZ and MP2/cc-pVTZ, respectively. Obvious spatial transformation due to energetic factors has been found in almost all the trimers. Systematic analysis in weak interaction energy components has shown that: (1) in these trimer systems, the bonding structure and the cooperative effect combine to determine the stability of both HB1 and HB2. For HB2, the structure of the constituent amino acid residue also plays a crucial role by interfering with the neighboring moieties; (2) the large contribution of the cooperative effect to the overall hydrogen bonding energy has claimed the importance of cooperativity in our systems; (3) the non-hydrogen bonding weak interaction components are found to be non-negligible in these trimer systems; (4) moreover, the cooperative effect between these non-hydrogen bonding components is always found to be positive. The good performances of PBE1PBE and PM6 have been established by comparisons between these methods.     

Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Theoretical study on stabilities of multiple hydrogen bonded dimers

A series of self-constituted multiple hydrogen bonded (MHB) complexes has been investigated systematically by density functional theory (PBE1PBE /6-31G**), the Morokuma energy decomposition method (HF/6-31G**) and MP2 (6-31G** and 6-311++G**) calculation. We have discovered that (i) for doubly hydrogen bonded (DHB) complexes, both the interaction energy and stability increase with the charge transfer energy; (ii) for quadruple hydrogen bonded (QHB) complexes, cooperativity is the most important factor determining stability of the complex: stronger cooperative energy correlates well with larger interaction energy and thus more stable complex and vice versa; (iii) correlation energy plays an important role in intermolecular interactions. The correlation energy, mainly consisting of dispersive energy, also exhibits cooperativity in MHB dimers: positive for M-aadd and generally negative for other complexes.     

Prediction of Henry's law constant of benzene derivatives using quantum chemical continuum‐solvation models

Semiempirical (SM2, SM5.4A, MST‐AM1, COSMO‐AM1) and ab inito (HF/PCM‐vdW, MP2//PCM‐vdW, COSMO‐DFT) dielectric continuum‐solvation models as well as the surface‐tension model SM5.0R are analyzed with respect to predicting Henry's law constant at 25°C using a compound set of benzene and 39 benzene derivatives. Both hydrophilic and hydrophobic compounds are covered with a total variation in Henry's law constant of almost eight orders of magnitude corresponding to 44 kJ/mol, and the data set is selected such that there are cases where subtle changes in the molecular structure result in substantial changes of the free energy of solvation. The calculations with SM2, COSMO‐AM1, and COSMO‐DFT include solution‐phase geometry optimization, and the ab initio results refer to polarized basis sets of double‐zeta quality, with two gradient‐corrected functionals (BPW and BLYP) being used for the DFT‐based models. The results show considerable differences in performance between the different continuum‐solvation models, and among the methods yielding solvation free energies the systematic error ranges from −0.9 kJ/mol (SM5.0R) to 12.1 kJ/mol (MP2//PCM‐vdW). In particular, the nonelectrostatic solvation energy contributions of SM2, SM5.4A, MST‐AM1, and PCM‐vdW do not correlate with each other, and with PCM‐vdW omission of the nonelectrostatic component significantly improves the relative trend. The best statistics after scaling through linear regression are achieved with the electrostatic component of MP2//PCM‐vdW (r=0.94) and with COSMO‐DFT (r=0.93). The discussion includes detailed analyses of pecularities associated with certain functional groups, deviations from the expected relationship between dipole moment and solvation energy, and a simple approach to model dispersion interaction and cavitation energy by surface area terms that differentiate between individual atom types. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 17–34, 2000     

Assessment of density functional theory to calculate the phase transition pressure of ice

To assess the accuracy of density functional theory (DFT) methods in describing hydrogen bonding in condensed phases, we benchmarked their performance in describing phase transitions among different phases of ice. We performed DFT calculations of ice for phases Ih, II, III, VI and VII using BLYP, PW91, PBE, PBE-D, PBEsol, B3LYP, PBE0, and PBE0-D, and compared the calculated phase transition pressures between Ih-II, Ih-III, II-VI, and VI-VII with the 0 K experimental values of Whalley [J. Chem. Phys., 1984, 81, 4087]. From the geometry optimization of many different candidates, we found that the most stable proton orientation as well as the phase transition pressure does not show much functional dependence for the generalized gradient approximation and hybrid functionals. Although all these methods overestimated the phase transition pressure, the addition of van der Waals (vdW) correction using PBE-D and PBE0-D reduced the transition pressure and improved the agreement for Ih-II. On the other hand, energy ordering between VI and VII reversed and gave an unphysical negative transition pressure. Binding energy profiles of a few conformations of water dimers were calculated to understand the improvement for certain transitions and failures for others with the vdW correction. We conclude that vdW dispersion forces must be considered to accurately describe the hydrogen bond in many different phases of ice, but the simple addition of the R(-6) term with a small basis set tends to over stabilize certain geometries giving unphysical ordering in the high density phases.     

The Nature of the Binding of Au, Ag, and Pd to Benzene, Coronene, and Graphene: From Benchmark CCSD(T) Calculations to Plane-Wave DFT Calculations

The adsorption of Ag, Au, and Pd atoms on benzene, coronene, and graphene has been studied using post Hartree-Fock wave function theory (CCSD(T), MP2) and density functional theory (M06-2X, DFT-D3, PBE, vdW-DF) methods. The CCSD(T) benchmark binding energies for benzene-M (M = Pd, Au, Ag) complexes are 19.7, 4.2, and 2.3 kcal/mol, respectively. We found that the nature of binding of the three metals is different: While silver binds predominantly through dispersion interactions, the binding of palladium has a covalent character, and the binding of gold involves a subtle combination of charge transfer and dispersion interactions as well as relativistic effects. We demonstrate that the CCSD(T) benchmark binding energies for benzene-M complexes can be reproduced in plane-wave density functional theory calculations by including a fraction of the exact exchange and a nonempirical van der Waals correction (EE+vdW). Applying the EE+vdW method, we obtained binding energies for the graphene-M (M = Pd, Au, Ag) complexes of 17.4, 5.6, and 4.3 kcal/mol, respectively. The trends in binding energies found for the benzene-M complexes correspond to those in coronene and graphene complexes. DFT methods that use empirical corrections to account for the effects of vdW interactions significantly overestimate binding energies in some of the studied systems.     

Ab initio static and molecular dynamics study of 4-styrylpyridine.

We report an in‐depth theoretical study of 4‐styrylpyridine in its singlet S₀ ground state. The geometries and the relative stabilities of the trans and cis isomers were investigated within density functional theory (DFT) as well as within Hartree–Fock (HF), second‐order Møller–Plesset (MP2), and coupled cluster (CC) theories. The DFT calculations were performed using the B3LYP and PBE functionals, with basis sets of different qualities, and gave results that are very consistent with each other. The molecular structure is thus predicted to be planar at the energy minimum, which is associated with the trans conformation, and to become markedly twisted at the minimum of higher energy, which is associated with the cis conformation. The results of the calculations performed with the post‐HF methods approach those obtained with the DFT methods, provided that the level of treatment of the electronic correlation is high enough and that sufficiently flexible basis sets are used. Calculations carried out within DFT also allowed the determination of the geometry and the energy of the molecule at the biradicaloid transition state associated with the thermal cis?trans isomerization and at the transition states associated with the enantiomerization of the cis isomer and with the rotations of the pyridinyl and phenyl groups in the trans and cis isomers. Car–Parrinello molecular dynamics simulations were also performed at 50, 150, and 300 K using the PBE functional. The studies allowed us to evidence the highly flexible nature of the molecule in both conformations. In particular, the trans isomer was found to exist mainly in a nonplanar form at finite temperatures, while the rotation of the pyridinyl ring in the cis isomer was incidentally observed to take place within ≈1 ps during the simulation carried out at 150 K on this isomer.     

Ab initio reaction path for cisplatin interaction with L‐cysteine and L‐methionine

Ab initio calculations are used to track the reaction pathway of interaction between cisplatin and the sulfur‐containing amino acids cysteine (Cys) and methionine (Met). Structures of all reactive species as well as thermodynamic and kinetic properties were calculated and discussed based on the role played by the level of theory. Twenty‐three different levels of theory were examined including HF, DFT, and perturbation theory at MP2 and MP4(SDQ) orders. The rate constant for a second‐order associative ligand exchange mechanism (k₂) was calculated by means of transition state theory. This quantity is quite sensitive to small fluctuation of activation free energy, therefore is a good benchmark to assess the performance of different methods of calculations. The k₂ values predicted by DFT methods were in best agreement with experiment, found equal to (10²k₂ in M^?1 s^?1) 3.42 for Met (PBE1PBE) and 1.90 for Cys (B3P86). The experimental values are 3.6 and 2.2 for Met and Cys, respectively. The solvent effect plays a primary role to the kinetic properties, accounting for ～30% of the activation Gibbs free energy. The outcomes from the present study promptly show the adequacy of distinct theoretical approaches to describe the reactivity of cisplatin, thus might be useful for further studies involving other Pt(II) complexes. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Ab initio and density functional studies on bonding nature of the N?N bonds in 1,2,5‐trinitroimidazole and 1,2,4,5‐tetranitroimidazole

The bonding nature of the N N bonds in 1,2,5‐trinitroimidazole ( I ) and 1,2,4,5‐tetranitroimidazole ( II ) was examined with various levels of ab initio and density functional (DF) theories. The second‐order Møller–Plesset perturbation method (MP2) with the 6‐31G** basis set has predicted significantly long N N bond lengths in I and II , that is, 1.737 and 1.824 Å, respectively. Two DF theories, BLYP/6‐31G** and BP86/6‐31G**, provided similar results to those of MP2/6‐31G**. On the other hand, Hartree–Fock (HF) calculation with the 6‐311++G** basis set evaluated these bond lengths of I and II to be 1.443 and 1.414 Å, respectively. Bond properties including the bond critical density are strongly dependent on the equilibrium bond length. Thus, accurate prediction of geometric parameters is of particular importance to derive reliable bond properties. Especially, a substantial difference in bonding properties is observed when the electron correlation effect is included. According to our analyses with bonding natures and CHELPG charges at the MP2 level, (1) the N N bonds of I and II appear to have a significant ionic nature, and (2) the 1‐nitro group bears a considerable positive charge and has attractive electrostatic interactions with O atoms of adjacent nitro groups. Although all the theories utilized in this study predict that both I and II are stable in their potential‐energy surfaces, significantly long N N bond lengths calculated with MP2 and DF theories imply a strong hyperconjugation effect, which may explain a tendency to form a salt in these compounds easily. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 145–154, 1999     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k(->) points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 A? from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C(2)H(2))(m)-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α(xx) and γ(xxxx) of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α(xx) and 10(10) for γ(xxxx)). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable.