An examination of density functional theories on isomerization energy calculations of organic molecules

Long-range corrected (LC) density functional theories (DFTs) were applied to the isomerization energy calculations of organic molecules to make clear why conventional DFTs including B3LYP have given poor isomerization reaction energies. Combining with local response dispersion (LRD) method, we performed LC-DFT calculations for the benchmark set of isomerization reactions. Consequently, we found that LC-DFT?+?LRD methods give accurate reaction energies equivalent to up-to-date DFTs containing many semi-empirical parameters. This result indicates that long-range exchange and intramolecular dispersion correlation interactions, which have been neglected in conventional DFTs, play prominent roles in isomerization reactions. However, we also found that these interactions are not sufficient to give accurate isomerization energies especially for cyclization reactions. Considering that Gaussian-attenuated LC-DFTs (LCgau-DFTs) give better isomerization reaction energies than LC-DFTs, we suggested that the isomerization energies will be further improved by correcting the short-range part of exchange functionals in DFT with keeping the whole long-range exchange interactions.     

An examination of density functionals on aldol, Mannich and ��-aminoxylation reaction enthalpy calculations

The reaction enthalpies of aldol, Mannich and ??-aminoxylation reactions were calculated by density functional theory (DFT) using long-range-corrected (LC), hybrid B3LYP and other up-to-date functionals to show why conventional DFT including B3LYP has given poor enthalpies for these reactions. As a result, we found that long-range exchange interactions significantly affect the reaction enthalpies. We therefore proposed that the poor enthalpies of B3LYP are due to its insufficient long-range exchange effect. On the other hand, LC functionals accurately reproduce reaction enthalpies for these reactions. However, we noticed that even LC functionals present poor reaction enthalpies for specific reactions, in which many branches are produced or very small molecules such as methane molecule participate.     

Accelerated long-range corrected exchange functional using a two-gaussian operator combined with one-parameter progressive correlation functional [LC-BOP(2Gau)]

Recently, we proposed a simple yet efficient method for the computation of a long-range corrected (LC) hybrid scheme [LC-DFT(2Gau)], which uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. This method dramatically reduced the computational time while maintaining the improved features of the LC density functional theory (DFT). Here, we combined an LC hybrid scheme using a two-Gaussian attenuating operator with one-parameter progressive correlation functional and Becke88 exchange functional with varying range-separation parameter values [LC-BOP(2Gau) with various μ values of 0.16, 0.2, 0.25, 0.3, 0.35, 0.4, and 0.42] and demonstrated that LC-BOP(2Gau) reproduces well the thermochemical and frontier orbital energies of LC-BOP. Additionally, we revised the scaling factors of the Gaussian multipole screening scheme for LC-DFT(2Gau) to correspond to the angular momentum of orbitals, which decreased the energy deviations from the energy with the no-screening scheme. © 2018 Wiley Periodicals, Inc.     

Reaction energetics on long‐range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies. © 2012 Wiley Periodicals, Inc.     

A density-functional study on pi-aromatic interaction: benzene dimer and naphthalene dimer

The long-range correction (LC) scheme of density-functional theory (DFT) was applied to the calculation of the pi-aromatic interaction of the benzene dimer and naphthalene dimer. In previous calculations, it was confirmed that the LC scheme [Iikura et al., J. Chem. Phys. 115, 3540 (2001)] gives very accurate potential- energy surfaces (PESs) of small van der Waals (vdW) complexes by combining with the Anderson-Langreth-Lundqvist (ALL) vdW correlation functional [Andersson et al., Phys. Rev. Lett. 76, 102 (1996)] (LC-DFT + ALL). In this study, LC-DFT+ALL method was examined by calculating a wide range of PES of the benzene dimer including parallel, T-shaped, and parallel-displaced configurations. As a result, we succeeded in reproducing very accurate PES within the energy deviance of less than 1 kcalmol in comparison with the results of high-level ab initio molecular-orbital methods at all reference points on the PES. It was also found that LC-DFT + ALL gave accurate results independent of exchange-correlation functional used, in contrast with the strong functional dependencies of conventional pure functionals. This indicates that both exchange repulsion and van der Waals attractive interactions should be correctly incorporated in conventional pure functionals in order to calculate accurate pi-aromatic interactions. We also found that LC-DFT + ALL method has a low basis-set dependency in the calculations of pi-aromatic interactions. The present scheme was also successfully applied to the pi,[ellipsis (horizontal)],pi stacking interactions of naphthalene dimer. This may suggest that LC-DFT + ALL method would be a powerful tool in the calculations of large molecules such as biomolecules.     

Simultaneous benchmarking of ground- and excited-state properties with long-range-corrected density functional theory

We present benchmark calculations using several long-range-corrected (LRC) density functionals, in which Hartree-Fock exchange is incorporated asymptotically using a range-separated Coulomb operator, while local exchange is attenuated using an ansatz introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)]. We calculate ground-state atomization energies, reaction barriers, ionization energies, and electron affinities, each as a function of the range-separation parameter mu. In addition, we calculate excitation energies of small- and medium-sized molecules, again as a function of mu, by applying the LRC to time-dependent density functional theory. Representative examples of both pure and hybrid density functionals are tested. On the basis of these results, there does not appear to be a single range-separation parameter that is reasonable for both ground-state properties and vertical excitation energies. Reasonable errors in atomization energies and barrier heights are achieved only at the expense of excessively high excitation energies, at least for the medium-sized molecules, whereas values of mu that afford reasonable excitation energies yield some of the largest errors for ground-state atomization energies and barrier heights in small molecules. Notably, this conclusion is obscured if the database of excitation energies includes only small molecules, as has been the case in previous benchmark studies of LRC functionals.     

First hyperpolarizability of polymethineimine with long-range corrected functionals

Using the long-range corrected (LC) density functional theory (DFT) scheme introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)] and the Coulomb-attenuating model (CAM-B3LYP) of Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], we have calculated the longitudinal dipole moments and static electronic first hyperpolarizabilities of increasingly long polymehtineimine oligomers. For comparison purposes Hartree-Fock (HF), Moller-Plesset perturbation theory (MP2), and conventional pure and hybrid functionals have been considered as well. HF, generalized gradient approximation (GGA), and conventional hybrids provide too large dipole moments for long oligomers, while LC-DFT allows to reduce the discrepancy with respect to MP2 by a factor of 3. For the first hyperpolarizability, the incorrect evolution with the chain length predicted by HF is strongly worsened by BLYP, Perdew-Burke-Ernzerhof (PBE), and also by B3LYP and PBE0. On the reverse, LC-BLYP and LC-PBE hyperpolarizabilities are correctly predicted to be positive (but for the two smallest chains). Indeed, for medium and long oligomers LC hyperpolarizabilities are slightly smaller than MP2 hyperpolarizabilities, as it should be. CAM-B3LYP also strongly improves the B3LYP results, though a bit less impressively for small chain lengths. The present study demonstrates the efficiency of long-range DFT, even in very pathological cases.     

Insight and performance of LC-DFT vs DFT in the NMR shielding and chemical shift calculations: Case of CHClCH?CF3

Fifteen density functional theory (DFT) methods and fifteen long-range corrected density functional theory (LC-DFT) methods were used in the present work to assess nuclear magnetic resonance parameters such as nuclear shielding constant (NSC), nuclear chemical shift (NCS), and nuclear anisotropic shielding constant (NAS). These different methods were associated with the full basis set 6-311++G(3df,3pd). The gauge-independent atomic orbital was used for the calculation of nuclear shielding tensors of the nuclei contained in the stereoisomers cis- and trans-CHClCHCF₃. Thus, the effects of LC are clearly observed for heavy nuclei (¹³C, ¹⁹F, ³⁵Cl). The results of NSC, NCS, and NAS from DFT are better described than LC-DFT with regard to the KT3 method. Moreover, the results from the LC-DFT are better described than the standard DFT with regard to CCSD(T). Based on the latter method used as the benchmark, the NSCs of nuclei are well fitted by the competitive functionals LC-TPSSTPSS and LC-PKZBPKZB. In the particular case of the trans-isomer, mPWPKZB was found to be the best method. For the NCSs, the more accurate methods include the latter two LC functionals and the non-LC functionals TPSSTPSS and mPWPKZB. The accuracy of NAS depends strongly on the nuclei. Thus, CAM-B3LYP describes it well for ¹⁹F and LC-PKZBPKZB for ³⁵Cl. The rest of nuclei are well fitted by all the methods except ¹³C₁ and ¹³C₂, which are better reproduced by the LC-DFT except the LC-PKZBPKZB, LC-TPSSTPSS, and CAM-B3LYP functionals.     

Assessment of the efficiency of long-range corrected functionals for some properties of large compounds

Using the long-range correction (LC) density functional theory (DFT) scheme introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)] and the Coulomb-attenuating model (CAM-B3LYP) of Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], we have calculated a series of properties that are known to be poorly reproduced by standard functionals: Bond length alternation of pi-conjugated polymers, polarizabilities of delocalized chains, and electronic spectra of extended dyes. For each of these properties, we present cases in which traditional hybrid functionals do provide accurate results and cases in which they fail to reproduce the correct trends. The quality of the results is assessed with regard to experimental values and/or data arising from electron-correlated wave function approaches. It turns out that (i) both LC-DFT and CAM-B3LYP provide an accurate bond length alternation for polyacetylene and polymethineimine, although for the latter they decrease slightly too rapidly with chain length. (ii) The LC generalized gradient approximation and MP2 polarizabilities of long polyphosphazene and polymethineimine oligomers agree almost perfectly. In the same way, CAM-B3LYP corrects the major part of the B3LYP faults. (iii) LC and CAM techniques do not help in correcting the nonrealistic evolution with chain length of the absorption wavelengths of cyanine derivatives. In addition, though both schemes significantly overestimate the ground to excited state transition energy of substituted anthraquinone dyes, they provide a more consistent picture once a statistical treatment is performed than do traditional hybrid functionals.     

Are calculated enthalpies of formation sometimes more reliable than experimental? A test on alkyl substituted benzoic acids

Energies of 20 alkyl-substituted benzoic acids were calculated at the levels B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) and MP2/6-311+G(d,p)//MP2/6-311+G(d,p); the pertinent enthalpies at 298 K were calculated at the same levels. Comparison with experimental enthalpies of formation Delta(f)H degrees (g)(298) was carried out in terms of isodesmic reactions, that is, in the relative values. Of the four calculated quantities, the DFT enthalpies yielded best correlation with the standard deviation of 2.1 kJ mol(-1), near to the experimental uncertainty; the DFT energies are only slightly worse and the MP2 enthalpies or energies much worse. However, the DFT method overestimated systematically the substituent effects and had to be calibrated. Comparison with the experimental gas-phase acidities was less telling and the fit was worse because both methods overestimated the substituent effects. Extending the base in selected examples did not give better results. Although the systematic deviations are evidently due to the imperfections of the theoretical models, individual big deviations should be attributed to experimental errors or to the abnormal behavior of certain compounds at the experimental conditions. From this point of view, three examples of the so-called long-range effect claimed in the case of different benzoic acid derivatives, always for substituents in the meta position, must be refused as unproven because the experimental energies were not confirmed by calculations.     

Assessment of the OLYP and O3LYP density functionals for first-row transition metals

We have investigated the performance of the OLYP and O3LYP density functionals for predicting atomic excitation energies and ionization potentials, and bond dissociation energies, geometries, and vibrational frequencies for selected first-row transition metal compounds, including hydrides (MH) and singly charged methylene and methyl cations. The OLYP and O3LYP functionals are similar to the well-known BLYP and B3LYP functionals, respectively, but use a new optimized exchange functional (OPTX) developed by Handy and Cohen (Mol Phys 2001, 99, 403) in place of the standard B88 exchange. A previous study by us on organic reactions (J Chem Phys 2002, 117, 1331) indicated that both OLYP and O3LYP gave results for heats of reaction and barrier heights that were overall superior to those using the popular B3LYP functional. For transition metals, however, although OLYP is overall superior to BLYP for molecular calculations, it is inferior to B3LYP. O3LYP provides results for molecules of about the same quality as B3LYP. For atomic excitation and 4s ionization energies, unless relativistic effects are included, OLYP and O3LYP are clearly worse than both BLYP and B3LYP. There is thus no real incentive to use either OLYP or O3LYP in place of B3LYP for calculations involving first-row transition metals.     

Water cluster anions studied by the long-range corrected density functional theory

Long-range corrected density functional theory (LC-DFT) is applied to a series of small water cluster anions(n= 2-6) to compute their vertical detachment energies (VDEs). The LC scheme is shown to eliminate an unphysical overestimation of the electron-water attraction in the hybrid functional by properly accounting for the long-range exchange repulsions. It is shown that a correct correlation energy behavior for a rapidly varying density is also important for describing a spatially extent, excess electron. The one-parameter progressive (OP) correlation functional, which satisfies this condition, leads to a remarkable improvement in the calculated VDE over the conventional one. The LC-BOP method produces highly accurate VDEs with a mean absolute deviation of 13.8 meV from the reference CCSD(T) results, reducing the error of B3LYP by more than 15 times. LC-BOP is found to be more accurate than MP2 which yields an excess electron underbound by 43.6 meV. The effect of basis sets on the calculated VDE is also examined. The aug-cc-pVDZ basis set with an extra diffuse function is found to be more accurate and reliable than the extended Pople-type basis sets used in the previous works. The extrapolation of the calculated VDE of different electron binding motifs is compared with the VDEs of experimentally observed three isomers (Verlet, J. R. R.; Bragg,A. E.; Kammrath, A.; Cheshnovsky, O.; Neumark, D. M. Science 2005, 307, 93).     

Electronic structure benchmark calculations of CO2 fixing elementary chemical steps in RuBisCO using the projector-based embedding approach

Ribulose 1,5-bisphosphate carboxylase-oxygenase (RuBisCO) is the main enzyme involved in atmospheric carbon dioxide (CO₂) fixation in the biosphere. This enzyme catalyzes a set of five chemical steps that take place in the same active-site within magnesium (II) coordination sphere. Here, a set of electronic structure benchmark calculations have been carried out on a reaction path proposed by Gready et al. by means of the projector-based embedding approach. Activation and reaction energies for all main steps catalyzed by RuBisCO have been calculated at the MP2, SCS-MP2, CCSD, and CCSD(T)/aug-cc-pVDZ and cc-pVDZ levels of theory. The treatment of the magnesium cation with post-HF methods is explored to determine the nature of its involvement in the mechanism. With the high-level ab initio values as a reference, we tested the performance of a set of density functional theory (DFT) exchange-correlation (xc) functionals in reproducing the reaction energetics of RuBisCO carboxylase activity on a set of model fragments. Different DFT xc-functionals show large variation in activation and reaction energies. Activation and reaction energies computed at the B3LYP level are close to the reference SCS-MP2 results for carboxylation, hydration and protonation reactions. However, for the carbon–carbon bond dissociation reaction, B3LYP and other functionals give results that differ significantly from the ab initio reference values. The results show the applicability of the projector-based embedding approach to metalloenzymes. This technique removes the uncertainty associated with the selection of different DFT xc-functionals and so can overcome some of inherent limitations of DFT calculations, complementing, and potentially adding to modeling of enzyme reaction mechanisms with DFT methods.     

Spin-forbidden ligand binding to the ferrous-heme group: ab initio and DFT studies

The potential energy surfaces (PESs) and associated energy barriers that characterize the spin-forbidden recombination reactions of the gas-phase ferrous deoxy-heme group with CO, NO, and H2O ligands have been calculated using density functional theory (DFT). The bond energy for binding of O2 has also been calculated. Extensive large basis set CCSD(T) calculations on two small models of the heme group have been used to calibrate the accuracy of different DFT functionals for treating these systems. Pure functionals are shown to overestimate the stability of the low-spin forms of the deoxy-heme model, and to overestimate the binding energy of H2O and CO, whereas hybrid functionals such as B3PW91 and B3LYP yield accurate results. Accordingly, the latter functionals have been used to explore the PESs for binding. CO binding is found to involve a significant barrier of ca. 3 kcal mol-1 due to the need to change from the deoxy-heme quintet ground state to the bound singlet state. Binding of water does not involve a barrier, but the resulting bond is weak and may be further weakened in the protein environment, which should explain why water binding is not usually observed in heme proteins such as myoglobin. NO binding involves a low barrier, which is consistent with observed rapid geminate recombination. The calculated bond energies are in good agreement with previous reported values and in fair agreement with experiment for CO and O2. The value for NO is significantly lower than the experimentally derived bond energy, suggesting that B3LYP is less accurate in this case.     

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

Theoretical study of the nitroalkane thermolysis. 1. Computation of the formation enthalpy of the nitroalkanes, their isomers and radical products

The gas phase enthalpies of formation of mono-, di-, tri-, tetranitromethane and nitroethane, as well as of their nitrite and aci-form isomers were calculated using different multilevel (G2, G3, G2M(CC5)) and density functional theory (DFT)-based (B3LYP, MPW1B95 and MPWB1K) techniques. The enthalpies of the C-N bond dissociation and isomerization of these nitroalkanes were also calculated. The calculated values of the formation and reaction enthalpies were compared with the experimental data when these data were available. It was found that only the G3 procedure gave accurate (within 1 kcal/mol) results for the formation enthalpy of nitroalkanes, their isomers, and radical products. The G3 procedure and two new hybrid meta DFT methods proposed by Truhlar's group (Zhao, Y.; Truhlar, D. J. Phys. Chem. A 2004, 108, 6908) showed good results for the reaction enthalpies of the nitromethane isomerization and the C-N bond dissociation. Our calculation results were used to analyze thermodynamics of the dissociation and isomerization reactions of the poly nitro-substituted methanes.     

Theoretical Studies on the Reaction Mechanism of 1-Chloroethane with Hydroxyl Radical

The reaction mechanism of 1-chloroethane with hydroxyl radical has been inves- tigated by using density functional theory (DFT) B3LYP/6-31G (d, p) method. All bond dissociation enthalpies were computed at the same theoretical level. It was found that hydrogen abstraction pathway is the most favorable. There are two hydrogen abstraction pathways with activation barriers of 0.630 and 4.988 kJ/mol, respectively, while chlorine abstraction pathway was not found. It was observed that activation energies have a more reasonable correlation with the reaction enthalpy changes (△Hr) than with bond dissociation enthalpies (BDE).