Long-range corrected density functional calculations of chemical reactions: redetermination of parameter

Chemical reaction calculations were carried out using the long-range correction (LC) scheme, which improves long-range exchange effects in density functional theory (DFT) [J. Chem. Phys. 115, 3540 (2001); 120, 8425 (2004)]. A new determination of the LC scheme parameter mu was made by a root mean square fit of the percent error in calculated atomization energies. As a result, the parameter mu was optimized as 0.47, which is higher than the previous one (mu=0.33). Using this new parameter mu, LC-DFT was firstly applied to geometry optimizations of the G2 benchmark set molecules. Consequently, this new LC-DFT gave more accurate bond lengths and bond angles than previous LC-DFT and hybrid B3LYP results. Following this result, the authors calculated reaction barrier height energies of benchmark reaction sets, which have been underestimated in conventional DFT calculations. Calculated results showed that LC-DFT provided much more accurate barrier height energies with errors less than half those of previous LC-DFT and B3LYP studies. To test the general validity of the new LC-DFT, the authors finally calculated reaction enthalpies. As a result, they found that the LC scheme using the new mu clearly improved the accuracy of calculated enthalpies. The authors therefore conclude that the insufficient inclusion of long-range exchange effects is responsible for the underestimation of reaction barriers in DFT calculations and that LC-DFT using the new parameter is a powerful tool for theoretically investigating chemical reactions.     

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.     

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.     

Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.     

The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the ‘Right Answer for the Right Reason’

Reliable thermochemical measurements and theoretical predictions for reactions involving large transition metal complexes in which long-range intramolecular London dispersion interactions contribute significantly to their stabilization are still a challenge, particularly for reactions in solution. As an illustrative and chemically important example, two reactions are investigated where a large dipalladium complex is quenched by bulky phosphane ligands (triphenylphosphane and tricyclohexylphosphane). Reaction enthalpies and Gibbs free energies were measured by isotherm titration calorimetry (ITC) and theoretically ‘back-corrected’ to yield 0 K gas-phase reaction energies (ΔE). It is shown that the Gibbs free solvation energy calculated with continuum models represents the largest source of error in theoretical thermochemistry protocols. The (‘back-corrected’) experimental reaction energies were used to benchmark (dispersion-corrected) density functional and wave function theory methods. Particularly, we investigated whether the atom-pairwise D3 dispersion correction is also accurate for transition metal chemistry, and how accurately recently developed local coupled-cluster methods describe the important long-range electron correlation contributions. Both, modern dispersion-corrected density functions (e.g., PW6B95-D3(BJ) or B3LYP-NL), as well as the now possible DLPNO-CCSD(T) calculations, are within the ‘experimental’ gas phase reference value. The remaining uncertainties of 2–3 kcal mol⁻¹ can be essentially attributed to the solvation models. Hence, the future for accurate theoretical thermochemistry of large transition metal reactions in solution is very promising.     

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.     

Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn-Sham method

The long-range correction (LC) scheme for the exchange functional of density-functional theory (DFT) was combined with the coupled-perturbed Kohn-Sham (CPKS) method to calculate nonlinear optical response properties. By using this LC-CPKS method, we calculated the hyperpolarizabilities of typical molecules and the dipole moments, polarizabilities, and hyperpolarizabilities of push-pull pi-conjugated systems: p-nitroaniline, 4-amino-4'-nitrostilbene, and alpha,omega-nitroaminopolyenes. It was found that the LC scheme clearly improved the calculation of these optical properties for all of these systems, which have been significantly overestimated by conventional DFTs. We therefore concluded that the long-range exchange interaction played an important role in calculating the optical properties using the DFT formalism.     

Long‐range corrected density functionals combined with local response dispersion: A promising method for weak interactions

Density functional theory, in general, is considered to underestimate the weak van der Waals type of intermolecular interactions. We optimized parameters of the local response dispersion (LRD) method applied to the long‐range corrected exchange‐correlation functionals (LC‐BOP12+LRD and LCgau‐BOP+LRD) on the interaction energy for the complexes in the recently compiled S66 database and found to be comparable with the high‐level wave function‐based methods reported in ?ezá? et al. (J. Chem. Theory Comput. 2011 , 7, 2427). Our calculations with the S66 intermolecular complexes at equilibrium geometries suggests that the LC‐BOP12+LRD and LCgau‐BOP+LRD are well‐balanced and lower cost alternatives to the methods reported in the database. Further, test on the S66X8 database (with eight nonequilibrium points) and the HBC6 and NBC10 database shows LC+LRD method with newly optimized parameters is a promising candidate for dealing such weak interactions. Finally, the new parameterized LC+LRD method was tested on X40 benchmark halogenated complexes.Copyright © 2013 Wiley Periodicals, Inc.     

Calculations of long-range potential wells for highly excited homonuclear and heteronuclear alkali dimers

The weakly bound long-range potential curves between a highly excited alkali atom M(*)(n(e)s) and a ground state alkali atom M(n(g)s) are calculated using simple but reasonably accurate models for long-range dispersion and exchange interactions for all homonuclear and heteronuclear combinations. For K(2), where experimental results are available, the agreement is quite good (binding energies of observed vibrational levels within approximately 10%). We find that at least a zero-point vibrational level occurs for n(e)-n(g)相似文献   

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).     

Model potential approaches for describing the interaction of excess electrons with water clusters: incorporation of long-range correlation effects

In this work we focus on the binding of excess electrons to water clusters, a problem for which dispersion interactions, which originate from long-range correlation effects, are especially important. Two different model potential approaches, one using quantum Drude oscillators and the other using polarization potentials, are investigated for describing the long-range correlation effects between the weakly bound excess electron and the more tightly bound electrons of the monomers. We show that these two approaches are related in that the polarization potential models can be derived from the quantum Drude model approach by use of an adiabatic separation between the excess electron and the Drude oscillators. The model potential approaches are applied to clusters containing up to 45 water monomers. Where possible, comparison is made with the results of ab initio electronic structure calculations. Overall, the polarization potential approach is found to give electron binding energies in good agreement with those from the Drude model and ab initio calculations, with the greatest discrepancies being found for "cavity-bound" anion states.     

An improved theoretical approach to the empirical corrections of density functional theory

An empirical correction to density functional theory (DFT) has been developed in this study. The approach, called correlation corrected atomization–dispersion (CCAZD), involves short- and long-range terms. Short-range correction consists of bond (1,2-) and angle (1,3-) interactions, which remedies the deficiency of DFT in describing the proto-branching stabilization effects. Long-range correction includes a Buckingham potential function aiming to account for the dispersion interactions. The empirical corrections of DFT were parameterized to reproduce reported ΔH _f values of the training set containing alkane, alcohol and ether molecules. The ΔH _f of the training set molecules predicted by the CCAZD method combined with two different DFT methods, B3LYP and MPWB1K, with a 6-31G* basis set agreed well with the experimental data. For 106 alkane, alcohol and ether compounds, the average absolute deviations (AADs) in ΔH _f were 0.45 and 0.51 kcal/mol for B3LYP- and MPWB1K-CCAZD, respectively. Calculations of isomerization energies, rotational barriers and conformational energies further validated the CCAZD approach. The isomerization energies improved significantly with the CCAZD treatment. The AADs for 22 energies of isomerization reactions were decreased from 3.55 and 2.44 to 0.55 and 0.82 kcal/mol for B3LYP and MPWB1K, respectively. This study also provided predictions of MM4, G3, CBS-QB3 and B2PLYP-D for comparison. The final test of the CCAZD approach on the calculation of the cellobiose analog potential surface also showed promising results. This study demonstrated that DFT calculations with CCAZD empirical corrections achieved very good agreement with reported values for various chemical reactions with a small basis set as 6-31G*.     

On Koopmans' theorem in density functional theory

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.     

Quantum dynamics study on multichannel dissociation and isomerization reactions of formaldehyde

We study quantum dynamics of the multichannel reactions of H(2)CO including the molecular and radical dissociation channels as well as the isomerization ones, H(2)CO-->trans-HCOH and trans-HCOH-->cis-HCOH. For this purpose, the previously developed potential energy function [T. Yonehara and S. Kato, J. Chem. Phys. 117, 11131 (2002)] is refined to give accurate transition state energies and to describe the radical dissociation channel. The cumulative reaction probabilities for the molecular dissociation and two isomerization channels are calculated by using the full Watson Hamiltonian. We also carry out wave packet dynamics calculations starting from the transition state region for the molecular dissociation. A contracted basis set for the angular coordinates is constructed to reduce the size of dynamics calculations. The intramolecular vibrational relaxation dynamics is found to be fast and almost complete within 300 fs. Using the energy filtered wave functions, the time propagation of HCOH population is obtained in the energy range from 81 to 94 kcal/mol. The branching ratio of the radical product is estimated by calculating the time dependent reactive fluxes to the molecular and radical dissociation products.     

The performance and relationship among range-separated schemes for density functional theory

The performance and relationship among different range-separated (RS) hybrid functional schemes are examined using the Coulomb-attenuating method (CAM) with different values for the fractions of exact Hartree-Fock (HF) exchange (α), long-range HF (β), and a range-separation parameter (μ), where the cases of α + β = 1 and α + β = 0 were designated as CA and CA0, respectively. Attenuated PBE exchange-correlation functionals with α = 0.20 and μ = 0.20 (CA-PBE) and α = 0.25 and μ = 0.11 (CA0-PBE) are closely related to the LRC-ωPBEh and HSE functionals, respectively. Time-dependent density functional theory calculations were carried out for a number of classes of molecules with varying degrees of charge-transfer (CT) character to provide an assessment of the accuracy of excitation energies from the CA functionals and a number of other functionals with different exchange hole models. Functionals that provided reasonable estimates for local and short-range CT transitions were found to give large errors for long-range CT excitations. In contrast, functionals that afforded accurate long-range CT excitation energies significantly overestimated energies for short-range CT and local transitions. The effects of exchange hole models and parameters developed for RS functionals for CT excitations were analyzed in detail. The comparative analysis across compound classes provides a useful benchmark for CT excitations.     

Bimolecular reactions of vibrationally excited molecules. Roaming atom mechanism at low kinetic energies

Quasiclassical trajectory calculations have been performed for the H + H'X(v) → X + HH' abstraction and H + H'X(v) → XH + H' (X = Cl, F) exchange reactions of the vibrationally excited diatomic reactant at a wide collision energy range extending to ultracold temperatures. Vibrational excitation of the reactant increases the abstraction cross sections significantly. If the vibrational excitation is larger than the height of the potential barrier for reaction, the reactive cross sections diverge at very low collision energies, similarly to capture reactions. The divergence is quenched by rotational excitation but returns if the reactant rotates fast. The thermal rate coefficients for vibrationally excited reactants are very large, approach or exceed the gas kinetic limit because of the capture-type divergence at low collision energies. The Arrhenius activation energies assume small negative values at and below room temperature, if the vibrational quantum number is larger than 1 for HCl and larger than 3 for HF. The exchange reaction also exhibits capture-type divergence, but the rate coefficients are larger. Comparisons are presented between classical and quantum mechanical results at low collision energies. At low collision energies the importance of the exchange reaction is enhanced by a roaming atom mechanism, namely, collisions leading to H atom exchange but bypassing the exchange barrier. Such collisions probably have a large role under ultracold conditions. The calculations indicate that for roaming to occur, long-range attractive interaction and small relative kinetic energy in the chemical reaction at the first encounter are necessary, which ensures that the partners can not leave the attractive well. Large orbital angular momentum of the primary products (equivalent to large rotational excitation in a unimolecular reaction) is favorable for roaming.     

The mechanism of proton exchange: guided ion beam studies of the reactions, H(H2O)n+ (n=1-4)+D2O and D(D2O)n+ (n=1-4)+H2O

Reactions of protonated water clusters, H(H(2)O)(n) (+) (n=1-4) with D(2)O and their "mirror" reactions, D(D(2)O)(n) (+) (n=1-4) with H(2)O, are studied using guided-ion beam mass spectrometry. Absolute reaction cross sections are determined as a function of collision energy from thermal energy to over 10 eV. At low collision energies, we observe reactions in which H(2)O and D(2)O molecules are interchanged and reactions where H-D exchange has occurred. As the collision energy is increased, the H-D exchange products decrease and the water exchange products become dominant. At high collision energies, processes in which one or more water molecules are lost from the reactant ions become important, with simple collision-induced dissociation processes, i.e., those without H-D exchange, being dominant. Threshold energies of endothermic channels are measured and used to determine binding energies of the proton bound complexes, which are consistent with those determined by thermal equilibrium measurements and previous collision-induced dissociation studies. A kinetic scheme that relies only on the ratio of isomerization and dissociation rate constants successfully accounts for the kinetic energy dependence observed in the branching ratios for H-D and water exchange products in all systems. Rice-Ramsperger-Kassel-Marcus theory and ab initio calculations confirm the feasibility and establish the details of this kinetic model.