New generalized gradient approximation functionals

Spectroscopy and dynamics of A [2B1] allyl radical

The A [(2)B1] <--X [(2)A2] band system between 380 and 420 nm was observed in a supersonic jet expansion. The allyl radical was found to dissociate following electronic excitation, releasing a hydrogen atom. Monitoring the appearance of the hydrogen atom photoproduct as a function of the excitation laser wavelength, similar spectral features are observed as in earlier absorption experiments. Time- and frequency-resolved photoionization of the hydrogen atom product provides information on the unimolecular dissociation dynamics. The measured dissociation rates and kinetic energy releases of both allyl radical, C3H5, and partially deuterated allyl radical, C3DH4, suggest direct loss of the central hydrogen atom, leading to allene as the major product.

Assessment of the performance of density-functional methods for calculations on iron porphyrins and related compounds

The behaviors of a large number of GGA, meta-GGA, and hybrid-GGA density functionals in describing the spin-state energetics of iron porphyrins and related compounds have been investigated. There is a large variation in performance between the various functionals for the calculations of the high-spin state relative energies. Most GGA and meta-GGA functionals are biased toward lower-spin states and so fail to give the correct ground state for the high-spin systems, for which the meta-GGA functionals show more or less improvement over the GGA ones. The GGA functionals that use the OPTX correction for exchange show remarkably high performance for calculating the high-spin state energetics, but their results for the intermediate-spin states are somewhat questionable. A heavily parameterized GGA functional, HCTH/407, provides results which are in qualitative agreement with the experimental findings for the iron porphyrins [FeP, FeP(Cl), FeP(THF)2], but its relative energies for the high-spin states are probably somewhat too low. The high-spin state relative energies are then even more underestimated by the corresponding meta-GGA functional tau-HCTH. For the hybrid-GGA functionals, the Hartree-Fock (HF)-type (or exact) exchange contribution strongly stabilizes the high-spin states, and so the performance of such functionals is largely dependent upon the amount of the HF exchange admixture in them. The B3LYP, B97, B97-1, and tau-HCTH-hyb functionals are able to provide a satisfactory description of the energetics of all the systems considered.

Semiempirical GGA-type density functional constructed with a long-range dispersion correction

A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

Bayesian error estimation in density-functional theory

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.

Cisplatin interaction with cysteine and methionine, a theoretical DFT study

Interactions of hydrated cisplatin complexes with sulphur-containing amino acids cysteine and methionine were explored. The square-planar cis-[Pt(NH3)2(H2O)X]+ complexes (where X=Cl- and OH-) were chosen as mono- and dihydrated reactants. Calculations using density functional theory (DFT) techniques with B3LYP functional were performed. The isolated molecules and the supermolecular approaches were employed for the determination of the reaction energies. Bond dissociation energies (BDE) were estimated in the model of isolated molecules and supermolecules were used for the determination of the association energies between the two interacting parts. Formation of monodentate complexes by replacing the aqua-ligand with the S, N, and O-sites of both amino acids represents an exothermic process. The highest BDE was found in cysteine structures for the Pt-S coordination. The bonding energy is about 114 kcal/mol, which is comparable with cisplatin-guanine adducts. Analogous BDE for methionine complexes is smaller by about 40 kcal/mol. This correlates well with the known fact that cysteine forms irreversible cisplatin adducts while similar adducts in the methionine case are reversible. The formation of chelate structures is an exothermic reaction only for the hydroxo-form of reactants in the supermolecular approach where additional association interactions between the released water and chelate molecules sufficiently stabilize the final product.

About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error

The effect of the correction of the self-interaction error on the calculation of exchange coupling constants with methods based on density-functional theory has been tested in simple model systems. The inclusion of the self-interaction correction cancels the nondynamical correlation energy contributions simulated by the commonly used functionals. Hence, such correction should be important in the accurate determination of exchange coupling constants. We have also tested several recent functionals to calculate exchange coupling constants in transition-metal complexes, such as meta-GGA functionals or new formulations of hybrid functionals. The influence of the basis set and of the use of pseudopotentials on the calculated J values has also been evaluated for a Fe(III) dinuclear complex in which the paramagnetic centers bear several unpaired electrons.

Oxidative Addition of the Fluoromethane C−F Bond to Pd. An ab Initio Benchmark and DFT Validation Study

We have computed a state-of-the-art benchmark potential energy surface (PES) for two reaction pathways (oxidative insertion, OxIn, and S(N)2) for oxidative addition of the fluoromethane C-F bond to the palladium atom and have used this to evaluate the performance of 26 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing these reactions. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods (HF, MP2, CCSD, CCSD(T)) in combination with a hierarchical series of seven Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -5.3 (-6.1) kcal/mol for the formation of the reactant complex, 27.8 (25.4) kcal/mol for the activation energy for oxidative insertion (OxIn) relative to the separate reactants, 37.5 (31.8) kcal/mol for the activation energy for the alternative S(N)2 pathway, and -6.4 (-7.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.4-2.7 kcal/mol and errors in activation energies ranging from 0.3 to 2.8 kcal/mol. The B3LYP functional compares very well with a slight underestimation of the overall barrier for OxIn by -0.9 kcal/mol. For comparison, the well-known BLYP functional underestimates the overall barrier by -10.1 kcal/mol. The relative performance of these two functionals is inverted with respect to previous findings for the insertion of Pd into the C-H and C-C bonds. However, all major functionals yield correct trends and qualitative features of the PES, in particular, a clear preference for the OxIn over the alternative S(N)2 pathway.

The effect of proton disorder on the structure of ice-Ih: A theoretical study

A precise and accurate measurement of the crystal structure of ice-Ih is hindered by its disordered H-bond network. In this work, we carried out first-principle calculations to study the effects of H-bond topology on the structure of ice-Ih with emphasis on the molecular geometry of water and the distortion in oxygen lattice. An analytic algorithm based on group and graph theory is employed to enumerate all possible configurations in a given unit cell and to select a set of structures for detailed examinations. In total we have studied more than 60 ice-Ih structures in a hexagonal unit cell of 48 water molecules by quantum-chemical methods and found a significant amount of static distortion in the oxygen positions from their crystallographic positions which is in good agreements with highly significant higher-order terms obtained from both x-ray and neutron-diffraction data. Much debated structural information such as H-O-H angle and O-H bond length is found to be 106.34+/-0.36 degrees and 0.9997+/-0.0008 A, compared to experimental value of 106.6+/-1.5 degrees and 0.986+/-0.005 A. Detailed benchmarking calculations were carried out to gauge the influence of using different exchange and correlation functionals, pseudopotentials, and unit-cell sizes. Our results have proven that first-principle methods are useful complementary tools to experiments, especially for cases in which experimental accuracy is limited by intrinsic orientational disorder.

Oxidative addition of the ethane CC bond to Pd. Anab initiobenchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.

Assessment of Recently Developed Multicoefficient Strategies for the Treatment of π-Conjugated Molecules

Newly developed hybrid functionals (MPW1k and BB1k) have been systematically applied for the description of conjugation effects in organic molecules. These functionals are also used as part of the recently developed general-purpose multicoefficient methods MC3MPW and MC3BB. The performance of the various approaches is compared not only for relative energies but also through the calculation of torsion energy profiles for critical comparison with available reference data; thus, a numerical criterion depending on local behavior could be correspondingly defined. The results show that MC3-based methods are very accurate when faced to other approaches having comparable computational cost; thus, paving the way toward new applications and achievements in the field of conjugated materials.

C5H4?BR2 Bending in Ferrocenylboranes: A Delocalized Through-Space Interaction Between Iron and Boron

A comparison of the molecular structures of mono-, di- and tetraborylated ferrocenes [Fc{B(R(1))(R(2))}] (R(1)/R(2)=Br/Br, Br/Fc, Br/Me, Me/Me, Me/OH, OMe/OMe), 1,1'-[fc{B(R(1))(R(2))}(2)] (R(1)/R(2)=Br/Br, Br/Me, OMe/OMe), and 1,1',3,3'-[Fe{C(5)H(3)(BMe(2))(2)}(2)] revealed the boryl substituent(s) to be bent out of the Cp ring plane towards the iron center. The corresponding dip angle alpha* decreases with decreasing Lewis acidity of the boron atom and with increasing degree of borylation at the ferrocene core. This trend is well reproduced by DFT calculations (including [FcBH(2)], not yet accessible experimentally). A Bader analysis of the electron density topology of [FcBH(2)] (alpha*=26.5 degrees ; BP86/TZVP) clearly showed that there is no direct iron-boron bonding in this compound. Instead, strongly delocalized orbital interactions have been identified that involve the boron p orbital, C(ipso) of the adjacent Cp ring, d orbitals at iron, and a through-space interaction with the second Cp ring. A second important factor is attractive electrostatic interactions, which are enhanced upon ligand bending. Cyclic voltammetric measurements on the series [FcBMe(2)], 1,1'-[fc(BMe(2))(2)], and 1,1',3,3'-[Fe{C(5)H(3)(BMe(2))(2)}(2)] indicate a substantial anodic shift in the oxidation potential of the central iron atom upon introduction of BMe(2) substituents. Addition of 4-dimethylaminopyridine (DMAP) does not just counterbalance this effect, but leads to a cathodic shift of the Fe(II)/Fe(III) redox transition far beyond the half-wave potential of parent ferrocene. In the Mossbauer spectra, a continuous decrease in the quadrupole splitting (QS) is observed upon going from parent ferrocene to [FcBMe(2)], to 1,1'-[fc(BMe(2))(2)], and to 1,1',3,3'-[Fe{C(5)H(3)(BMe(2))(2)}(2)]. In contrast, no significant differences are found between the QS values of ferrocene, [Fc(BMe(2)-DMAP)], and 1,1'-[fc(BMe(2)-DMAP)(2)].

The influence of temperature and density functional models in ab initio molecular dynamics simulation of liquid water

The performance of density functional theory methods for the modeling of condensed aqueous systems is hard to predict and validation by ab initio molecular simulation of liquid water is absolutely necessary. In order to assess the reliability of these tests, the effect of temperature on the structure and dynamics of liquid water has been characterized with 16 simulations of 20 ps in the temperature range of 280-380 K. We find a pronounced influence of temperature on the pair correlation functions and on the diffusion constant including nonergodic behavior on the time scale of the simulation in the lower temperature range (which includes ambient temperature). These observations were taken into account in a consistent comparison of a series of density functionals (BLYP, PBE, TPSS, OLYP, HCTH120, HCTH407). All simulations were carried out using an ab initio molecular dynamics approach in which wave functions are represented using Gaussians and the density is expanded in an auxiliary basis of plane waves. Whereas the first three functionals show similar behavior, it is found that the latter three functionals yield more diffusive dynamics and less structure.

The importance of spin-orbit coupling and electron correlation in the rationalization of the ground state of the CUO molecule

We present calculations at the relativistic coupled cluster theory that predict the (1)Sigma(0) (+) ground state of CUO to lie 58.2 kJ/mol below the first excited state, (3)Phi(2). This can be contrasted with the outcome of earlier density functional theory and complete active space second order perturbation theory (CASPT2) calculations that both predicted a (3)Phi(2) ground state upon inclusion of spin-orbit coupling in the calculations. Our result gives further justification to the interpretation of the measured frequency shifts of this species in various noble gas matrices as being caused by significant interaction between the uranium and the heavier noble gas atoms.

Development of density functionals for thermochemical kinetics

A density functional theory exchange-correlation functional for the exploration of reaction mechanisms is proposed. This functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a general-purpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct "back" the excess exact exchange mixing for ground-state properties, possibly simulating variable exchange.

Assessment of recently developed exchange-correlation functionals for the description of torsion potentials in π-conjugated molecules

Newly developed exchange-correlation functionals in density functional theory (DFT) have been applied to describe conjugation effects in organic molecules. The performance of the various approaches is assessed through the calculation of torsion energy profiles and their critical comparison with available experimental data. Our results indicate that the OPTX-B95 exchange-correlation functional as well as its corresponding hybrid versions perform better than the well-established BLYP or B3LYP schemes when dealing with pi-conjugated molecules. In contrast, the recently introduced VSXC functional is not as reliable as other DFT methods for the systems examined here.

Dispersion corrections to density functionals for water aromatic interactions

We investigate recently published methods for extending density functional theory to the description of long-range dispersive interactions. In all schemes an empirical correction consisting of a C6r(-6) term is introduced that is damped at short range. The coefficient C6 is calculated either from average molecular or atomic polarizabilities. We calculate geometry-dependent interaction energy profiles for the water benzene cluster and compare the results with second-order Møller-Plesset calculations. Our results indicate that the use of the B3LYP functional in combination with an appropriate mixing rule and damping function is recommended for the interaction of water with aromatics.

Deprotonation of a histidine residue in aqueous solution using constrained ab initio molecular dynamics

The dissociation of a weak acid - a histidine residue - in water was investigated by means of constrained Car-Parrinello ab initio molecular dynamics. Both linear and coordination constraints were employed, and the structural, electronic, and dynamical transformations along the respective reaction coordinates were analyzed. The calculated potentials of mean force for the dissociation of a hydrogen atom from the Nepsilon and Ndelta positions of the imidazole ring reveal that protonated forms are approximately 9.0-9.5 kcal/mol more stable than the deprotonated. This result seems to agree well with the experimental estimate based on pKa. A possible transition state for the deprotonation has also been identified. Analysis of the electron localization function indicates that the proton transfer along the selected reaction path is not a fully concerted process.

Catalytic role of metal ion in the selection of competing reaction paths: a first principles molecular dynamics study of the enzymatic reaction in ribozyme

By using finite temperature first principles molecular dynamics, the mechanism of the enzymatic reaction of ribozyme was investigated for both the anionic and the radical charge states of the modeled RNA fragment. In the case of the anionic system, a pseudorotation and the subsequent 3' --> 2' migration occur in a vacuum, rather than the self-cleavage of the phosphodiester. On the other hand, when either a divalent metal ion (Mg(2+)) catalyst or the continuous hydrogen bond network of the solvent is present, the reaction path of the anionic species changes dramatically, going toward the transesterification channel. In a radical system, the transesterification can occur without a metal catalyst, as a consequence of the displacement of a hole (empty electronic state) along the reaction path. Thus, the present analysis suggests that a metal ion might be essential not only in lowering the activation barrier but also in selecting the reaction path among those corresponding to possible different charge states of the intermediate structure in vivo. Furthermore, simulation of the anionic species in solution shows that, in the absence of a metal catalyst, water molecules cooperate with the proton transfer via a proton wire mechanism and the hydrogen bond network plays a crucial role in preventing pseudorotations. On the other hand, when a metal cation is present in the vicinity of the site where the nucleophilic attack occurs, the hydrogen bond network is interrupted and detachment of the proton, enhanced by the catalyst, does not give rise to any proton-transfer process.

Density functional theory for efficient ab initio molecular dynamics simulations in solution

We present a density functional for first-principles molecular dynamics simulations that includes the electrostatic effects of a continuous dielectric medium. It allows for numerical simulations of molecules in solution in a model polar solvent. We propose a smooth dielectric model function to model solvation into water and demonstrate its good numerical properties for total energy calculations and constant energy molecular dynamics.