Comparison of the Accurate Kohn−Sham Solution with the Generalized Gradient Approximations (GGAs) for the SN2 Reaction F- + CH3F → FCH3 + F-: A Qualitative Rule To Predict Success or Failure of GGAs

Stepwise walden inversion in nucleophilic substitution at phosphorus

We have studied the mechanism of S(N)2@P reactions in the model systems X(-) + PMe(2)Y and X(-) + POR(2)Y (with R=Me, OH, OMe; and X, Y=Cl, OH, MeO) using density functional theory at OLYP/TZ2P. Our main purpose is to analyze the nature of the Walden inversion in our model nucleophilic substitution reactions. Walden inversion is well-known to proceed, in general, as a concerted umbrella motion of the substituents at the central atom. Interestingly, we find here that, in certain model reactions, Walden inversion can also proceed in a stepwise fashion in which the individual substituents of the umbrella flip, consecutively, from the educt to the product conformation via separate barriers on the reaction profile. We also examine how variation in nucleophile and leaving group may tune the pentavalent transition structure between labile transition state (TS) and stable transition complex (TC). Furthermore, we explore the various competing multistep pathways in the symmetric (X=Y) and asymmetric (X not equal Y) substitution reactions in our model reaction systems.

Hartree-Fock orbitals significantly improve the reaction barrier heights predicted by semilocal density functionals

Semilocal density functional theory predictions for the barrier heights of representative hydrogen transfer, heavy-atom transfer, and nucleophilic substitution reactions are significantly improved in non-self-consistent calculations using Hartree-Fock orbitals. Orbitals from hybrid calculations yield related improvements. These results provide insight into compensating for one-electron self-interaction error in semilocal density functional theory.

Nucleophilic substitution at phosphorus centers (SN2@p)

We have studied the characteristics of archetypal model systems for bimolecular nucleophilic substitution at phosphorus (SN2@P) and, for comparison, at carbon (SN2@C) and silicon (SN2@Si) centers. In our studies, we applied the generalized gradient approximation (GGA) of density functional theory (DFT) at the OLYP/TZ2P level. Our model systems cover nucleophilic substitution at carbon in X(-)+CH3Y (SN2@C), at silicon in X(-)+SiH3Y (SN2@Si), at tricoordinate phosphorus in X(-)+PH2Y (SN2@P3), and at tetracoordinate phosphorus in X(-)+POH2Y (SN2@P4). The main feature of going from SN2@C to SN2@P is the loss of the characteristic double-well potential energy surface (PES) involving a transition state [X--CH3--Y]- and the occurrence of a single-well PES with a stable transition complex, namely, [X--PH2--Y]- or [X--POH2--Y](-). The differences between SN2@P3 and SN2@P4 are relatively small. We explored both the symmetric and asymmetric (i.e. X, Y=Cl, OH) SN2 reactions in our model systems, the competition between backside and frontside pathways, and the dependence of the reactions on the conformation of the reactants. Furthermore, we studied the effect, on the symmetric and asymmetric SN2@P3 and S(N)2@P4 reactions, of replacing hydrogen substituents at the phosphorus centers by chlorine and fluorine in the model systems X(-)+PR2Y and X(-)+POR2Y, with R=Cl, F. An interesting phenomenon is the occurrence of a triple-well PES not only in the symmetric, but also in the asymmetric SN2@P4 reactions of X(-)+POCl2--Y.

Comparison of density functionals for reactions of sulfur ylides with aldehydes and olefins

The reactions of a model sulfur ylide with formaldehyde and 1,1-dicianoethylene, leading to the formation of an epoxyde and a cyclopropane, respectively, have been studied using different computational methods, and the results have been compared to those obtained with the CBS-QB3 method. The second step of these reactions presents transition states similar to that of an SN2 reaction. Depending on the degree of electron delocalization at the transition state, a different amount of exact exchange is necessary in the exchange functional to obtain accurate energy barriers. This amount is larger for the reaction of formaldehyde, in which the transition state is more delocalized, than for the reaction of 1,1-dicianoethylene. Similar results have been obtained for symmetric and non-symmetric SN2 reactions. The calculation of the reaction path has shown that the error relative to CBS-QB3 tends to increase when approaching the transition state. Among the different computational methods, PBE1PBE is the one to provide the most accurate energy barriers and reaction energies, whereas BB1K leads to the best results for the reaction path before the transition state.

Implications of protonation and substituent effects for C-O and O-P bond cleavage in phosphate monoesters

A recent study of phosphate monoesters that broke down exclusively through C-O bond cleavage and whose reactivity was unaffected by protonation of the nonbridging oxygens (Byczynski et al. J. Am. Chem. Soc. 2003, 125, 12541) raised several questions about the reactivity of phosphate monoesters, R-O-P(i). Potential catalytic strategies, particularly with regard to selectively promoting C-O or O-P bond cleavage, were investigated computationally through simple alkyl and aryl phosphate monoesters. Both C-O and O-P bonds lengthened upon protonating the bridging oxygen, R-O(H(+))-P(i), and heterolytic bond dissociation energies, DeltaH(C)(-)(O) and DeltaH(O)(-)(P), decreased. Which bond will break depends on the protonation state of the phosphoryl moiety, P(i), and the identity of the organosubstituent, R. Protonating the bridging oxygen when the nonbridging oxygens were already protonated favored C-O cleavage, while protonating the bridging oxygen of the dianion form, R-O-PO(3)(2)(-), favored O-P cleavage. Alkyl R groups capable of forming stable cations were more prone to C-O bond cleavage, with tBu > iPr > F(2)iPr > Me. The lack of effect on the C-O cleavage rate from protonating nonbridging oxygens could arise from two precisely offsetting effects: Protonating nonbridging oxygens lengthens the C-O bond, making it more reactive, but also decreases the bridging oxygen proton affinity, making it less likely to be protonated and, therefore, less reactive. The lack of effect could also arise without bridging oxygen protonation if the ratio of rate constants with different protonation states precisely matched the ratio of acidity constants, K(a). Calculations used hybrid density functional theory (B3PW91/6-31++G) methods with a conductor-like polarizable continuum model (CPCM) of solvation. Calculations on Me-phosphate using MP2/aug-cc-pVDZ and PBE0/aug-cc-pVDZ levels of theory, and variations on the solvation model, confirmed the reproducibility with different computational models.

Duocarmycins binding to DNA investigated by molecular simulation

Duocarmycins are a potent class of antitumor agents, whose activity arises through their covalent binding to adenine nucleobases of DNA.(1-3) Here, we perform molecular dynamics (MD) and hybrid Car-Parinello QM/MM simulations to investigate aspects of duocarmycin binding to the d(pGpApCpTpApApTpTpGpApC) oligonucleotide. We focus on the derivatives (+)-duocarmycin SA (DSA) and (+)-duocarmycin SI (DSI), for which structural information of the covalent complex with the oligonucleotide is available, as well as on the related, but less reactive, NBOC-duocarmycin SA (NBOC-DSA), interacting with the same oligonucleotide. Comparison is made with adenine alkylation reaction in water performed by the smallest of these compounds (NBOC-DSA). The MD calculations suggest that, in noncovalent complexes, (i) drug binding causes a partial dehydration of the minor groove, without inducing a significant conformational changes, and (ii) DSA and DSI occupy a more favorable position for nucleophilic attack than NBOC-DSA, consistently with the lower reactivity of the latter. The QM/MM calculations, which are used to investigate the first step of the alkylation reaction, turn out to provide strongly underestimated free energy barriers. Within these approximations, our calculations suggest that an important ingredient for the experimentally observed DNA catalytic power is the polarization of the drug by the biomolecular scaffold.

Backbone cleavages and sequential loss of carbon monoxide and ammonia from protonated AGG: a combined tandem mass spectrometry, isotope labeling, and theoretical study

The fragmentation characteristics of protonated alanylglycylglycine, [AGG + H](+), were investigated by tandem mass spectrometry in MALDI-TOF/TOF, ion trap, and hybrid sector instruments. b(2) is the most abundant fragment ion in MALDI-TOF/TOF, ion trap, and hybrid sector metastable ion (MI) experiments, while y(2) is slightly more abundant than b(2) in collision activated dissociation (CAD) performed in the sector instrument. The A-G amide bond is cleaved on the a(1)-y(2) pathway resulting in a proton-bound dimer of GG and MeCH=NH. Depending on the fragmentation conditions employed, this dimer can then (1) be detected as [AGG + H - CO](+), (2) dissociate to produce y(2) ions, [GG + H](+), (3) dissociate to produce a(1) ions, [MeCH=NH + H](+), or (4) rearrange to expel NH(3) forming a [AGG + H - CO - NH(3)](+) ion. The activation method and the experimental timescale employed largely dictate which of, and to what extent, these processes occur. These effects are qualitatively rationalized with the help of quantum chemical and RRKM calculations. Two mechanisms for formation of the [AGG + H - CO - NH(3)](+) ion were evaluated through nitrogen-15 labeling experiments and quantum chemical calculations. A mechanism involving intermolecular nucleophilic attack and association of the GG and imine fragments followed by ammonia loss was found to be more energetically favorable than expulsion of ammonia in an S(N)2-type reaction.

Ab Initio Static and Molecular Dynamics Study of 4-Styrylpyridine

We report an in-depth theoretical study of 4-styrylpyridine in its singlet S(0) 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 approximately 1 ps during the simulation carried out at 150 K on this isomer.

Influence of N7 protonation on the mechanism of the N-glycosidic bond hydrolysis in 2'-deoxyguanosine. A theoretical study

The influence of N7 protonation on the mechanism of the N-glycosidic bond hydrolysis in 2'-deoxyguanosine has been studied using density functional theory (DFT) methods. For the neutral system, two different pathways (with retention and inversion of configuration at the C1' anomeric carbon) have been found, both of them consisting of two steps and involving the formation of a dihydrofurane-like intermediate. The Gibbs free energy barrier for the first step is very high in both cases (53 and 46 kcal/mol for the process with inversion and with retention, respectively). However, the N7-protonated system shows a very different mechanism which consists of two steps. The first one leads to the formation of an oxacarbenium ion intermediate, with a Gibbs free energy barrier of 27 kcal/mol, and the second one corresponds to the nucleophilic attack of the water molecule to the oxacarbenium ion and takes place with a barrier of 1.3 kcal/mol. Thus, these results agree with a stepwise SN1 mechanism (DN*AN), with a discrete intermediate formed between the leaving group and the nucleophile approach, and show that N7 protonation strongly catalyzes the hydrolysis of the N-glycosidic bond, making the guanine a better leaving group. Finally, kinetic isotope effects have been calculated for the protonated system, and the results obtained are in very good agreement with experimental data for analogous systems.

Energy landscapes of nucleophilic substitution reactions: A comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.

Assessment of the exchange-correlation functionals for the physical description of spin transition phenomena by density functional theory methods: All the same?

This study aims to assess present day density functionals in the description of spin crossover iron(II) complexes. Two recently synthesized spin crossover complexes were considered. Theoretical calculations were made using 53 of the most popular exchange-correlation density functionals with triple zeta plus polarization quality basis sets. The present work shows that even though different density functionals can lead to different energy gaps between spin states, most of them are very similar for these two compounds when a comparison between energy gaps is sought. The present work shows that even though different exchange correlations can lead to different energy gaps between spin states, the difference between these gaps calculated at different geometries and that calculated at a given reference geometry is surprisingly independent of the choice of functional. The reasons for the similarities and the differences among exchange and correlation functional combinations are discussed.

Ab initio molecular dynamics study of the hydrolysis reaction of diborane

The hydrolysis reaction of the diborane molecule in aqueous solution has been studied by a series of Car-Parrinello Molecular Dynamics simulations in the Blue Moon Ensemble. The total reaction has been divided into two parts: one dealing with the breaking of B(2)H(6) molecule and the formation of a BH(4)(-) ion, a H(2)BOH molecule and a H(+) ion; the second leads to the formation of two hydrogen molecules and another H(2)BOH molecule, starting from BH(4)(-), two water molecules and a H(+) ion. The total reaction studied in this work has been B(2)H(6) + 2H(2)O --> 2H(2)BOH + 2H(2). We have described both structurally and electronically the reagents and the products through the radial distribution functions and the Wannier Function Center positions calculations, with attention to the solvent effects on the compounds. The free energy barrier value for the first part of the reaction and a detailed mechanisms for both parts have been reported. An interesting behavior of BH(3) and H(2) molecules in solution has been observed. They form a quite stable three center bond between the electron pair of the hydrogen molecule and the empty orbital of the boron atom in BH(3), which has been described from both a structural and electronic point of view.

Spin-Polarized Conceptual Density Functional Theory Study of the Regioselectivity in Ring Closures of Radicals

The regioselectivity of ring-forming radical reactions is investigated within the framework of the so-called spin-polarized conceptual density functional theory. Two different types of cyclizations were studied. First, a series of model reactions of alkyl- and acyl-substituted radicals were investigated. Next, attention was focused on the radical cascade cyclizations of N-alkenyl-2-aziridinylmethyl radicals (a three-step mechanism). In both of these reactions, the approaching radical (carbon or nitrogen centered) adds to a carbon-carbon double bond within the same molecule to form a radical ring compound. In this process, the number of electrons is changing from a local point of view (a charge transfer occurs from one part of the molecule to another one) at constant global spin number Ns (both the reactant and the product ring compound are in the doublet state). It is shown that the experimentally observed regioselectivities for these ring-closure steps can be predicted using the spin-polarized Fukui functions for radical attack, f0NN(r).

Charge Localization in Stacked Radical Cation DNA Base Pairs and the Benzene Dimer Studied by Self-Interaction Corrected Density-Functional Theory

The incomplete cancellation of the electron self-interaction can be a serious shortcoming of density-functional theory especially when treating odd-electron systems. In this work, several popular and potentially viable correction schemes are applied in order to characterize the electronic structure of stacked molecular pairs, consisting of a neutral molecule and adjacent radical cation, as a function of separation distance. The unphysical sharing of the positive charge between adjacent molecules separated by 6-7 A is corrected for by applying a new empirical scheme proposed by VandeVondele and Sprik [Phys. Chem. Chem. Phys. 2005, 7, 1363] with a unique choice of parameters. This method is subsequently applied to characterize the electronic structure of two neighboring guanines excised from a canonical Arnott B-DNA structure and will be used in future investigations of certain model DNA fibers.

Reaction-Path Dynamics and Theoretical Rate Constants for the CHnF4-n + O3 → HOOO + CHn-1F4-n (n = 2,3) Reactions

We present a theoretical study of the hydrogen abstraction reactions from CH(3)F and CH(2)F(2) by an ozone molecule. The geometries and harmonic vibrational frequencies of all stationary points are calculated at the MPW1K, BHandHLYP, and MPWB1K levels of theory. The energies of all of the stationary points were refined by using both higher-level (denoted as HL) energy calculations and QCISD(T)/6-311++G(2df,2pd) calculations based on the optimized geometries at the MPW1K/6-31+G(d,p) level of theory. The minimum energy paths (MEPs) were obtained by the MPW1K/6-31+G(d,p) level of theory. Energetic information of the points along the MEPs is further refined by the HL method. The rate constants were evaluated on the basis of the MEPs from the HL level of theory in the temperature range 200-2500 K by using the conventional transition-state theory (TST), the canonical variational transition-state theory (CVT), the microcanonical variational transition-state theory (microVT), the CVT coupled with the small-curvature tunneling (SCT) correction (CVT/SCT), and the microVT coupled with the Eckart tunneling correction (microVT/Eckart) based on the ab initio calculations. A general agreement was found among the TST, CVT, and microVT theories. The fitted three-parameter Arrhenius expressions of the calculated forward CVT/SCT and microVT/Eckart rate constants of the ozonolysis of fluoromethane are k(CVT/SCT)(T) = 2.76 x 10(-34)T(5.81)e((-13975/)(T)) and k(microVT/Eckart)(T) = 1.15 x 10(-34)T(5.97)e((-14530.7/)(T)), respectively. The fitted three-parameter Arrhenius expressions of the calculated forward CVT/SCT and microVT/Eckart rate constants of the ozonolysis of difluoromethane are k(CVT/SCT)(T) = 2.29 x 10(-36)T(6.42)e((-15451.6/)(T)) and k(microVT/Eckart)(T) = 1.31 x 10(-36)T(6.45)e((-15465.8/)(T)), respectively.

Structure, redox, pK a, spin. A golden tetrad for understanding metalloenzyme energetics and reaction pathways

After a review of the current status of density functional theory (DFT) for spin-polarized and spin-coupled systems, we focus on the resting states and intermediates of redox-active metalloenzymes and electron transfer proteins, showing how comparisons of DFT-calculated spectroscopic parameters with experiment and evaluation of related energies and geometries provide important information. The topics we examine include (1) models for the active-site structure of methane monooxygenase intermediate Q and ribonucleotide reductase intermediate X; (2) the coupling of electron transfer to proton transfer in manganese superoxide dismutase, with implications for reaction kinetics; (3) redox, pK(a), and electronic structure issues in the Rieske iron-sulfur protein, including their connection to coupled electron/proton transfer, and an analysis of how partial electron delocalization strongly alters the electron paramagnetic resonance spectrum; (4) the connection between protein-induced structural distortion and the electronic structure of oxidized high-potential 4Fe4S proteins with implications for cluster reactivity; (5) an analysis of cluster assembly and central-atom insertion into the FeMo cofactor center of nitrogenase based on DFT structural and redox potential calculations.

Reaction of C-Silylated α-Diazophosphines as Nucleophiles toward Carbonyl Compounds: A Mechanistic Study and Application to the Synthesis of Alkynes and α-Hydroxyphosphonamides

Diversely substituted alpha-hydroxyphosphonamides and alkynes have been efficiently synthesized through the reaction of C-silylated alpha-diazophosphines with different types of aldehydes (2 equiv) in a neutral medium under very mild conditions. The reaction with some chiral aldehydes is highly diastereoselective leading to phosphonamides as single diastereomers. The novel reaction is influenced by electronic and steric effects being precluded for aromatic aldehydes containing electron-releasing substituents on the phenyl ring and for bulky aliphatic aldehydes. The mechanistic studies of these processes, which are highly exothermic, provide evidence for a nucleophilic attack of the diazophosphine to the aldehyde leading to a betaine that rapidly rearranges to a diazomethylenephosphorane, which has been detected or captured in some instances. The diazomethylenephosphorane reacts with a second molecule of aldehyde according to a Wittig-type condensation, and the rate-determining step of the whole process is believed to be the decomposition of the resultant oxaphosphetane to afford the hydroxyphosphonamide and a diazocumulene. Finally, this intermediate loses molecular nitrogen giving a transient carbene that rapidly evolves toward the alkyne.

Assessing a new nonempirical density functional: Difficulties in treating π-conjugation effects

The reliability of the Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation functional for the description of conjugation effects in model pi-conjugated systems has been thoroughly assessed through the calculation of torsion energy profiles. The functional reproduces qualitatively the shape of torsional potentials but, interestingly, the mixing of TPSS and exact exchange governs the quantitative results: thus, well-defined hybrid extensions of the functional are consistently employed to improve the results. The hybrid approaches led to more accurate descriptions of conjugation effects but, however, the finest performance along the whole range of dihedral angles was obtained by a customized mixing of pure or hybrid TPSS functionals and wave function methods in a multicoefficient fashion. Despite the successful construction of this nonempirical functional, higher rungs of the ladder of methods in which TPSS is based are hoped to reduce the errors with respect to reference data for pi-conjugated systems.

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.

Calculation of Ionization Potentials of Small Molecules: A Comparative Study of Different Methods

With the help of various theoretical methods, ionization potentials (IPs) have been computed for a panel of small molecules containing atoms of group 14, 15, or 16 and representing different singly, doubly, or triply bonded systems with or without an interacting heteroatom lone pair. Comparison of experimental IP values to theoretical results indicates that (i) the standard outer valence green function (OVGF), density functional theory (DFT), and DeltaSCF methods lead to rather accurate values, (ii) the CASPT2 method systematically underestimates IPs, (iii) the method of deducing IPs from a shift of some standard DFT eigenvalue spectrum is a straightforward approach leading to rather accurate IPs, (iv) the eigenvalue spectrum obtained with the so-called statistical average of different orbital model potential (SAOP) exchange-correlation model potential is an efficient approach leading directly to quite accurate IPs, and (v) a good prediction of the IP spectrum can be obtained from the shifted excitation spectra of the system calculated by the time-dependent DFT (TD-DFT) method. It is also shown that the TD-DFT calculations of the ionized species bring a significant improvement over the calculations of the neutral molecules, indicating that a great part of the electronic relaxation is already taken into account (in a similar way for all ionizations). Finally, in the case of TD-DFT calculations of neutral molecules, the statistical average of different orbital model potential (SAOP) functional does not lead to significantly better results than the B3LYP functional.

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.

A Recipe for the Computation of the Free Energy Barrier and the Lowest Free Energy Path of Concerted Reactions

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.

Generalizing the Breakdown of the Maximum Hardness and Minimum Polarizabilities Principles for Nontotally Symmetric Vibrations to Non-π-Conjugated Organic Molecules

In previous works we have shown that certain pi-conjugated organic molecules possess nontotally symmetric vibrations that break the maximum hardness (MHP) and minimum polarizability principles (MPP). We have also derived a set of simple rules to determine a priori without calculations whether a particular pi-conjugated organic molecule violates these two principles. In the present work, we generalize these results, and we show that not only pi-conjugated organic molecules but also other molecules without pi-conjugated structure or even pi-bonds can exhibit nontotally symmetric molecular distortions that do not follow these two principles. We have also found that the breakdowns of the MHP and the MPP are not necessarily connected, since the polarizability is not always proportional to the softness. Finally, we also introduced a methodology based on the diagonalization of the hardness Hessian matrix with respect to the vibrational normal coordinates to determine the nontotally symmetric molecular displacements that do not follow the MHP.

Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

To obtain a set of consistent benchmark potential energy surfaces (PES) for the two archetypal nucleophilic substitution reactions of the chloride anion at carbon in chloromethane (S(N)2@C) and at silicon in chlorosilane (S(N)2@Si), we have explored these PESes using a hierarchical series of ab initio methods [HF, MP2, MP4SDQ, CCSD, CCSD(T)] in combination with a hierarchical series of six Gaussian-type basis sets, up to g polarization. Relative energies of stationary points are converged to within 0.01 to 0.56 kcal/mol as a function of the basis-set size. Our best estimate, at CCSD(T)/aug-cc-pVQZ, for the relative energies of the [Cl(-), CH(3)Cl] reactant complex, the [Cl-CH(3)-Cl](-) transition state and the stable [Cl-SiH(3)-Cl](-) transition complex is -10.42, +2.52, and -27.10 kcal/mol, respectively. Furthermore, we have investigated the performance for these reactions of four popular density functionals, namely, BP86, BLYP, B3LYP, and OLYP, in combination with a large doubly polarized Slater-type basis set of triple-zeta quality (TZ2P). Best overall agreement with our CCSD(T)/aug-cc-pVQZ benchmark is obtained with OLYP and B3LYP. However, OLYP performs better for the S(N)2@C overall and central barriers, which it underestimates by 2.65 and 4.05 kcal/mol, respectively. The other DFT approaches underestimate these barriers by some 4.8 (B3LYP) to 9.0 kcal/mol (BLYP).

Interaction of lead atom with atmospheric hydroxyl radical. An ab initio and density functional theory study of the resulting complexes PbOH and HPbO

The two potential hypersurfaces 2A' (ground state) and 2A" (excited state) have been studied through ab initio and density functional theory (DFT) methods for the Pb(OH) complex. Two processes have been identified. The first one concerns the hydrogen inversion process in the coordination of PbOH and the second one the isomerization of PbOH into HPbO. Eight stationary points have been found; four of them correspond to the stable structures with symmetries PbOH(2A'), PbOH(2A"), HPbO(2A'), and HPbO(2Pi), and four correspond to transition states [TS] with the symmetries 2Pi, 2A', 2Sigma+, and 2A". The hydrogen inversion process in PbOH exhibits the so-called Renner-Teller effect with a rather low barrier, whereas the isomerization process PbOH-->HPbO exhibits a rather high barrier. The energetic, structural, spectroscopy, and thermodynamics results obtained at various levels through, e.g., DFT with BLYP, B3LYP exchange-correlation functionals, coupled clusters methods, namely CCSD (single and double excitations) and CCSD(T) (with triple excitations, by perturbation) are presented for the whole sets of the stationary points and their dissociation products. The relativistic effects, as well as spin-orbit interaction, taken into account in the case of the BLYP exchange-correlation functional, have been estimated and discussed in order to measure their importance in the case of system including heavy metals such as Pb. Reactions of lead (Pb) with oxidizing atmospheric molecules (OH, HO2, O2, and O3) have been studied at various levels of approximation in order to study the possible existence of PbOH in the atmosphere.