Nickel-catalyzed alkyl coupling reactions: evaluation of computational methods

The B3LYP, M06, M06L, M062X, MPW1K, and PBE1PBE DFT methods were evaluated for modeling nickel-catalyzed coupling reactions. The reaction consists of a nucleophilic attack by a carbanion equivalent on the nickel complex, S(N)2 attack by the anionic nickel complex on an alkyl halide, and reductive elimination of the coupled alkane product, regenerating the nickel catalyst. On the basis of CCSD(T)//DFT single-point energies, the B3LYP, M06, and PBE1PBE functionals were judged to generate the best ground state geometries. M06 energies are generally comparable or superior to B3LYP and PBE1PBE energies for transition state calculations. The MP2 and CCSD methods were also evaluated for single-point energies at the M06 geometries. The rate-determining step of this reaction was found to be nucleophilic attack of a L(2)NiR anion on the alkyl halide.     

Electronic spectroscopy of UO2(2+), NUO(+) and NUN: an evaluation of time-dependent density functional theory for actinides

The performance of the time-dependent density functional theory (TDDFT) approach has been evaluated for the electronic spectrum of the UO(2)(2+), NUO(+) and NUN molecules. Different exchange-correlation functionals (LDA, PBE, BLYP, B3LYP, PBE0, M06, M06-L, M06-2X, CAM-B3LYP) and the SAOP model potential have been investigated, as has the relative importance of the adiabatic local density approximation (ALDA) to the exchange-correlation kernel. The vertical excitation energies have been compared with reference data obtained using accurate wave-function theory (WFT) methods.     

Theoretical approaches to estimating homolytic bond dissociation energies of organocopper and organosilver compounds

Although organocopper and organosilver compounds are known to decompose by homolytic pathways among others, surprisingly little is known about their bond dissociation energies (BDEs). In order to address this deficiency, the performance of the DFT functionals BLYP, B3LYP, BP86, TPSSTPSS, BHandHLYP, M06L, M06, M06-2X, B97D, and PBEPBE, along with the double hybrids, mPW2-PLYP, B2-PLYP, and the ab initio methods, MP2 and CCSD(T), have been benchmarked against the thermochemistry for the M-C homolytic BDEs (D(0)) of Cu-CH(3) and Ag-CH(3), derived from guided ion beam experiments and CBS limit calculations (D(0)(Cu-CH(3)) = 223 kJ·mol(-1); D(0)(Ag-CH(3)) = 169 kJ·mol(-1)). Of the tested methods, in terms of chemical accuracy, error margin, and computational expense, M06 and BLYP were found to perform best for homolytic dissociation of methylcopper and methylsilver, compared with the CBS limit gold standard. Thus the M06 functional was used to evaluate the M-C homolytic bond dissociation energies of Cu-R and Ag-R, R = Et, Pr, iPr, tBu, allyl, CH(2)Ph, and Ph. It was found that D(0)(Ag-R) was always lower (～50 kJ·mol(-1)) than that of D(0)(Cu-R). The trends in BDE when changing the R ligand reflected the H-R bond energy trends for the alkyl ligands, while for R = allyl, CH(2)Ph, and Ph, some differences in bond energy trends arose. These trends in homolytic bond dissociation energy help rationalize the previously reported (Rijs, N. J.; O'Hair, R. A. J. Organometallics2010, 29, 2282-2291) fragmentation pathways of the organometallate anions, [CH(3)MR](-).     

Calculations of ionization energies and electron affinities for atoms and molecules: A comparative study with different methods

In the present work, we examined the performance of 36 density functionals, including the newly developed doubly hybrid density functional XYG3 (Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Natl. Acad. Sci, USA, 2009, 106, 4963), to calculate ionization energies (IEs) and electron affinities (EAs). We used the well-established G2-1 set as reference, which contains 14 atoms and 24 molecules for IE, along with 7 atoms and 18 molecules for EA. XYG3 leads to mean absolute deviations (MADs) of 0.057 and 0.080 eV for IEs and EAs, respectively, using the basis set of 6-311 + G (3df,2p). In comparison with some other functionals, MADs for IEs are 0.109 (B2PLYP), 0.119 (M06-2X), 0.159 (X3LYP), 0.161 (PBE), 0.162 (B3LYP), 0.165 (PBE0), 0.173 (TPSS), 0.200 (BLYP), and 0.215 eV (LC-BLYP). MADs for EAs are 0.090 (X3LYP), 0.090 (B2PLYP), 0.102 (PBE), 0.103 (M06-2X), 0.104 (TPSS), 0.105 (BLYP), 0.106 (B3LYP), 0.126 (LC-BLYP), and 0.128 eV (PBE0).     

Diels-Alder Reactivity of a Chiral Anthracene Template with Symmetrical and Unsymmetrical Dienophiles: A DFT Study

In this work, we used Density Functional Theory calculations to assess the factors that control the reactivity of a chiral anthracene template with three sets of dienophiles including maleic anhydrides, maleimides and acetoxy lactones in the context of Diels-Alder cycloadditions. The results obtained here (at the M06-2X/6-311++G(d,p) level of theory) suggest that the activation energies for maleic anhydrides and acetoxy lactones are dependent on the nature of the substituent in the dienophile. Among all studied substituents, only −CN reduces the energy barrier of the cycloaddition. For maleimides, the activation energies are independent of the heteroatom of the dienophile and the R group attached to it. The analysis of frontier molecular orbitals, charge transfer and the activation strain model (at the M06-2X/TZVP level based on M06-2X/6-311++G(d,p) geometries) suggest that the activation energies in maleic anhydrides are mainly controlled by the amount of charge transfer from the diene to the dienophile during cycloaddition. For maleimides, there is a dual control of interaction and strain energies on the activation energies, whereas for the acetoxy lactones the activation energies seem to be controlled by the degree of template distortion at the transition state. Finally, calculations show that considering a catalyst on the studied cycloadditions changes the reaction mechanism from concerted to stepwise and proceed with much lower activation energies.     

Electronic structure and absorption spectra of supramolecular complexes of a fullerene crown ether with a π-extended TTF derivative

The present work is a theoretical investigation on supramolecular complexes of a fullerene crown ether (A and B isomers) with a derivative of π-extended tetrathiafulvalene (T). The geometry and the electronic structure of seven different conformers of the complex of dibenzo-18-crown-6 ether of fullero-N-methylpyrrolidine with a N-benzyl-N-(4-{[9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracen-2-yl]ethynyl}benzyl)ammonium cation were determined. We calculated the complexation energies and the absorption spectra, i.e., the lowest 50 excited electronic states of the complexes have been determined at the ground state optimum geometry. All calculations were carried out employing the density functional theory (DFT) and the time-dependent DFT, using the B3LYP, CAM-B3LYP, ωB97X-D, and M06-2X functionals in conjunction with the 6-31G(d,p) basis set. Various types of van der Waals interactions are observed in the complexes. Conformer complexation energies (CE) range from 2.54 to 2.14 eV in the gas phase and from 1.75 to 1.34 eV in CHCl(3) solvent at the ωB97X-D/6-31G(d,p)//M06-2X/6-31G(d,p) level of theory. There are three major features at about 390, 330, and 290 nm in the calculated absorption spectra of all the conformers. The major peaks correspond to T→T, T→T/F (electron density in both T and the fullerene F of B) and to T→F transitions, depending on the particular conformer. Other charge transfer T→F transitions are observed close to the T→T transition, indicating the possibility of photoinduced electron transfer in all these complexes.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Theoretical study of substituent effect on the charge mobility of 2,5-bis(trialkylsilylethynyl)-1,1,3,4-tetraphenylsiloles

The theoretical calculation of the charge mobility of 2,5-bis(trialkylsilylethynyl)-1,1,3,4-tetraphenylsiloles is presented. B3LYP/6-31* calculations demonstrated that these silole molecules possessed large coupling matrix elements and reorganization energies for electron and hole transfers and high electron mobilities. The bulkiness of the trialkyl substituents influenced the charge mobility of the silole molecules, with the smaller trimethyl group imparting higher charge mobility than triethyl and triisopropyl substituents.     

Computing reliable energetics for conjugate addition reactions

The performance of various density functionals along with second-order perturbation treatments has been tested for a set of conjugate addition reactions relevant to stereoselective organocatalysis. It is shown that B3LYP predictions seriously underestimate the reaction energies, whereas two newly designed functionals (M05-2X and M06-2X) and the SCS-MP2 method provide very accurate data. These new methods represent promising alternative approaches in future mechanistic studies.     

Direct dynamics simulation of dioxetane formation and decomposition via the singlet [middle dot]O-O-CH(2)-CH(2)[middle dot] biradical: Non-RRKM dynamics

Electronic structure calculations and direct chemical dynamics simulations are used to study the formation and decomposition of dioxetane on its ground state singlet potential energy surface. The stationary points for (1)O(2) + C(2)H(4), the singlet [middle dot]O-O-CH(2)-CH(2)[middle dot] biradical, the transition state (TS) connecting this biradical with dioxetane, and the two transition states and gauche [middle dot]O-CH(2)-CH(2)-O[middle dot] biradical connecting dioxetane with the formaldehyde product molecules are investigated at different levels of electronic structure theory including UB3LYP, UMP2, MRMP2, and CASSCF and a range of basis sets. The UB3LYP∕6-31G? method was found to give representative energies for the reactive system and was used as a model for the simulations. UB3LYP∕6-31G? direct dynamics trajectories were initiated at the TS connecting the [middle dot]O-O-CH(2)-CH(2)[middle dot] biradical and dioxetane by sampling the TS's vibrational energy levels, and rotational and reaction coordinate energies, with Boltzmann distributions at 300, 1000, and 1500 K. This corresponds to the transition state theory model for trajectories that pass the TS. The trajectories were directed randomly towards both the biradical and dioxetane. A small fraction of the trajectories directed towards the biradical recrossed the TS and formed dioxetane. The remainder formed (1)O(2) + C(2)H(4) and of these ～ 40% went directly from the TS to (1)O(2) + C(2)H(4) without getting trapped and forming an intermediate in the [middle dot]O-O-CH(2)-CH(2)[middle dot] biradical potential energy minimum, a non-statistical result. The dioxetane molecules which are formed dissociate to two formaldehyde molecules with a rate constant two orders of magnitude smaller than that predicted by Rice-Ramsperger-Kassel-Marcus theory. The reaction dynamics from dioxetane to the formaldehyde molecules do not follow the intrinsic reaction coordinate or involve trapping in the gauche [middle dot]O-CH(2)-CH(2)-O[middle dot] biradical potential energy minimum. Important non-statistical dynamics are exhibited for this reactive system.     

DFT studies on the tetranuclear cubane complex [Ni4(ampd)4(Cl4)]·MeCN

Density functional theory (DFT) is used to investigate the structural properties of Ni(II) cubane [Ni₄(ampdH)₄Cl₄]·MeCN. The structural features and ground state geometry calculations are computed at the B3LYP/6-31G* (LANL2DZ) level of theory. We shed light on the highest occupied molecular orbital and lowest unoccupied molecular orbital. The absorption spectrum is calculated using time-dependent DFT. The absorption wavelengths are calculated using different functionals, i.e., pw91pw91, B3LYP, BHandHLYP, CAM-B3LYP, LC-BLYP, and M06. The LC-BLYP is in good agreement with the experimental data.     

用含时密度泛函方法研究和设计推拉结构的荧光分子

应用密度泛函理论(DFT)和含时密度泛函理论(TDDFT)方法及连续极化模型研究了六种荧光材料分子基态和第一激发态的电子结构性质.这六种分子是:3-(二氰亚甲基)-5,5-二甲基-1-(3-[9-(2-乙基-己基)-咔唑基]-乙烯基)环己烷(DCDHCC),DCDHCC2,3-(二氰亚甲基)-5,5-二甲基-1-(4-二苯基氨基-苯乙烯基)环己烷(DCDPC),DCDPC2,3-(二氰亚甲基)-5,5-二甲基-1-(4-[9-咔唑基]-乙烯基)环己烷(DCDCC)和3-(二氰亚甲基)-5,5-二甲基-1-(4-二甲基氨基-苯乙烯基)环己烷(DCDDC).它们可作为有机发光显示器件的发光材料.比较了PBE0、M06、BMK、M062X和CAM-B3LYP五种泛函,其中BMK方法很好地再现了各个分子在丙酮溶剂中的吸收和发射光谱.同时计算了分子的电子亲和能和电离势并用于评价分子的电荷注入性质.研究表明,当使用双π桥和双受体时,分子的发射光谱会红移到理想的发光区域.据此设计了两个新的分子DCDCC2和DCDDC2,它们分别是DCDCC和DCDDC的双支对应分子.计算结果表明这两个分子也具有作为荧光发射体的良好性质.     

Studies on the structure, stability, and spectral signatures of hydride ion-water clusters

The gas-phase structure, stability, spectra, and electron density topography of H(-)W(n) clusters (where n = 1-8) have been calculated using coupled-cluster CCSD(T) and M?ller-Plesset second-order perturbation (MP2) theory combined with complete basis set (CBS) approaches. The performance of various density functional theory (DFT) based methods such as B3LYP, M05-2X, M06, M06-L, and M06-2X using 6-311++G(d,p), and aug-cc-pVXZ (aVXZ, where X = D, T, and Q) basis sets has also been assessed by considering values calculated using CCSD(T)/CBS limit as reference. The performance of the functionals has been ranked based on the mean signed/unsigned error. The comparison of geometrical parameters elicits that the geometrical parameters predicted by B3LYP/aVTZ method are in good agreement with those values obtained at MP2/aVTZ level of theory. Results show that M05-2X functional outperform other functionals in predicting the energetics when compared to CCSD(T)/CBS value. On the other hand, values predicted by M06-2X, and M06 methods, are closer to those values obtained from MP2/CBS approach. It is evident from the calculations that H(-)W(n) (where n = 5-8) clusters adopt several interesting structural motifs such as pyramidal, prism, book, Clessidra, cubic, cage, and bag. The important role played by ion-water (O-H···H(-)) and water-water (O-H···O) interactions in determining the stability of the clusters has also been observed. Analysis of the results indicates that the most stable cluster is made up of minimum number of O-H···H(-) interaction in conjugation with the maximum number of O-H···O interactions. The Bader theory of atoms in molecules (AIM) and natural bond orbital (NBO) analyses has also been carried out to characterize the nature of interactions between hydride ion and water molecules. It can be observed from the vibrational spectra of H(-)W(n) clusters, the stretching frequencies involving ion-water interaction always exhibit larger redshift and intensities than that of water-water (inter solvent) interactions.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.     

Performance of SM8 on a test to predict small-molecule solvation free energies

The SM8 quantum mechanical aqueous continuum solvation model is applied to a 17-molecule test set proposed by Nicholls et al. (J. Med. Chem. 2008, 51, 769) to predict free energies of solvation. With the M06-2X density functional, the 6-31G(d) basis set, and CM4M charge model, the root-mean-square error (RMSE) of SM8 is 1.08 kcal mol(-1) for aqueous geometries and 1.14 kcal mol(-1) for gas-phase geometries. These errors compare favorably with optimal explicit and continuum models reported by Nicholls et al., having RMSEs of 1.33 and 1.87 kcal mol(-1), respectively. Other models examined by these workers had RMSEs of 1.5-2.6 kcal mol(-1). We also explore the use of other density functionals and charge models with SM8 and the RMSE increases to 1.21 kcal mol(-1) for mPW1/CM4 with gas-phase geometries, to 1.50 kcal mol(-1) for M06-2X/CM4 with gas-phase geometries, and to 1.27-1.64 kcal mol(-1) with three different models at B3LYP gas-phase geometries.     

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.