Trends in R-X bond dissociation energies (R = Me, Et, i-Pr, t-Bu; X = H, CH3, OCH3, OH, F): a surprising shortcoming of density functional theory

The performance of a variety of high-level composite procedures, as well as lower-cost density functional theory (DFT)- and second-order perturbation theory (MP2)-based methods, for the prediction of absolute and relative R-X bond dissociation energies (BDEs) was examined for R = Me, Et, i-Pr and t-Bu, and X = H, CH(3), OCH(3), OH and F. The methods considered include the high-level G3(MP2)-RAD and G3-RAD procedures, a variety of pure and hybrid DFT methods (B-LYP, B3-LYP, B3-P86, KMLYP, B1B95, MPW1PW91, MPW1B95, BB1K, MPW1K, MPWB1K and BMK), standard restricted (open-shell) MP2 (RMP2), and two recently introduced variants of MP2, namely spin-component-scaled MP2 (SCS-MP2) and scaled-opposite-spin MP2 (SOS-MP2). The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the lower-level DFT- and MP2-based procedures. The best DFT methods (KMLYP and particularly BMK) provide very reasonable predictions for the absolute heats of formation and R-X BDEs for the systems studied. However, all of the DFT methods overestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu, leading in some cases to incorrect qualitative behavior. In contrast, the MP2-based methods generally show larger errors (than the best DFT methods) in the absolute heats of formation and BDEs, but better behavior for the relative BDEs, although they do tend to underestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu. The potentially less computationally expensive SOS-MP2 method offers particular promise as a reliable method that might be applicable to larger systems.     

Reliable low-cost theoretical procedures for studying addition-fragmentation in RAFT polymerization

Enthalpies for the beta-scission reactions, R'SC(*)(Z)SR --> R'SC(Z)=S + (*)R (for R, R' = CH(3), CH(2)CH(3), CH(2)CN, C(CH(3))(2)CN, CH(2)COOCH(3), CH(CH(3))COOCH(3), CH(2)OCOCH(3), CH(2)Ph, C(CH(3))(2)Ph, and CH(CH(3))Ph and Z = CH(3), H, Cl, CN, CF(3), NH(2), Ph, CH(2)Ph, OCH(3), OCH(2)CH(3), OCH(CH(3))(2), OC(CH(3))(3), and F) have been calculated using a variety of DFT, MP2, and ONIOM-based methods, as well as G3(MP2)-RAD, with a view to identifying an accurate method that can be practically applied to larger systems. None of the DFT methods examined can reproduce the quantitative, nor qualitative, values of the fragmentation enthalpy; in most cases the relative errors are over 20 kJ mol(-1) and in some cases as much as 55 kJ mol(-1). The ROMP2 methods fare much better, but fail when the leaving group radical (R(*)) is substituted with a group (such as phenyl or CN) that delocalizes the unpaired electron. However, provided the primary substituents on the leaving group radical are included in the core system, an ONIOM-based approach in which the full system is studied via ROMP2 (or SCS- or SOS-MP2) calculations with the 6-311+G(3df,2p) basis set and the core system is studied at G3(MP2)-RAD can reproduce the corresponding G3(MP2)-RAD values of the full systems within 5 kJ mol(-1) and is a practical method for use on larger systems.     

Assessment of Contemporary Theoretical Methods for Bond Dissociation Enthalpies

The density functional theory (DFT) is the most popular method for evaluating bond dis-sociation enthalpies (BDEs) of most molecules. Thus, we are committed to looking for alternative methods that can balance the computational cost and higher precision to the best for large systems. The performance of DFT, double-hybrid DFT, and high-level com-posite methods are examined. The tested sets contain monocyclic and polycyclic aromatic molecules, branched hydrocarbons, small inorganic molecules, etc. The results show that the mPW2PLYP and G4MP2 methods achieve reasonable agreement with the benchmark values for most tested molecules, and the mean absolute deviations are 2.43 and 1.96 kcal/mol after excluding the BDEs of branched hydrocarbons. We recommend the G4MP2 is the most appropriate method for small systems (atoms number ≤20); the double-hybrid DFT methods are advised for large aromatic molecules in medium size (20 ≤atoms number ≤50), and the double-hybrid DFT methods with empirical dispersion correction are recommended for long-chain and branched hydrocarbons in the same size scope; the DFT methods are advised to apply for large systems (atoms number ≥50), and the M06-2X and B3P86 methods are also favorable. Moreover, the di erences of optimized geometry of different methods are discussed and the effects of basis sets for various methods are investigated.     

BDE261: a comprehensive set of high-level theoretical bond dissociation enthalpies

We have used the high-level W1w protocol to compile a comprehensive collection of 261 bond dissociation enthalpies (BDEs) for bonds connecting hydrogen, first-row and second-row p-block elements. Together they cover 45 bond types, and we term this the BDE261 set. We have used these benchmark values to assess the performance of computationally less demanding theoretical procedures, including density functional theory (DFT), double-hybrid DFT (DHDFT), and high-level composite procedures. We find that the M06-2X (DFT), ROB2-PLYP and DuT-D3 (DHDFT), and G3X(MP2)-RAD and G4(MP2)-6X (composite) procedures yield absolute BDEs with satisfactory to excellent accuracy. Overall, we recommend G4(MP2)-6X as an accurate and relatively cost-effective procedure for the direct computation of BDEs. One important finding is that the deviations for DFT and (especially) DHDFT procedures are often quite systematic. This allows an alternative approach to obtaining accurate absolute BDEs, namely, to evaluate accurate relative BDEs (RBDEs) using a computationally less demanding procedure, and to use these RBDEs in combination with appropriate and accurate reference BDEs to give accurate absolute BDEs. We recommend DuT-D3 for this purpose. For a still less computationally demanding approach, we introduce the deviation from additivity of the RBDE (DARBDE), and demonstrate that the combination of lower-level DARBDEs for larger systems and higher-level (W1w) reference RBDEs and BDEs for small systems can be utilized to obtain improved RBDEs for multiply substituted systems at low cost.     

Correlations between computation and experimental thermodynamics of halogen bonding

Correlations between experimental, solution-phase thermodynamic data and calculated gas-phase energies of interaction are investigated for noncovalent halogen bonding interactions between electron-deficient iodo compounds and Lewis bases. The experimental data consist of free energies of interaction spanning roughly 7 kcal/mol; they encompass halogen bonds involving both organic (iodoperfluoroarene or iodoperfluoroalkane) and inorganic (I(2), IBr, ICN) donors with nitrogen- and oxygen-based acceptors and are divided into two sets according to the identity of the solvent in which they were determined (alkanes or CCl(4)). Adiabatic energies of halogen bonding were calculated using a variety of methods, including 22 DFT exchange-correlation functionals, using geometries optimized at the MP2/6-31+G(d,p) level of theory. Certain DFT functionals, particularly the B97-1, B97-2, and B98 family, provide outstanding linear correlations with the experimental thermodynamic data, as assessed by a variety of statistical methods.     

Solvent effects on the S(N)2 reaction: Application of the density functional theory-based effective fragment potential method

The performance of the density functional theory (DFT)-based effective fragment potential (EFP) method is assessed using the S(N)2 reaction: Cl- + nH2O + CH3Br = CH3Cl + Br- + nH2O. The effect of the systematic addition of water molecules on the structures and relative energies of all species involved in the reaction has been studied. The EFP1 method is compared with second-order perturbation theory (MP2) and DFT results for n = 1, 2, and 3, and EFP1 results are also presented for four water molecules. The incremental hydration effects on the barrier height are the same for all methods. However, only full MP2 or MP2 with EFP1 solvent molecules are able to provide an accurate treatment of the transition state (TS) and hence the central barriers. Full DFT and DFT with EFP1 solvent molecules both predict central barriers that are too small. The results illustrate that the EFP1-based DFT method gives reliable results when combined with an accurate quantum mechanical (QM) method, so it may be used as an efficient alternative to fully QM methods in the treatment of larger microsolvated systems.     

Ab initio quantum chemistry on the Cray T3E massively parallel supercomputer: II

Gaussian-94 is the series of electronic structure programs. It is an integrated system to model a broad range of molecular systems under a variety of conditions, performing its calculations from the basic laws of quantum chemistry. This new version includes methods and algorithms for scalable massively parallel systems such as the Cray T3E supercomputer. In this study, we discuss the performance of Gaussian using large number of processors. In particular, we analyze the scalability of methods such as Hartree–Fock and density functional theory (DFT), including first and second derivatives. In addition, we explore scalability for CIS, MP2, and MCSCF calculations. Scalability and speedups were investigated for most of the examples with up to 64 process elements. A single-point energy calculation (B3-LYP/6-311++G3df,3p) was tested with up to 512 process elements. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1053–1063, 1998     

High-level ab initio versus DFT calculations on (H2O2)2 and H2O2–H2O complexes as prototypes of multiple hydrogen bond systems

The performance of B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91 density functionals to describe multiple hydrogen bond systems was studied. For this purpose we have chosen the dimers of hydrogen peroxide and the hydrogen peroxide–water complexes. The geometries and vibrational frequencies obtained with a 6-311+G(d,p) basis set were compared with those obtained at the MP2 level using the same basis set expansion. The corresponding dimerization energies were obtained using a 6-311+G(3df,2p) basis set and compared with those obtained using the G2(MP2) theory. Red shiftings of the OH donor stretching frequencies were predicted by all approaches investigated; however, in all cases, the DFT values were sizably larger than the MP2 ones. Similarly, the blue shifting of the torsion of the hydrogen peroxide subunit was larger when evaluated at the DFT level. All functionals reproduced the G2(MP2) relative stabilities of the different local minima quite well. With the exception of the B-LYP and B3-PW91 approaches, all functionals yielded binding energies which deviated from the G2(MP2) values by less than 0.5 kcal/mol, provided that G2-type basis sets were used and that the corresponding BSSE corrections were included. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1124–1135     

Accurate ab initio prediction of propagation rate coefficients in free-radical polymerization: Acrylonitrile and vinyl chloride

A systematic methodology for calculating accurate propagation rate coefficients in free-radical polymerization was designed and tested for vinyl chloride and acrylonitrile polymerization. For small to medium-sized polymer systems, theoretical reaction barriers are calculated using G3(MP2)-RAD. For larger systems, G3(MP2)-RAD barriers can be approximated (to within 1 kJ mol⁻¹) via an ONIOM-based approach in which the core is studied at G3(MP2)-RAD and the substituent effects are modeled with ROMP2/6-311+G(3df,2p). DFT methods (including BLYP, B3LYP, MPWB195, BB1K and MPWB1K) failed to reproduce the correct trends in the reaction barriers and enthalpies with molecular size, though KMLYP showed some promise as a low cost option for very large systems. Reaction rates are calculated via standard transition state theory in conjunction with the one-dimensional hindered rotor model. The harmonic oscillator approximation was shown to introduce an error of a factor of 2–3, and would be suitable for “order-of-magnitude” estimates. A systematic study of chain length effects indicated that rate coefficients had largely converged to their long chain limit at the dimer radical stage, and the inclusion of the primary substituent of the penultimate unit was sufficient for practical purposes. Solvent effects, as calculated using the COSMO model, were found to be relatively minor. The overall methodology reproduced the available experimental data for both of these monomers within a factor of 2.     

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.     

Are AM1 ligand‐protein binding enthalpies good enough for use in the rational design of new drugs?

We have examined the performance of semiempirical quantum mechanical methods in solving the problem of accurately predicting protein-ligand binding energies and geometries. Firstly, AM1 and PM3 geometries and binding enthalpies between small molecules that simulate typical ligand-protein interactions were compared with high level quantum mechanical techniques that include electronic correlation (e.g., MP2 or B3LYP). Species studied include alkanes, aromatic systems, molecules including groups with hypervalent sulfur or with donor or acceptor hydrogen bonding capability, as well as ammonium or carboxylate ions. B3LYP/6-311+G(2d,p) binding energies correlated very well with the BSSE corrected MP2/6-31G(d) values. AM1 binding enthalpies also showed good correlation with MP2 values, and their systematic deviation is acceptable when enthalpies are used for the comparison of interaction energies between ligands and a target. PM3 otherwise gave erratic energy differences in comparison to the B3LYP or MP2 approaches. As one would expect, the geometries of the binding complexes showed the known limitations of the semiempirical and DFT methods. AM1 calculations were subsequently applied to a test set consisting of "real" protein active site-ligand complexes. Preliminary results indicate that AM1 could be a valuable tool for the design of new drugs using proteins as templates. This approach also has a reasonable computational cost. The ligand-protein X-ray structures were reasonably reproduced by AM1 calculations and the corresponding AM1 binding enthalpies are in agreement with the results from the "small molecules" test set.     

Molecular recognition in molecular tweezers systems: quantum-chemical calculation of NMR chemical shifts

Quantum-chemical calculations for molecular tweezers systems are presented, where the focus is not only on the recognition process in the host-guest systems, but on the self aggregation of the tweezers host as well. Such intermolecular interactions influence the corresponding NMR spectra strongly by up to 6 ppm for proton chemical shifts, since ring-current effects are particularly important. The quantum-chemical results allow one to reliably assign the spectra and to gain information both on the structure and on the importance of intra- and intermolecular interactions. In addition, we study the accuracy of a variety of density functionals for describing the present host-guest systems, where we observe a considerable underestimation of ring-current effects on (1)H NMR chemical shifts at the density functional theory (DFT) level using smaller basis sets such as 6-31G**, so that larger bases like TZP are required. This stands in contrast to the behavior of the Hartree-Fock scheme, where small basis sets, such as 6-31G**, provide reliable (1)H NMR shieldings for molecular tweezers systems.     

Energetics and structure of glycine and alanine based model peptides: Approximate SCC-DFTB,AM1 and PM3 methods in comparison with DFT,HF and MP2 calculations

We calculate relative energies and geometries of important secondary structural elements for small glycine and alanine based polypeptides containing up to eight residues. We compare the performance of the approximate methods AM1, PM3 and self-consistent charge, density-functional tight-binding (SCC-DFTB) to density-functional theory (DFT), Hartree–Fock (HF) and MP2. The SCC-DFTB is able to reproduce structures and relative energies of various peptide models reliably compared to DFT results. The AM1 and PM3 methods show deficiencies in describing important secondary structure elements like extended, helical or turn structures. The discrepancies between different ab initio (HF, MP2) and DFT (B3LYP) methods for medium sized basis sets (6-31G*) also show the need for higher level calculations, since systematic errors found for small molecules may add up when investigating longer polypeptides.     

Vibrational analysis and ionization potentials of XCH3 (X=Be,Mg,Ca) calculated by hybrid density functional theory and high order ab initio methods

The amount of attention dedicated to the theoretical and experimental investigation of small cationic organometallic systems in the literature is very limited. In this Letter we use the B3LYP method with a variety of basis sets as well as the very advanced CBS-Q, CBS-QB3, G1, G2MP2, G2, G3, and G3B3 ab initio methods in order to analyze the vibrational spectra as well as ionization potentials of BeCH₃,MgCH₃ and CaCH₃. The need for further addition of experimental data to the archives for these systems is discussed, as well as recommendations for which theoretical methods are optimum for a particular result.     

Bond dissociation energies and radical stabilization energies: an assessment of contemporary theoretical procedures

Various contemporary theoretical procedures have been tested for their accuracy in predicting the bond dissociation energies (BDEs) and the radical stabilization energies (RSEs) for a test set of 22 monosubstituted methyl radicals. The procedures considered include the high-level W1, W1', CBS-QB3, ROCBS-QB3, G3(MP2)-RAD, and G3X(MP2)-RAD methods, unrestricted and restricted versions of the double-hybrid density functional theory (DFT) procedures B2-PLYP and MPW2-PLYP, and unrestricted and restricted versions of the hybrid DFT procedures BMK and MPWB1K, as well as the unrestricted DFT procedures UM05 and UM05-2X. The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the comparatively less expensive DFT procedures. RMPWB1K and both RBMK and UBMK give very promising results for absolute BDEs, while additionally restricted and unrestricted X2-PLYP methods and UM05-2X give excellent RSE values. UM05, UB2-PLYP, UMPW2-PLYP, UM05-2X, and UMPWB1K are among the less well performing methods for BDEs, while UMPWB1K and UM05 perform less well for RSEs. The high-level theoretical results are used to recommend alternative experimental BDEs for propyne, acetaldehyde, and acetic acid.     

Multicoefficient extrapolated density functional theory studies of pi...pi interactions: the benzene dimer

We report tests of new (2005) and established (1999-2003) multilevel methods against essentially converged benchmark results for nonbonded interactions in benzene dimers. We found that the newly developed multicoefficient extrapolated density functional theory (DFT) methods (which combine DFT with correlated wave function methods) give better performance than multilevel methods such as G3SX, G3SX(MP3), and CBS-QB3 that are based purely on wave function theory (WFT); furthermore, they have a lower computational cost. We conclude that our empirical approach for combining WFT methods with DFT methods is a very efficient and effective way for describing not only covalent interactions (as shown previously) but also nonbonded interactions.     

Dihydrogen trioxide clusters, (HOOOH)n (n = 2-4), and the hydrogen-bonded complexes of HOOOH with acetone and dimethyl ether: implications for the decomposition of HOOOH

Hydrogen-bonded gas-phase molecular clusters of dihydrogen trioxide (HOOOH) have been investigated using DFT (B3LYP/6-311++G(3df,3pd)) and MP2/6-311++G(3df,3pd) methods. The binding energies, vibrational frequencies, and dipole moments for the various dimer, trimer, and tetramer structures, in which HOOOH acts as a proton donor as well as an acceptor, are reported. The stronger binding interaction in the HOOOH dimer, as compared to that in the analogous cyclic structure of the HOOH dimer, indicates that dihydrogen trioxide is a stronger acid than hydrogen peroxide. A new decomposition pathway for HOOOH was explored. Decomposition occurs via an eight-membered ring transition state for the intermolecular (slightly asynchronous) transfer of two protons between the HOOOH molecules, which form a cyclic dimer, to produce water and singlet oxygen (Delta (1)O 2). This autocatalytic decomposition appears to explain a relatively fast decomposition (Delta H a(298K) = 19.9 kcal/mol, B3LYP/6-311+G(d,p)) of HOOOH in nonpolar (inert) solvents, which might even compete with the water-assisted decomposition of this simplest of polyoxides (Delta H a(298K) = 18.8 kcal/mol for (H 2O) 2-assisted decomposition) in more polar solvents. The formation of relatively strongly hydrogen-bonded complexes between HOOOH and organic oxygen bases, HOOOH-B (B = acetone and dimethyl ether), strongly retards the decomposition in these bases as solvents, most likely by preventing such a proton transfer.     

High level of ab initio and density functional theory computational study of structural and energetic properties of tetrafluorhydrazine rotamers

The HF, MP2, MP3, MP4, and QCISD ab initio methods were compared with local, hybrid, and gradient-corrected density functional theory (DFT) methods for computing structures and energies of N2F4 rotamers. In all DFT calculations 6-311 + G(2d) basis set was used. The generated structures energies of trans- and gauche-N₂F₄ rotamers, and their dissociation energies to nitrogen difluoride were compared with experimental data. Suitable hybrid and gradient-corrected DFT methods for determining structures and energies for these and similar molecular systems were discussed.     

Electron affinities of metals computed by density functional theory and ab initio methods

An extensive computational study of the meal electron affinity was performed using the ab initio and density functional theory (DFT) methods. HF, MP2, MP3, MP4, QCISD, and QCISD(T) was used as computational methods, while the hybrid, local, and nonlocal DFT methods with the LYP, P86, PW91, and VWN correlation functionals were used. Two basis sets, one small and applicable to almost all metals (LanL2DZ) and one large [6-311 + + G(3df, 3 pd)] used only for small metals, were employed. The computed results were compared with the experimental data and the capabilities of the DFT methods to perform this study were discussed. © 1997 John Wiley & Sons, Inc.