The X1 method for accurate and efficient prediction of heats of formation

We propose the X1 method which combines the density functional theory method with a neural network (NN) correction for an accurate yet efficient prediction of heats of formation. It calculates the final energy by using B3LYP6-311+G(3df,2p) at the B3LYP6-311+G(d,p) optimized geometry to obtain the B3LYP standard heats of formation at 298 K with the unscaled zero-point energy and thermal corrections at the latter basis set. The NN parameters cover 15 elements of H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, and Cl. The performance of X1 is close to the Gn theories, giving a mean absolute deviation of 1.43 kcalmol for the G399 set of 223 molecules up to 10 nonhydrogen atoms and 1.48 kcal/mol for the X107 set of 393 molecules up to 32 nonhydrogen atoms.     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Further evidence for the inseparability of the theoretical enthalpic terminal and penultimate unit effects in the radical copolymerization of styrene with acrylonitrile

The theoretical enthalpies of propagation reactions at 0 K without zero‐point vibrational energy corrections according to terminal and penultimate models of the radical copolymerization of styrene with acrylonitrile are reported from molecular orbital calculations at the following levels of theory and basis sets: HF/6‐31G(d); B3‐LYP/6‐31G(d); B3‐LYP/6‐311G(d,p) and B3‐LYP/6‐311+G(3df)//6‐311G(d,p). Both the enthalpic terminal and penultimate unit effects, determined according to the theoretical thermochemistry, depend on the level of theory and basis set used for the molecular orbital calculations. The best performing B3LYP/6‐311+G(3df)//B3LYP/6‐311G(d,p) procedure gives theoretical enthalpies for the addition of styrene and acrylonitrile to CH that differ from experimental values by 0.6 and 1.6 kcal mol^?1, respectively. An analysis of the results obtained here leads to the conclusion that at least for the styrene–acrylonitrile monomer system, that is, a monomer system known as one of the few systems that do not conform to terminal model composition and microstructure equations, the enthalpic terminal unit effects seem to depend on the penultimate units of the growing radical. This finding, together with the outcome from our previous work on the dependence of the penultimate effects on the terminal units in a growing macroradical, indicates the inseparability of the enthalpic terminal (implicit) and explicit penultimate unit effects on the radical copolymerization. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1778–1787, 2003     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Transition state structure and energetics of the N(2)O + X (X = Cl,Br) reactions

The structural and vibrational properties of the transition state of the N(2)O + X (X = Cl,Br) reactions have been characterized by ab initio methods using density functional theory. We have employed Becke's hybrid functional (B3LYP), and transition state optimizations were performed with 6-31G(d), 6-311G(2d,2p), 6-311+G(3d,2p), and 6-311+G(3df,2p) basis sets. For the chlorine atom reaction the coupled-cluster method (CCSD(T)) with 6-31G(d) basis set was also used. All calculations resulted in transition state structures with a planar cis arrangement of atoms for both reactions. The geometrical parameters of transition states at B3LYP are very similar, and the reaction coordinates involve mainly the breaking of the N-O bond. At CCSD(T)/6-31G(d) level a contribution of the O-Cl forming bond is also observed in the reaction coordinate. In addition, several highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction energetics. All model chemistries predict exothermic reactions. The G3 and G2 methods result in the smallest deviations from experiment, 1.8 and 0 kcal mol(-1), for the enthalpies of reaction for N(2)O reaction with chlorine and bromine, respectively. The G3//B3LYP and G1 methods perform best among the composite methods in predicting energies of the transition state, with a deviation of 1.9 and 3.0 kcal mol(-1), respectively, in the activation energies for the above processes. However, the B3LYP/6-311+G(3df,2p) method gives smaller deviations of 0.4 and -1.0 kcal mol(-1), respectively. The performance of the methodologies applied in predicting transition state energies was analyzed.     

Conformational energies for 2-substituted butanes

The conformational free energies for some 2-substituted butanes where X = F, Cl, CN, and CCH were calculated using G3-B3, CBS-QB3, and CCSD(T)/6-311++G(2d,p) as well as other theoretical levels. The above methods gave consistent results with free energies relative to the trans conformers as follows: X = CCH, g+ = 0.77 +/- 0.05 kcal/mol. g- = 0.88 +/- 0.05 kcal/mol; X = CN, g+ = 0.85 +/- 0.05 kcal/mol, g- = 0.75 +/- 0.05 kcal/mol; X = Cl, g+ = 0.70 +/- 0.05 kcal/ml, g- = 0.80 +/- 0.05 kcal/mol; and X = F, g+ = 0.53 +/- 0.05 kcal/mol, g- = 0.83 +/- 0.05 kcal/mol. The conformational free energies also were estimated using the observed liquid phase IR spectra and intensities calculated using B3LYP/6-311++G** and MP2/6-311++G**. The rotational free energy profiles for all of the compounds were estimated at the G3-B3 level.     

Quantum monte carlo study of heats of formation and bond dissociation energies of small hydrocarbons

A quantum Monte Carlo (QMC) benchmark study of heats of formation at 298 K and bond dissociation energies (BDEs) of 22 small hydrocarbons is reported. Diffusion Monte Carlo (DMC) results, obtained using a simple product trial wavefunctions consisting of a single determinant and correlation function, are compared to experiment and to other theory including a version of complete basis set theory (CBS‐Q) and density functional theory (DFT) with the B3LYP functional. For heats of formation, the findings are a mean absolute deviation from experiment of 1.2 kcal/mol for CBS‐Q, 2.0 kcal/mol for B3LYP, and 2.2 kcal/mol for DMC. The mean absolute deviation of 31 BDEs is 2.0 kcal/mol for CBS‐Q, 4.2 kcal/mol for B3LYP, and 2.5 kcal/mol for DMC. These findings are for 17 BDEs of closed‐shell molecules that have mean absolute deviations from experiment of 1.7 kcal/mol (CBS‐Q), 4.0 kcal/mol (B3LYP), and 2.2 kcal/mol (DMC). The corresponding results for the 14 BDEs of open‐shell molecules studied are 2.4 kcal/mol (CBS‐Q), 4.3 kcal/mol (B3LYP), and 2.9 kcal/mol (DMC). The DMC results provide a baseline from which improvement using multideterminant trial functions can be measured. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 583–592, 2005     

Conformers and intramolecular hydrogen bonding of the oxalic acid monomer and its anions

Density functional theory, B3LYP/6‐31G** and B3LYP/6‐311+G(2d,p), and ab initio MP2/6‐31G** calculations have been carried out to investigate the conformers, transition states, and energy barriers of the conformational processes of oxalic acid and its anions. QCISD/6‐31G** geometrical optimization is also performed in the stable forms. Its calculated energy differences between the two most stable conformers are very near to the related observed value at 7.0 kJ/mol. It is found that the structures and relative energies of oxalic acid conformers predicted by these methods show similar results, and that the conformer L1 (C_2h) with the double‐interfunctional‐groups hydrogen bonds is the most stable conformer. The magnitude of hydrogen bond energies depends on the energy differences of various optimized structures. The hydrogen bond energies will be about 32 kJ/mol for interfunctional groups, 17 kJ/mol for weak interfunctional groups, 24 kJ/mol for intra‐COOH in (COOH)₂, and 60 kJ/mol for interfunctional groups in (COOH)COO⁻¹ ion if calculated using the B3LYP/6‐311+G(2d,p) method. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 541–551, 2000     

Effect of trimethylsilyl substitution on the structure and properties of phthalocyanine: A density functional theory study

The geometries of four isomers of the trimethylsilyl substituted phthalocyanine (Pc)— I , II , III , and IV —have been optimized at the B3LYP/3‐21G level of density functional theory. Normal‐mode vibrational analyses have been performed and their standard thermodynamic functions, molar fractions, and electronic absorption spectra calculated. Single‐point energies have been calculated at the B3LYP/6‐311G* level for all isomers to evaluate the heats of formation from an isodesmic reaction. It is found that substitution has little influence on the geometry and electronic structures of the Pc framework. The corresponding geometric parameters in various isomers are close. According to the B3LYP/6‐311G*//B3LYP/3‐21G results, substitution at the peripheral position of the isoindole with an inner hydrogen is most favorable. The energies increase in the order of IV < II < III < I , and the energy difference between IV and I is 5.75 kJ/mol. The molar fractions of IV , II , III , and I are 0.80, 0.17, 0.02, and 0.02 and the heats of formation are 2009.96, 2010.10, 2015.85, and 2016.52 kJ/mol, respectively. This indicates that nonperipheral substituted Pcs have higher energy and little production because they are not stable under the considered conditions. The electronic spectra of the substituted Pcs calculated using the ZINDO method have two strong Q absorption bands around 700 nm and one B band around 300 nm that are slightly shifted compared with those in Pc. The ratios of the oscillator strength of the B band to the Q bands are much lowered by trimethylsilyl substitution. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Conformations and rotational barriers of 2,2′‐bithiazole and 4,4′‐dimethyl‐2,2′‐bithiazole semiemperical,ab initio,and density functional theory calculations

Conformational properties of 2,2′‐bithiazole and 4,4′‐dimethyl‐2,2′‐ bithiazole have been studied by using AM1 and PM3 semiemperical methods and ab initio HF/6‐311+G* and B3LYP/6‐311+G* calculations. All methods agree that the planar s‐trans conformation is the global minimum and the perpendicular conformation is the transition state. Additional local minima were found using the Hartree–Fock (HF) and B3LYP levels for 2,2′‐bithiazole while for 4,4′‐dimethyl derivative the minima was located only at the MP2//B3LYP level. The barrier heights for rotation are 1.72, 7.69, and 7.88 kcal/mol at the PM3, HF, and B3LYP levels, respectively, and methyl substitution did not affect appreciably this value. Fourier expansion terms and bond orders were used to explain the origins of the rotational barrier in terms of π conjugation, electrostatic interaction, and steric effects, which represent the main factors in the shape of the rotational barrier. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 367–377, 2000     

Theoretical predictions of the structure,gas‐phase acidity,and aromaticity of tetrathiosquaric acid

Results of ab initio self‐consistent‐field and density functional theory calculations of the gas‐phase structure, acidity (free energy of deprotonation, ΔG⁰), and aromaticity of tetrathiosquaric acid (3,4‐dithiohydroxy‐3‐cyclobutene‐1,2‐dithione, H₂C₄S₄) are reported. The global minimum found on the potential energy surface of tetrathiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanedithione, and cyclobutenedithiol. The computed aromatic stabilization energy by homodesmotic reaction is −18.4 (MP2(fu)/6‐311+G**//RHF/6‐311+G**) and −15.1 kcal/mol (B3LYP//6‐311+G**// B3LYP/6‐311+G**). The aromaticity of tetrathiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −11.77 (CSGT(IGAIM)‐RHF/6‐311+G**// RHF/6‐311+G**) and −18.08 (CSGT(IGAIM)‐B3LYP/6‐311+G**// B3LYP/6‐311+G**). Thus, tetrathiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The most reliable theoretical gas‐phase acidities are $\Delta G^{0}_{1(298\mathrm{K})}=303.7$ and $\Delta G^{0}_{2(298\mathrm{K})}=394.1$ kcal/mol. Hence, tetrathiosquaric acid is a stronger acid than squaric acid (3,4‐dihydroxy‐3‐ cyclobutene‐1,2‐dione, H₂C₄O₄). Comparisons of the computed results of tetrathiosquaric acid with squaric acid have also been made. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 443–449, 2000     

Computational studies on carbohydrates: I. Density functional ab initio geometry optimization on maltose conformations

Ab initio geometry optimization was carried out on 10 selected conformations of maltose and two 2‐methoxytetrahydropyran conformations using the density functional denoted B3LYP combined with two basis sets. The 6‐31G* and 6‐311++G** basis sets make up the B3LYP/6‐31G* and B3LYP/6‐311++G** procedures. Internal coordinates were fully relaxed, and structures were gradient optimized at both levels of theory. Ten conformations were studied at the B3LYP/6‐31G* level, and five of these were continued with full gradient optimization at the B3LYP/6‐311++G** level of theory. The details of the ab initio optimized geometries are presented here, with particular attention given to the positions of the atoms around the anomeric center and the effect of the particular anomer and hydrogen bonding pattern on the maltose ring structures and relative conformational energies. The size and complexity of the hydrogen‐bonding network prevented a rigorous search of conformational space by ab initio calculations. However, using empirical force fields, low‐energy conformers of maltose were found that were subsequently gradient optimized at the two ab initio levels of theory. Three classes of conformations were studied, as defined by the clockwise or counterclockwise direction of the hydroxyl groups, or a flipped conformer in which the ψ‐dihedral is rotated by ∼180°. Different combinations of ω side‐chain rotations gave energy differences of more than 6 kcal/mol above the lowest energy structure found. The lowest energy structures bear remarkably close resemblance to the neutron and X‐ray diffraction crystal structures. © 2000 John Wiley & Sons, Inc. * J Comput Chem 21: 1204–1219, 2000     

Quadricyclane radical cation rearrangements: a computational study of the transformations to 1,3,5-cycloheptatriene and norbornadiene

An alternative skeletal rearrangement of the quadricyclane radical cation (Q*+) explains the side products formed in the one-electron oxidation to norbornadiene. First, the bicyclo[2.2.1]hepta-2-ene-5-yl-7-ylium radical cation, with an activation energy of 14.9 kcal mol(-1), is formed. Second, this species can further rearrange to 1,3,5-cycloheptatriene through two plausible paths, that is, a multistep mechanism with two shallow intermediates and a stepwise path in which the bicyclo[3.2.0]hepta-2,6-diene radical cation is an intermediate. The multistep rearrangement has a rate-limiting step with an estimated activation energy of 16.5 kcal mol(-1), which is 2.8 kcal mol(-1) lower in energy than the stepwise mechanism. However, the lowest activation energy is found for the Q*+ cycloreversion to norbornadiene that has a transition structure, in close correspondence with earlier studies, and an activation energy of 10.1 kcal mol(-1), which agrees well with the experimental estimate of 9.3 kcal mol(-1). The computational estimates of activation energies were done using the CCSD(T)/6-311+G(d,p) method with geometries optimized on the B3LYP/6-311+G(d,p) level, combined with B3LYP/6-311+G(d,p) frequencies.     

Nucleofugality of phenyl and methyl carbonates

A series of X,Y-substituted benzhydryl phenyl carbonates 1 and X,Y-substituted benzhydryl methyl carbonates 2 were subjected to solvolysis in different methanol/water, ethanol/water, and acetone/water mixtures at 25 degrees C. The LFER equation, log k = sf(Ef + Nf), was used to derive the nucleofuge-specific parameters (Nf and sf) for phenyl carbonate (1LG) and methyl carbonate (2LG) leaving groups in a given solvent in SN1 type reaction. Kinetic measurements showed that phenyl carbonates solvolyze one order of magnitude faster than methyl carbonates. Optimized geometries of 1LG and 2LG at B3LYP/6-311G(d,p), B3LYP/6-311++G(d,p), and MP2(full)/6-311++G(d,p) levels revealed that negative charge delocalization in carbonate anions to all three oxygen atoms occurs due to negative hyperconjugation. Phenyl carbonate (1LG) is a better leaving group (Nf = -0.84 +/- 0.07 in 80% v/v aq EtOH) than methyl carbonate 2LG (Nf = -1.84 +/- 0.07 in 80% v/v aq EtOH) because of more pronounced negative hyperconjugation, which is characterized with a more elongated RO-C bond and more increased RO-C-CO angle in 1LG than in 2LG. Calculated affinities of benzhydryl cation toward methyl and phenyl carbonate anions (DeltaDeltaEaff = 11.7 kcal/mol at the B3LYP/6-311++G(d,p) level and DeltaDeltaEaff = 2.7 kcal/mol at the PCM-B3LYP/6-311++G(d,p) level in methanol, respectively) showed that 1LG is more stabilized than 2LG, which is in accordance with greater solvolytic reactivity of 1 than 2.     

Theoretical Study of Heterocyclic Nitro Compounds for Use as Novel Explosives and Propellants

The heats of formation (HOFs) of heterocyclic nitro compounds were obtained by using a density functional theory B3LYP method with 6‐31G* and 6‐311+G** basis sets. The isodesmic reactions designed for the evaluation of HOFs keep most of the basic ring structures of the title compounds and thus ensure the credibility of the results. The values of HOFs are 567.90, 874.29 and 975.83 kJ/mol at the B3LYP/6‐31G* level for hexanitrohexazaadamantane ( A ), nonanitrononaza‐tetracyclo[7.3.1.1^3,7.1^5,11] pentadecane ( B ) and tetranitrotetrazacubane ( C ) respectively. The predicted detonation velocities of the title compounds are larger than, and detonation pressures are much larger than that of the widely used 1,3,5,7‐tetranitro‐1,3,5,7‐tetraazacyclooctane (HMX). The dissociation energy for the weakest C‐N bonds in the cage skeleton of the title compounds are 137‐144 kJ/mol at the B3LYP/6‐31G* level.     

Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.     

Energetic preferences for alpha,beta versus beta,gamma unsaturation

Density functional theory has been applied at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level to examine the energetics of alpha,beta- versus beta,gamma-unsaturation for some common organic functional groups. Specifically, the relative stabilities of allyl-X (H2C=CHCH2X) and 1-propenyl-X (H3CCH=CHX) isomers have been computed for X = methyl, vinyl, phenyl, formyl, acetyl, methoxy, methylthio, methylsulfinyl, methylsulfonyl, sulfamoyl, and methoxysulfonyl, and the results are compared to available experimental data. The intrinsic preference of 3 kcal/mol for the 1-propenyl isomer when X = CH3 is exceeded by 2-4 kcal/mol for first-row conjugating groups, but it is not met for the sulfur-containing groups. In particular, alpha,beta-unsaturation is favored by less than 1 kcal/mol for the sulfone and sulfonamide analogues, while it is preferred by 8 kcal/mol for the vinyl-substituted case. Detailed structural results and torsional energy profiles are also reported.     

CF3 rotation in 3-(trifluoromethyl)phenanthrene. X-ray diffraction and ab initio electronic structure calculations

The molecular and crystal structure of 3-(trifluoromethyl)phenanthrene has been determined by X-ray diffraction. The structure of the isolated molecule has been calculated using electronic structure methods at the HF/3-21G, HF/6-31G, MP2/6-31G and B3LYP/6-31G levels. The potential energy surfaces for the rotation of the CF3 group in both the isolated molecule and cluster models for the crystal were computed using electronic structure methods. The barrier height for CF3 rotation in the isolated molecule was calculated to be 0.40 kcal mol(-1) at B3LYP/6-311+G//B3LYP/6-311+G. The B3LYP/6-31G calculated CF3 rotational barrier in a 13-molecule cluster based on the X-ray data was found to be 2.6 kcal mol(-1). The latter is in excellent agreement with experimental results from the NMR relaxation experiments reported in the companion paper (Beckmann, P. A.; Rosenberg, J.; Nordstrom, K.; Mallory, C. W.; Mallory, F. B. J. Phys. Chem. A 2006, 110, 3947). The computational results on the models for the solid state suggest that the intermolecular interaction between nearest neighbor pairs of CF3 groups in the crystal accounts for roughly 75% of the barrier to rotation in the solid state. This pair is found to undergo cooperative reorientation. We attribute the CF3 reorientational disorder in the crystal as observed by X-ray diffraction to the presence of a pair of minima on the potential energy surface and the effects of librational motion.