The decomposition of the SCF interaction energy in hydrogen bonded dimers corrected for basis set superposition errors: An examination of the basis set dependence

A systematic examination of the components of the interaction energy, obtained with the Kitaura and Morokuma method, for nine H-bonded dimers without and with counterpoise corrections (CP ) is presented. The nine dimers H_n A …? HBH_m correspond to all the possible combinations of HF, H₂O, and NH₃ as electron donors and electron acceptors. The interaction energy and the corresponding components have been computed over a sizable interval of intermolecular distances with five basis sets (STO -3G, MINI -1, 3-21G, 4-31G, 6-31G**) selected among those most extensively used to study interactions in larger systems. The CP corrections to the ΔE components have been obtained with a method, implemented in our group, which permits assignment to the pertinent components of ΔE of a physically reasonable portion of the CP correction even though different CP corrections are adopted. We examine here three versions of the CP correction, namely, the full CP correction (i.e., the original version of Boys and Bernardi) and CP corrections limited to the virtual space of the partner or to the electron donor only. The resulting data are employed to assess the basis set dependence of several models of hydrogen bonding (the electrostatic model, the semiclassical model, etc.) both with and without CP corrections.     

A systematic preparation of new contracted Gaussian- type orbital sets. VII. MINI-3, MINI-4, MIDI-3, and MIDI-4 sets for transition metal atoms

Two minimal contracted Gaussian-type orbital (CGTO ) sets are developed for the transition metal atoms. The expansion terms for the first set, MINI -3, are 4, 3, 3, and 3 for s-type CGTO s and others are all three. The abbreviation would be (4333/33/3) where the slash divides symmetry. The expansion terms for the other set, MINI -4, is (4333/43/4). The split-type basis sets, MIDI -3 and MIDI -4, are derived directly from MINI -3 and MINI -4, MINI -3 and MIDI -3 provide the outer-shell orbital energies which are far better than those by single-zeta (SZ ) STO s. MINI -4 and MIDI -4 provide the outer-shell orbital energies which are almost as good as those by double-zeta (DZ ) STO s. The total energies given by the present sets are better than those of SZ except for MINI -3 for Sc and Ti: the energies by MINI -4 and MIDI -4 are only 0.8–1.7 a.u. higher than DZ . The basis sets were tested on the Cu₂ molecule, where a large basis set was also used.     

Refined ab initio 6-31G split-valence basis set optimization of the molecular structures of biphenyl in twisted,planar, and perpendicular conformations

Improved full ab initio optimizations of the molecular structure of biphenyl in twisted minimum energy, coplanar, and perpendicular conformations by use of Poles's GAUSSIAN 82 program have been performed in the 6-31G basis set. These lead to geometries and energies of much higher reliability than our earlier STO-3G results. The torsional angle Φ_min obtained now is 45.41° in close agreement with the recent experimental value of 44.4° ± 1.2°. Calculated CC distances may be converted to experimental ED r_g-values by means of independently determined linear regression correlations with very high statistical confidence, although they agree better with experimental x ray data for coplanar biphenyl without this correction. Calculated intramolecular angles are very similar for both STO-3G and 6-31G basis sets. The calculated torsional energy barrier towards Φ = 90° (ΔE⁹⁰) is 6.76 kJ/mol in close agreement with the experimental-31G value of 6.5 ± 2.0 kJ/mol. For coplanar biphenyl with D_2h-symmetry the calculated torsional energy barrier ΔE⁰ is 13.26 kJ/mol which is surprisingly much higher than the experimental value of 6.0 ± 2.1 kJ/mol. This discrepancy could not be resolved by optimizations assumed for two kinds of distortions of planarity of orthohydrogens from the molecular plane of the coplanar carbon atoms. But for the twisted minimum energy conformation asymmetric bending of ortho-H atoms lead to a torsional angle Φ_min = 44.74° together with a dihedral angle towards ortho-H of 1.22°, and consequently even to an increase of torsional energy barriers to ΔE⁰ = 13.51 and ΔE⁹⁰ = 6.91 kJ/mol.     

Searching blue-shifted O–H···Y hydrogen bond in CH<Subscript>3</Subscript>OH complexes with CF<Subscript>4</Subscript>, C<Subscript>2</Subscript>F<Subscript>2</Subscript>, OC,Ne, and He: a theoretical study

The hydrogen-bonded structures of the CH₃OH complexes with CF₄, C₂F₂, OC, Ne, and He are designated as the starting points for geometry optimizations without and with counterpoise (CP) correction at MP2 level of theory with the basis sets 6-31+G*, 6-31++G**, and 6-311++G**, respectively. Tight convergence criteria are applied throughout all geometry optimizations in order to reduce the computational errors. According to the optimizations without CP correction, a blue-shifted O–H···Y (where Y = F, O, Ne, or He) hydrogen bond exists in all these five complexes. The magnitudes of blue shifts of ν(O–H) of the former four complexes with respect to that of CH₃OH are reduced greatly when the polarization and diffuse functions of the hydrogen atoms are added (results from 6-31+G* versus those from 6-31++G**). However, for the complexes CH₃OH–CF₄ and CH₃OH–C₂F₂, our optimizations using the CP corrections did not find the hydrogen-bonded structure to be a stationary point. The energy minimum of both the complexes corresponds to a non-hydrogen-bonded structure.     

Ab initio study of reactions of hydroxyl radicals with chloro‐ and fluoro‐substituted methanes

Ab initio calculations at the unrestricted Hartree–Fock (UHF) level have been performed to investigate the hydrogen abstraction reactions of ^? OH radicals with methane and nine halogen‐substituted methanes (F, Cl). Geometry optimization and vibrational frequency calculations have been performed on all reactants, adducts, products, and transition states at the UHF/6‐31G* level. Single‐point energy calculations at the MP2/6‐31++G* level using the UHF/6‐31G* optimized geometries have also been carried out on all species. Pre‐ and postreaction adducts have been detected on the UHF/6‐31G* potential energy surfaces of the studied reactions. Energy barriers, ΔE^?, reaction energies, ΔE_r, reaction enthalpies, ΔH_r, and activation energies, E_a, have been determined for all reactions and corrected for zero‐point energy effects. Both E_a and ΔH_r come into reasonable agreement with the experiment when correlation energy is taken into account and when more polarized and diffuse basis sets are used. The E_a values, estimated at the PMP2/6‐31++G* level, are found to be in good agreement with the experimental ones and correctly reproduce the experimentally observed trends in fluorine and chlorine substitution effects. A linear correlation between E_a and ΔH_r is obtained, suggesting the presence of an Evans–Polanyi type of relationship. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 426–440, 2001     

Photoelectron-spectroscopic Evidence Concerning “Homo-aromaticity”

The first of the two π-bands in the photoelectron spectrum of cis-cis-cis-1, 4, 7-cyclononatriene (I, symmetry C_3v) shows a Jahn-Teller split. This is consistent with the prediction of molecular orbital theory that the top occupied orbitals of I are e (π) and a ₁(π) respectively. From the difference ?( e (π)) - ?( a ₁(π)) = 0.90 to 0.97 eV a value of β_1,3 = ?0.68 eV = 0.27 β (β = -2.5 eV) is obtained for the homoconjugative interaction of two π-orbitals in I. This value represents almost exclusively through-space interaction between the π-orbitals. Through-bond interaction (hyperconjugation) is a minor effect in I. A comparison of the photoelectron data of bicyclo [4.2.1] nonatriene with those of norbornene and cycloheptadiene shows that homoconjugation (homo-aromaticity) can only be detected by photoelectron spectroscopy if the interacting π-bonds (basis orbitals) are symmetry equivalent or have accidentally (almost) degenerate energies.     

Bemerkung zur Gleichheit der Aufspaltungen ΔI (zwischen den ersten beiden π-Ionisationspotentialen) und ΔE (zwischen den entsprechenden π* ← π Übergangsenergien) des Spiro[4,4]nonatetraens. Vorläufige Mitteilung

For a given molecule M, the difference ΔI between the first two vertical ionization potentials I_v,2 and I_v,2 (from MOs ψ₁ and ψ₂) and ΔE between the corresponding singlet-singlet excitation energies E₁ and E₂ (transitions ψ?₁ ←₁, ψ?₁ ψ₂) are related by ΔE = ΔI- (J_2,?1?J_1,?1) ?2(K_1,?1 ? K_2,?1), using Koopmans approximation. A simple MO model suggests that under certain conditions of symmetry and quasi-alternancy (e. g. in spiro[4,4]nonatetraene 1 ) the bracketed differences between the Coulomb- and exchange-integrals should vanish to first order, thus leading to the simple (almost) equality ΔE = ΔI. It is shown that the results from a photoelectron- and electron-spectroscopic investigation of 1 support this conclusion i.e. ΔI = 1.23 eV, ΔE = 1.19 to 1.23 eV.     

“Assessing the RAFT Equilibrium Constant via Model Systems: An EPR Study”—Response to a Comment

We have presented an EPR‐based approach for deducing the RAFT equilibrium constant, K_eq, of a dithiobenzoate‐mediated system [Meiser, W. and Buback M. Macromol. Rapid Commun. 2011 , 32, 1490]. Our value is by four orders of magnitude below K_eq from ab initio calculations for the identical monomer‐free system. Junkers et al. [Macromol. Rapid Commun. 2011 , 32, 1891] claim that our EPR approach would be model dependent and our data could be equally well fitted by assuming slow addition of radicals to the RAFT agent and slow fragmentation of the so‐obtained intermediate radical as well as high cross‐termination rate. By identification of all side products, our EPR‐based method is shown to be model independent and to provide reliable K_eq values, which demonstrate the validity of the intermediate radical termination model.     

Building the “Phosphoindigo” Backbone by Oxidative Coupling of Phosphindolin‐3‐ones with Selenium Dioxide

Oxidative coupling of racemic 1‐ethoxy‐1‐oxophosphindolin‐3‐one ( 1 ) and its 5‐CF₃‐derivative 6 with SeO₂ furnishes 1,1′‐diphosphaindigo derivatives 5 and 7 as bis‐phosphinic esters, i. e. as P^V‐compounds. Like indigo and thioindigo, 5 and 7 exist in the E‐configuration; the crude products of 5 and 7 are mixtures of isomers that are trans‐ and cis‐configurated with respect to the relative orientation of the ester groups oat phosphorus. The structure of the centrosymmetric E‐P(R)P′(S) isomer [(E)‐trans‐isomer] of 5 was determined by X‐ray crystallography. Ester cleavage of 5 , followed by addition of triethylamine to bis‐phosphinic acid 9 (the 1,1,1′,1′‐tetroxide of “phosphoindigo”), furnishes the related bis‐triethylammonium salt 10 as a crystalline hydrate that exhibits an extended hydrogen bonding network.     

Rotational barriers of disilane,hexafluorodisilane, and hexamethyldisilane: Ab initio,density functional,and molecular mechanics (MM3) studies

We investigated structures, vibrational frequencies, and rotational barriers of disilane (Si₂H₆), hexafluorodisilane (Si₂F₆), and hexamethyldisilane (Si₂Me₆) by using ab initio molecular orbital and density functional theories. We employed four different levels of theories (i.e., HF/6–31G*, MP2/6–31G*, BLYP/6–31G*, and B3LYP/6–31G*) to optimize the structures and to calculate the vibrational frequencies (except for Si₂Me₆ at MP2/6–31G*). MP2/6–31G* calculations reproduce experimental bond lengths well, while BLYP/6–31G* calculations largely overestimate some bond lengths. Vibrational frequencies from density functional theories (BLYP/6–31G* and B3LYP/6–31G*) were in reasonably good agreement with experimental values without employing additional correction factors. We calculated the ΔG^‡(298 K) values of the internal rotation by correcting zero-point vibration energies, thermal vibration energies, and entropies. We performed CISD/6–31G*//MP2/6–31G* calculations and found the ΔG^‡(298 K) values for the internal rotation of Si₂H₆, Si₂F₆, and Si₂Me₆ to be 1.36, 2.06, and 2.69 kcal/mol, respectively. The performance of this level was verified by using G2 and G2(MP2) methods in Si₂H₆. According to our theoretical results, the ΔG^‡(298 K) values were marginally greater than the ΔE^‡(0 K) values in Si₂F₆ and Si₂Me₆ due to the contribution of the entropy. In Si₂H₆ the ΔE^‡(0 K) and ΔG^‡(298 K) values were coincidently similar due to a cancellation of two opposing contributions between zero-point and thermal vibrational energies, and entropies. Our calculated ΔG^‡(298 K) values were in good agreement with experimental values published recently. In addition, we also performed MM3 calculations on Si₂H₆ and Si₂Me₆. MM3 calculated rotational barriers and thermodynamic properties were compared with high level ab initio results. Based on this comparison, MM3 calculations reproduced high level ab initio results in rotational barriers and thermodynamic properties of Si₂H₆ derivatives including vibrational energies and entropies, although large errors exist in some vibrational frequencies. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1523–1533, 1997     

Kinetics of the “a” and “b” band emissions of mercury excimers with added gases

The kinetics of the “a” and “b” band emissions arising from the ¹Σ ← ³O_u and ¹Σ ← ³l_u transitions of the diatomic mercury molecule at λ_max ～ 4850 Å and 3350 Å, respectively, have been studied at low concentrations of mercury in the presence of N₂, C₂H₆, C₃H₈, and N₂O. Rate constant values have been obtained for the following reactions of the excimer molecule: Hg₂(³l_u) + N₂ → Hg₂(³O_u) + N₂ and Hg₂(³O_u) + RH → Hg₂(¹Σ) + RH, where RH = C₂H₆ or C₃H₈. From a consideration of the detailed kinetics of band emissions, it was also possible to derive rate constants for the quenching reactions of Hg(³P₀) atoms. These values are in reasonable agreement with those obtained previously from monitoring atom concentrations directly by 4047 Å absorbiometry.     

Uracil and the tautomer 4-hydroxyuracil: An ab initio study with geometry optimization

Ab initio STO -3G geometries and relative energies for uracil (U) and the tautomer 4-hydroxyuracil (U*) were obtained with the HONDO program utilizing the rapidly convergent method of Murtaugh and Sargent for geometry optimization. ΔE for U?U* is 6.61 kcal/mole. The reaction field continuum model for solvent effect indicates a preferential stabilization of U* by 1.0 kcal/mole. The calculated gas phase K_t and solution K_t for U?U* are 1.44×10^?5 and 1.3×10^?4, respectively.     

Counterpoise corrections to the evaluation of the bimolecular interaction energy components

Counterpoise corrections to the coupling terms of the bimolecular interaction energy decomposition are introduced and examined on a set of electron donor-acceptor dimers X·BH₃ (X=H₂O, NH₃, PH₃, LiH, CO). The interaction energy decomposition of Kitaura and Morokuma, and the decoupling of E _MIXsuggested by Nagase Fueno, Yamabe and Kitaura have been employed.Counterpoise corrections have numerical influence on two terms only of the NFYK decoupling. This decoupling gives useful additional information on the nature of the chemical interaction when applied to STO-3G minimal basis set wavefunctions, but fails when applied the 4-31G wavefunctions.     

Effect of pressure on gas permeability coefficients. A new application of “free volume” theory

The present work is a continuation of a general study of the effect of pressure on gas and vapor permeation through nonporous polymeric membranes. Permeability coefficients have been measured for 1,1-difluoroethylene (C₂H₂F₂) and fluoroform (CHF₃) in polyethylene at penetrant pressures up to 35 atm and at temperatures between -18 and 70°C. The permeability coefficient P? for the 1,1-difluoroethylene—polyethylene system was found to increase with increasing pressure differential Δp across the membrane. Isothermal plots of log ΔP versus Δp are generally linear and can be represented by empirical relations of the form ΔP = P(0)exp{m Δp}, where P(0) and m are constants. The slope m of these isotherms decreases with increasing temperature. Plots of log P? versus Δp for the fluoroform—polyethylene system are also linear, but exhibit negative slopes, i.e., P? decreases with increasing Δp. An extension of Fujita's “free volume” theory of diffusion in polymers shows that the dependence of P? on pressure reflects how the free volume of the polymer is affected by this pressure. An increase in the penetrant pressure may result in two opposing effects: (a) the concentration of the penetrant dissolved in the membrane is increased, thereby increasing the free volume, and (b) the hydrostatic pressure on the membrane is also increased, which causes a decrease in the free volume. If the overall effect is an increase in the free volume of the polymer, then P? will also increase, and vice versa.     

Basis set dependence,precision, and accuracy of full ab initio gradient optimizations of molecular structures of nonstrained hydrocarbons. I. CC bond lengths

Different highly accurate experimental determinations of molecular structures (ED: r_g and r⁰_α, MW: r₀, r_s, and r_z, and X-ray distances) of 14 unstrained hydrocarbons have been linearly correlated with corresponding self-consistent field Hartree Fock (SCF HF) ab initio full gradient-optimized structures. From the eight applied basis sets (STO -3G, STO -6G; 3-21G, 4-31G, 6-31G, 6-311G; 6-31G*, and 6-31G**) the 6-31G basis set, although not best regarding total energies, yields statistically the most precise regression equation, which allows the prediction of ED r_g CC distances as reliable as the best experimental determinations. Surprisingly the accuracy of all calculated CC distances (measured as difference Δ between calculated CC distances and experimental ED r_g values) depends linearly on bond distances, with the largest deviations being observed for triple bonds. This seems to be a clear indication of different influences of correlation effects on calculated geometries which are neglected in the applied HF treatment. The linear regression equations presented here allow the prediction of any kind of experimental CC distance parameters for each of the eight basis sets considered. Even experimentally unknown r_e CC distances may be predicted from these single determinantal HF optimizations.     

Theoretical Study on Intermolecular Interactions and Thermodynamic Properties of Dimethylnitroamine Clusters

Ab initio SCF and Mφller-Plesset correlation correction methods in combination with counterpose procedure for BSSE correction have been applied to the theroetical studying of dimethylnitroamine and its dimers and trimers.Three optimized stable dimers and two trimers have been obtained.The corrected binding energies of the most stable dimer and trimer were predicted to be -24.68kJ/mol and -47.27kJ/mol,respectively at the MP2/6-31G^*//HF/6-31G^* level.The proportion of correlated interation energies to their total interaction energies for all clusters was at least 29.3 percent,and the BSSE of ΔE(MP2) was at least 10.0kJ/mol.Dispersion and/or electrostatic force were dominant in all clusters.There exist cooperative effects in both the chain and the cyclic trimers.The vibrational frequencies associated with N-O stretches or wags exhibit slight red shifts,but the modes associated with the motion of hydrogen atoms of the methyl group show somewhat blue shifts with respect to those of monomer.Thermodynamic properties of dimethylnitroamine and its clusters at different temperatures have been calculated on the basis of vibrational analyses.The changes of the Gibbs free energies for the aggregation from monomer to the most stable dimer and trimer were predicted to be 14.37kJ/mol and 30.40kJ/mol,respectively,at 1 atm and 298.15K.     

Theoretical Investigation into Electronic Structures and Charge Transfer Properties of π‐Conjugated System with Different Combinations of Thiophene and Vinyl/Butadiene

A series of combinations of thiophene and vinyl/butadiene were investigated by ab initio and DFT methods to explore their electronic structures and charge transfer properties. The results show that increasing thiophene ring and vinyl number is a rational strategy to raise the HOMO energy levels and lower the LUMO energy levels. Moving the vinyl from the periphery to the core has the slight effect on the HOMO and LUMO energy levels. Furthermore, replacing the middle vinyl and end‐capped vinyl of 3b (T5V4) with the butadiene can lower LUMO energy levels and then facilitate the electron injection. Above all, the close hole and electron reorganization energies (λ_h and λ_e) are observed from these compounds. However, the λ_es are smaller than their respective λ_hs in some compounds, which is relatively rare in organic materials. Especially, the promising ambipolar material 3c (T5B4) is recommended theoretically for possessing the equivalent minimum λ_h (0.24 eV) and λ_e (0.24 eV). The absorption wavelengths exhibit red shifts with the increasing of the thiophene ring and the vinyl number under the same configuration, which correspond to the reverse order of ΔE_H‐L and E_g. The linear relationships are found between experimental lowest singlet excited energies (E_exp) with theoretical values ΔE_H‐L and E_g.     

Ab initio calculations of guanidinium–carboxylate interaction

Ab initio calculations (self-consistent-field Hartree–Fock) using 6-31G and STO -4G basis sets are used to investigate the interaction between guanidinium and methylguanidinium ion with the carboxylate group of formate. Binding energies and optimum geometries are obtained and compared with reported results using a smaller basis set (STO -3G). The importance of this interaction in proteinsubstrate binding is discussed.     

Synthesis and thermal analysis of branched and “kinked” poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) was synthesized by self-condensation of bis-(2-hydroxyethyl) terephthalate (BHET). Copolymerization of BHET with ethyl, bis-3,5-(2-hydroxyethoxy) benzoate (EBHEB) and ethyl, 3-(2-hydroxyethoxy) benzoate (E3HEB) yielded copolymers that contain varying amounts of branching and kinks, respectively. Copolymers of BHET with ethyl, 4-(2-hydroxyethoxy) benzoate (E4HEB), in which only the backbone symmetry is broken but without disruption of the linearity, were also prepared for comparison. The composition of the copolymers were established from their ¹H-NMR spectra. The intrinsic viscosity of all the copolymers indicated that they were of reasonably high molecular weights. The thermal analysis of the copolymers using DSC showed that both the melting temperatures (T_m) and the percent crystallinity (as seen from the enthalpies of melting) (ΔH_m) decreased with increasing comonomer (defect concentration) content, although their glass transition temperatures (T_g) were less affected. This effect was found to be most pronounced in the case of branching, while the effects of kinks and linear disruptions, on both T_m and ΔH_m, were found to be similar. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 309–317, 1998