On the accuracy of correlation energy calculated by the correlation factor method: first- and second-row atoms

Summary The correlation energy of two- and four-isoelectronic series, a representative example for which the existing spin-density functionals fails, is calculated using the Colle and Salvetti method, considering mono- and multideterminantal wave functions. The results are in agreement with experimental data, and show the potentiality of this method when it is applied to wave functions including the most relevant configurational features. Also, results for the ionization energies and electron affinities of first- and second-row atoms are reported.     

A method for molecular correlation energy calculations. Application to the determination of dissociation energies of diatomic and polyatomic molecules

A simple and economical method for molecular correlation energy calculations is developed. In this method, the internal part of the correlation energy is calculated by means of a CI in a minimal basis set and the non-internal part (semi-internal and all-external) is evaluated using an original atoms-in-molecule method. It is successfully applied to the determination of dissociation energies of some diatomic (H₂, NH, C₂, CN, N₂, CO, NO, O₂, F₂) and polyatomic (H₂O, N₂O, CO₂, N₃H, CH₂N₂, CH₂CO, C₂N₂) molecules. The results are compared to those obtained using very elaborate variational methods.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms. I. Methodological developments

An extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms is presented. In addition to the use of pseudo-potentials in the calculations, the consequences of this extension on the different components of the energy partition which is the basic idea of the method, is analysed. Particular emphasis is placed on the specific role played by the 3d orbitals in each of the energy components. First, at the zeroth order, the energy is found to be very sensitive to the optimization of the 3d polarization functions. Secondly, the internal correlation energy, calculated by CI, requires the optimization of distinct 3d correlation orbitals to describe adequately the strong near-degeneracy effects that occur within the valence space. Finally it is shown that the 3d orbitals contribute partially to the non-internal correlation energy and that, the atoms-in-molecule structures corresponding typically to all-external contributions are negligible. The concept of error energy is introduced in place of the non-internal correlation energy: it includes the relativistic contributions within the semi-empirical tables. Such tables are presented for second row atoms and for the chlorine atom. From these tables, predicted values for some atomic term energies, experimentally undetermined, are derived. The methodological tests are limited here to the chlorine atom which is chosen for further applications in the next paper of this series. The conclusions concerning the applicability of the method to third row atoms are however quite general.Boursier I.R.S.I.A     

Gas-phase acidity, bond dissociation energy and enthalpy of formation of fluorine-substituted benzenes: A theoretical study

A variety of theoretical methods have been used to study the gas-phase acidity of benzene and its eleven fluorine-substituted derivatives: fluorobenzene, three isomers of difluorobenezene, three isomers of trifluorobenzene, three isomers of tetrafluorobenzene and 1,2,3,4,5-pentafluorobenzene. The high-level ab initio methods, G3//B3-LYP and CBS-QB3, are shown to reproduce experimental data to within an average of 1.9 and 1.4 kcal mol⁻¹, respectively. Of the lower-cost methods studied, M05-2X and MP2 showed the best overall performance with mean absolute deviations of just 1.2 and 1.1 kcal mol⁻¹, respectively. The effect of substitution and position on the acidity of the protons in the various compounds are studied and the structure-reactivity trends in these heterolytic C-H bond dissociation energies (BDEs) are compared with the corresponding homolytic C-H BDEs for the same species.     

General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part I. Theory

Measured additive properties of polyprotic acids and bases as functions of the pH of the solution can be used for the determination of the dissociation constants. A rigorous general equation is derived in this paper for this purpose. The equation relates the additive property of the acid or base to the dissociation constants, the limiting values and activity coefficients of the solute species, and to the pH of the solution. The equation is used to obtain the dissociation constants by fitting it to the experimental data in a nonlinear least-square fitting procedure. Overlapping dissociation constants pose no problem in this method. Applications to spectrophotometry and reversed-phase high performance liquid chromatography are presented in a following paper (Part II of this series).     

Population analysis based on occupation numbers II. Relationship between shared electron numbers and bond energies and characterization of hypervalent contributions

The population analysis based on occupation numbers, originally proposed by Davidson, is briefly reviewed. A new way is proposed to determine modified AOs and to characterize hypervalent contributions. This is discussed in application to the molecules NSF, NSF₃, SF₆, OPCl, OPCl₂, O₂PCl, SO₂, ClO ₄ ^– . It is the main objective of this work to investigate the connection between shared electron numbers — considered as a measure of covalent bond strength — and bond energies, is found to be a reliable measure of bond energies.     

Computational studies of bond dissociation energies, ionization potentials, and heat of formation for NH and NH+. Are hybrid density functional theory methods as accurate as quadratic complete basis set and Gaussian-2 ab initio methods?

Ionization potentials, bond dissociation energies, and heat of formation for NH and NH⁺ molecular species as well as for their elements were computed with highly reliable quadratic complete basis set and Gaussian-2 ab initio methods. The results are compared with experimental results and the assurance of these ab initio approaches is assessed. The same studies were also performed with three hybrid density functional methods (B3LYP, B3P86, and B3PW91) in combination with variously sized basis sets. The computational results are discussed in light of density functional theory reliability for exploring the potential energy of small polar molecular systems. Received: 21 July 1997 / Accepted: 8 December 1997     

Complete basis set ab initio computational study of ionization potential, electron affinity and the C-F bond dissociation energy for perfluorinated methane derivatives

A computational study of perfluorinated methane derivatives was performed with complete basis set ab initio methods. The total energies for their neutral, cation, and anionic states were computed. From these values, the energy gaps between different electronic states, ionization potentials, electron affinities, and C-F bond dissociation energies were calculated. The computed values are compared with experimental data and the reliability of complete basis set ab initio methods is discussed. New values for C-F bond dissociation energies are suggested. Received: 12 January 1998 / Accepted: 2 April 1998 / Published online: 29 July 1998     

Quantum mechanical studies of the protonation and NBr bond dissociation of the biologically important N-bromosuccinimide

N-Bromosuccinimide (NBS) is a brominating and oxidizing agent that is used as a source of bromine. The proton affinities, the tautomeric forms and NBr bond dissociation of NBS have been computed using the B3LYP functional as implemented in the density functional approach. The electronic structures of all possible tautomeric forms of NBS have been thoroughly investigated. The keto form of NBS has been shown to be more stable than any other tautomeric forms. The geometries and relative energies for various stationary structures were determined. The results indicate clearly that O-site protonation is strongly favored over N-site protonation for the studied compound in case of mono- and di-protonation. The bond dissociation energies (BDEs), involving the formation of the bromine radical, cation, and anion, of the NBr bond have been investigated. The NBr BDE of the Br radical formation is lower than that of the Br anion or cation. These conclusions are in good agreement with the experimental results.     

A theoretical study on NH bond dissociation enthalpies of oxo, thio and seleno carbamates and their N-protonated and N-deprotonated species

The effect of N-protonation and N-deprotonation on structure, NH bond dissociation enthalpies (BDEs) and stabilities of radicals formed on H-abstraction from nitrogen atom of carbamates and their thio- and seleno-analogs have been investigated. For those molecules where experimental results are available for comparison, the ROB3LYP/6-311++G(d,p)//B3LYP/6-31+G* theoretical level is in agreement within the estimated experimental uncertainty. The NH BDE of carbamates H₂NC(=X)YCH₃ [X = O; Y = O, S, Se] are higher but lower when X = S, Se and Y = O, S, Se in comparison to NH BDE of NH₃. DFT calculations indicate that the NH bond dissociation enthalpies are decreased by protonation and deprotonation at nitrogen atom; but the effect of deprotonation is rather smaller than the protonation. The variations are analyzed in terms of stabilities of molecules, their protonated and deprotonated species along with their respective radicals. The electron delocalization from nitrogen, X and Y atoms, electrostatic interactions, conjugative interactions and spin delocalization are the important factors affecting the stability. The spin delocalization and shift of radical center to chalcogen X (X = S, Se) are the main determinants for radical stability.     

Electronic and geometrical structures of cyclopropanes, part 51. fluorocyclopropanes. linear correlation of orbital energies with C–C bond lengths. further improvement of the two-orbitals model

The electronic and geometrical structures of fluorocyclopropanes (1–12) have been analysed using DFT B3LYP calculations. A linear relationship, Δɛ_ω=−0.172 Δr−0.171 (n=12, R=0.931), between Δɛ_ω (in eV), the difference of the energies of the Walsh orbitals ω_S and ω_A, and Δr (in pm), the difference of vicinal and distal C–C bond lengths, is established. Correcting the orbital splitting by the basic value at Δr=0.00 pm, an even better linear correlation Δɛ_ω ^eff=0.0720 Δr (n=12, R=0.984) is obtained. The results confirm the general applicability of the two-orbitals model for the relationship between geometrical and electronic structures for substituted cyclopropanes. ¹For Part 4 see Ref. [17].     

The influence of electron correlation on reaction energies. The dimerization energies of BH3 and LiH

Results of rigorous computations employing extended Gaussian-type basis sets are reported for BH₃, B₂H₆, LiH, and Li₂H₂ in their respective equilibrium geometries. The dimerization energy of BH₃ is calculated as −20.7 kcal/mol within the Hartree-Fock approximation and as −36.6 kcal/mol if electron correlation is included. The corresponding results for the dimerization of LiH are −47.3 kcal/mol and −48.3 kcal/mol. Partitioning of the correlation energy contributions allows to attribute the effect of electron correlation to the increase of next neighbour bond interactions on the dimerization of BH₃ and LiH. The difficulties of accurate computations of reaction energies are discussed in detail.     

Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides

Summary The effective core potential and model potential methods were used in post-SCF calculations on HC1, HBr, Cl₂, and Br₂ in order to gain insight into the effect of insufficient representation of inner nodes in the valence orbitals of the approximate methods. The results show that while the correlation energy may be slightly overestimated (by 1–7%), both the electric moment functions and the quantities depending on energy differences are consistently similar for the methods studied and close to the results from all-electron calculations.Dedicated to Prof. Klaus Ruedenberg     

Many-Body Rayleigh-Schrödinger Perturbation calculations of the correlation energy of open shell molecules in the restricted Roothaan-Hartree-Fock formalism. Application to heats of reaction and energies of activation

The title technique was applied to a series of elementary chemical reactions. Second and third order contributions to the correlation energy were computed for the basis sets of the double zeta and double zeta plus polarization quality. Calculated heats of reaction and energies of activation were compared with the experimental data and the results of the bestab initio calculations reported in the literature.     

Study of minimum energy conformers of N-substituted derivatives of piperidine and pyrrolidine. Evidence of weak H-bonding by theoretical correlation with experimental NMR data

Four N-substituted piperidines and four N-substituted pyrrolidines were synthesized and characterized by common spectroscopic techniques. In order to investigate the dynamic behavior of these important heterocyclic building blocks, a conformational study was carried out, using suitable tools of computational chemistry. The comparison of computed and experimental NMR chemical shifts is now accepted as a valuable aid in the elucidation of structures and that was the strategy followed in the present study. After a conformational search by statistical methods, the lowest three minimum-energy conformers of each piperidine/pyrrolidine derivative were analyzed (24 conformers in total). The relative proportion of each conformer was estimated by thermodynamic calculations, involving the Boltzmann weighting factor; P_i. Using DFT methods, the geometry of each conformer was fully optimized and their chemical shifts (¹H, ¹³C) were calculated. A very good coincidence between calculated and experimental data of both, ¹H and ¹³C shifts was found, indicating that the theoretical geometries obtained were reliable enough for the study of structure-properties relationships. For all the conformers, specific weak unusual hydrogen bonding involving H-C instead of H-X (where X=electronegative atom) was observed. The nitrogen atom and the carbonyl oxygen participate in these interactions and could play an important role in the activity of these compounds and, therefore, they should be considered in the modeling of bioactive compounds. Furthermore, the good quality of theoretical/experimental data validates the theoretical methods used. The solvent effect (CDCl₃ in this case) was found of small significance on the observed H-bonding.     

Additivity of electron correlation energy and the ab initio MO calculation of (0–0) S1←S0 transition energies: polychlorinated dibenzofurans

The energies of the S₀ and S₁ states of polychlorinated dibenzofurans (PCDFs) were calculated using the Hartree–Fock (HF) and configuration interaction-singles (CIS) methods. We can obtain the (0–0) transition energies of PCDFs with good accuracy if the energies calculated using the HF and CIS methods are adjusted to take the electron correlation energy into account. The correlation energy of the S₀ state was calculated using the Møller–Plesset correlation correction truncated at the second order (MP2), and that of the S₁ state was determined using experimental data. The correlation energies for both S₀ and S₁ states were expressed as the sum of the contributions arising from dibenzofuran (DF) and substituted chlorine atoms. The energy of the ground state calculated using the additivity approximation was in good agreement with the energy given directly by the MP2 method. The (0–0) S₁←S₀ transition energies corrected for electron correlation energy agreed well with the available experimental data. The approach proposed in this paper may be useful for the estimation of the electronic transition energy for large aromatic molecules.     

Pyramidane 2. Further computational studies: potential energy surface, basicity and acidity, electron-withdrawing and electron-donating power, ionization energy and electron affinity, heat of formation and strain energy, and NMR chemical shifts

The novel cycloalkane pyramidane (tetracyclo[2.1.0.0^1,30^2,5]pentane, [3.3.3.3]fenestrane), C₅H₄, with a pyramidal carbon atom, was investigated further. Calculations at the B3LYP/6-31G^* and G2(MP2) levels supported earlier conclusions from QCISD(T)/6-31G^*//MP2(FC)/6-31G^* energies that pyramidane lies in a deep well (ca. 100 kJ mol⁻¹) on the potential energy surface. The pyramidal carbon is predicted to have a lone electron pair, and calculations (CBS-4) indicate that pyramidane is remarkably basic for a saturated hydrocarbon (proton affinity 976, cf. 922 and 915 kJ mol⁻¹ for pyridine and aniline, respectively). The calculated (CBS-4) acidity is similar to that of tetrahedrane and toluene; the pyramidyl group (C₅H₃) attached to an atom bearing a lone electron pair appears to be much more strongly electron-withdrawing than the phenyl group. The infrared CO stretching frequency and C–CHO rotational barriers of pyramCHO, PhCHO and cyclopropylCHO indicate that the pyramidyl group is comparable to phenyl and cyclopropyl in its ability to donate electrons to an electron-deficient carbon. The adiabatic ionization energy of pyramidane is ca. 9.0 eV (MP2/6-31G^*, energy differences and Koopmans’ theorem), similar to that of typical cycloalkanes. The heat of formation of pyramidane was calculated by the G2(MP2) method and isodesmic reactions to be to be 585 kJ mol⁻¹ and the strain energy was estimated to be 622 kJ mol⁻¹; pyramidane is 122 kJ mol⁻¹ more strained than its isomer spiropentadiene. Application of the NMR NICS method, varying the position of the probe nucleus, gave no evidence for benzenoid-type aromaticity in the potentially cyclobutadiene cation-like base of pyramidane.     

Synthesis, photophysics, electrochemistry, theoretical, and transient absorption studies of luminescent copper(I) and silver(I) diynyl complexes. X-ray crystal structures of [Cu3(micro-dppm)3(micro3-eta1-C triple bond CC triple bond CPh)2]PF6 and [Cu3(micro-dppm)3(micro3-eta1-C triple bond CC triple bond CH)2]PF6

A series of soluble trinuclear copper(I) and silver(I) complexes containing bicapped diynyl ligands, [M(3)(micro-dppm)(3)(micro(3)-eta(1)-C triple bond CC triple bond CR)(2)]PF(6) (M = Cu, R = Ph, C(6)H(4)-CH(3)-p, C(6)H(4)-OCH(3)-p, (n)C(6)H(13), H; M = Ag, R = Ph, C(6)H(4)-OCH(3)-p), has been synthesized and their electronic, photophysical, and electrochemical properties studied. The X-ray crystal structures of [Cu(3)(micro-dppm)(3)(micro(3)-eta(1)-C triple bond CC triple bond CPh)(2)]PF(6) and [Cu(3)(micro-dppm)(3)(micro(3)-eta(1)-C triple bond CC triple bond CH)(2)]PF(6) have been determined.     

Exocyclic push–pull conjugated compounds. Part 3. An experimental NMR and theoretical MO ab initio study of the structure, the electronic properties and barriers to rotation about the exocyclic partial double bond in 2-exo-methylene- and 2-cyanoimino-quinazolines and -benzodiazepines

The structure of a number of 2-exo-methylene substituted quinazolines and benzodiazepines, respectively, 1, 3a,b, 4 (X=–CN,–COOEt) and their 2-cyanoimino substituted analogues 2, 3c,d (X=–CN,–SO₂C₆H₄–Me(p) was completely assigned by the whole arsenal of 1D and 2D NMR spectroscopic methods. The E/Z isomerism at the exo-cyclic double bond was determined by both NMR spectroscopy and confirmed by ab initio quantum chemical calculations; the Z isomer is the preferred one, its amount proved dependent on steric hindrance. Due to the push–pull effect in this part of the molecules the restricted rotation about the partial C²,C¹¹ and C²,N¹¹ double bonds, could also be studied and the barrier to rotation measured by dynamic NMR spectroscopy. The free energies of activation of this dynamic process proved very similar along the compounds studied but being dependent on the polarity of the solvent. Quantum chemical calculations at the ab initio level were employed to prove the stereochemistry at the exo-cyclic partial double bonds of 1–4, to calculate the barriers to rotation but also to discuss in detail both the ground and the transition state of the latter dynamic process in order to better understand electronic, inter- and intramolecular effects on the barrier to rotation which could be determined experimentally. In the cyanoimino substituted compounds 2, 3c,d, the MO ab initio calculations evidence the isomer interconversion to be better described by the internal rotation process than by the lateral shift mechanism.