Hartree-Fock-Heitler-London method. 2. First and second row diatomic hydrides

The Hartree-Fock-Heitler-London, HF-HL, method is a new ab initio approach which variationally combines the Hartree-Fock, HF, and the Heitler-London, HL, approximations, yielding correct dissociation products. Furthermore, the new method accounts for nondynamical correlation and explicitly considers avoided crossing. With the HF-HL model we compute the ground-state potential energy curves for H2 [1Sigma+g], LiH [X 1Sigma+], BeH [2Sigma+], BH [1Sigma+], CH [2Pi], NH [3Sigma-], OH [2Pi], and FH [1Sigma+], obtaining in average 80% of the experimental binding energy with a correct representation of bond breaking. Inclusion of ionic configurations improves the computed binding energy. The computed dipole moment is in agreement with laboratory data. The dynamical and nondynamical correlation energies for atomic and molecular systems with 2-10 electrons are analyzed. For BeH the avoided crossing of the two lowest [2Sigma+] states is considered in detail. The HF-HL function is proposed as the zero-order reference wave function for molecular systems. To account for the dynamical correlation energy a post-HF-HL technique based on multiconfiguration expansions is presented. We have computed the potential energy curves for H2 [1Sigma+g], HeH [2Sigma+], LiH [X1Sigma+], LiH [A1Sigma+], and BeH [2Sigma+]. The corresponding computed binding energies are 109.26 (109.48), 0.01 (0.01), 57.68 (58.00), 24.19 (24.82), and 49.61 (49.83) kcal/mol, with the experimental values given in parentheses. The corresponding total energies are -1.1741, -3.4035, -8.0695, -7.9446, and -15.2452 hartrees, respectively, the best ab initio variational published calculations, H2 excluded.     

The Hartree-Fock-Heitler-London method, III: Correlated diatomic hydrides

In a recently proposed model, called Hartree-Fock-Heitler-London (HF-HL) (Corongiu, G. J. Phys. Chem. A 2006, 110, 11584), the molecular wave function was variationally obtained by merging two traditional models, Hartree-Fock (HF) and Heitler-London (HL). In the new method, the non-dynamical correlation energy-which includes state avoided crossing-is explicitly calculated with a few configurations. In this work the dynamical correlation energy for diatomic hydrides of the first and second period is computed both ab initio, via short MC-HF and MC-HL expansions-including ionic and excited covalent structures-and semiempirically, using the Coulomb hole algorithm, a density functional proposed by Clementi in the early 1960s. The Coulomb Hole correction is applied to HF and HF-HL functions, and, departing from tradition, also to HL functions. Few ab initio HF-HL configurations with inclusion of ionic structures yield reasonable binding energies not only for the hydrides considered but also for the van der Waals HeH molecule. The computed binding energies (in kcal/mol) from HF-HL functions corrected with the Coulomb hole functional are as follows: 109.48 (109.48) for H2[1Sigma+g]; 0.01 (0.01) for HeH [2Sigma+]; 59.22 (58.00) for LiH [1Sigma+], 49.55 (49.83) for BeH [2Sigma+], 86.77 (84.1) for BH [1Sigma+], 82.65 (83.9) for CH [2Pi], 81.57 (80.5) for NH [3Sigma-], 107.18 (106.6) for OH [2Pi], and 140.91 (141.5) for HF [1Sigma+]; experimental values are given in parentheses. The computed total energies are in good agreement with exact nonrelativistic values. The combined availability of the correlation and binding energies from HF, HL, and HF-HL models allows a novel analyses on the hydrides chemical bond, in agreement with accepted physical chemistry concept derived from MO and VB theories.     

On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions

A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X1(2)II(3/2) states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-. After determining the frozen core, complete basis set (CBS) limit CCSD(T) values, corrections were added for core-valence correlation, relativistic effects (scalar and spin-orbit), the pseudopotential approximation (BrO and IO), iterative connected triple excitations (CCSDT), and iterative quadruples (CCSDTQ). The final ab initio equilibrium bond lengths and harmonic frequencies for ClO and BrO differ from their accurate experimental values by an average of just 0.0005 A and 0.8 cm-1, respectively. The bond length of IO is overestimated by 0.0047 A, presumably due to an underestimation of molecular spin-orbit coupling effects. Spectroscopic constants for the spin-orbit excited X2(2)III(1/2) states are also reported for each species. The predicted bond lengths and harmonic frequencies for the closed-shell anions are expected to be accurate to within about 0.001 A and 2 cm-1, respectively. The dissociation energies of the radicals have been determined by both direct calculation and through use of negative ion thermochemical cycles, which made use of a small amount of accurate experimental data. The resulting values of D0, 63.5, 55.8, and 54.2 kcal/mol for ClO, BrO, and IO, respectively, are the most accurate ab initio values to date, and those for ClO and BrO differ from their experimental values by just 0.1 kcal/mol. These dissociation energies lead to heats of formation, DeltaH(f) (298 K), of 24.2 +/- 0.3, 29.6 +/- 0.4, and 29.9 +/- 0.6 kcal/mol for ClO, BrO, and IO, respectively. Also, the final calculated electron affinities are all within 0.2 kcal/mol of their experimental values. Improved pseudopotential parameters for the iodine atom are also reported, together with revised correlation consistent basis sets for this atom.     

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     

Binding energies of protonated betaine complexes: a probe of zwitterion structure in the gas phase

The dissociation kinetics of proton-bound dimers of betaine with molecules of comparable gas-phase basicity were investigated using blackbody infrared radiative dissociation (BIRD). Threshold dissociation energies were obtained from these data using master equation modeling. For bases that have comparable or higher gas-phase basicity, the binding energy of the protonated base.betaine complex is ~1.4 eV. For molecules that are ~2 kcal/mol or more less basic, the dissociation energy of the complexes is ~1.2 eV. The higher binding energy of the former is attributed to an ion-zwitterion structure which has a much larger ion-dipole interaction. The lower binding energy for molecules that are ~2 kcal/mol or more less basic indicates that an ion-molecule structure is more favored. Semiempirical calculations at both the AM1 and PM3 levels indicate the most stable ion-molecule structure is one in which the base interacts with the charged quaternary ammonium end of betaine. These results indicate that the measurement of binding energies of neutral molecules to biological ions could provide a useful probe for the presence of zwitterions and salt bridges in the gas phase. From the BIRD data, the gas-phase basicity of betaine obtained from the kinetic method is found to be 239.2 +/- 1.0 kcal/mol. This value is in excellent agreement with the value of 239.3 kcal/mol (298 K) from ab initio calculations at the MP2/6-31+g** level. The measured value is slightly higher than those reported previously. This difference is attributed to entropy effects. The lower ion internal energy and longer time frame of BIRD experiments should provide values closer to those at standard temperature.     

Fitting atomic correlation parameters for RECEP (rapid estimation of correlation energy from partial charges) method to estimate molecular correlation energies within chemical accuracy

The accuracy of the RECEP method [Chem Phys 1997, 224, 33 and Chem Phys Lett 1999, 307, 469] has been increased considerably by the use of fitted atomic correlation parameters. This method allows an extremely rapid, practically prompt calculation of the correlation energy of molecules after an HF‐SCF calculation. The G2 level correlation energy and HF‐SCF charge distribution of 41 closed‐shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2 thermochemistry database were used to obtain the fitted RECEP atomic correlation parameters. Four different mathematical definitions of partial charges, as a multiple choice, were used to calculate the molecular correlation energies. The best results were obtained using the natural population analysis, although the other three are also recommended for use. For the 41 molecules, the G2 results were approached within a 1.8 kcal/mol standard deviation (the mean absolute difference was 1.5 kcal/mol). The RECEP atomic correlation parameters were also tested on a different, nonoverlapping set of other 24 molecules from the G2 thermochemistry database. The G2 results of these 24 molecules were approached within a 2.3 kcal/mol standard deviation (the mean absolute difference was 1.9 kcal/mol). This method is recommended to estimate total correlation energies of closed shell ground‐state neutral molecules at stationary (minimums and transition states) points on the potential surface. Extension of the work for charged molecules, radicals, and molecules containing other atoms is straightforward. Numerical example as a recipe is also provided. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 241–254, 2001     

First principles investigation of the electronic structure of the iron carbide cation, FeC+

We have studied 40 states of the diatomic iron carbide cation FeC(+) by multireference methods coupled with relatively large basis sets. For most of the states, we have constructed complete potential energy curves, reporting dissociation energies, usual spectroscopic parameters, and bonding mechanisms for the lowest of the studied states. The ground state is of (2)Delta symmetry, with the first excited state (a(4)Sigma(-)) lying 18 kcal/mol higher. The X(2)Delta state displays a triple-bond character, with an estimated D(0) value of 104 kcal/mol with respect to the adiabatic products or 87 kcal/mol with respect to the ground-state fragments.     

Approaching chemical accuracy with quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.     

Ab initio investigation of the ground and low-lying states of the diatomic fluorides TiF, VF, CrF, and MnF

The electronic structure of the ground and low-lying states of the diatomic fluorides TiF, VF, CrF, and MnF was examined by multireference and coupled cluster methods in conjunction with extended basis sets. For a total of 34 states we report binding energies, spectroscopic constants, dipole moments, separation energies, and charge distributions. In addition, for all states we have constructed full potential curves. The suggested ground state binding energies of TiF(X (4)Phi), VF(X (5)Pi), CrF(X (6)Sigma(+)), and MnF(X (7)Sigma(+)) are 135, 130, 110, and 108 kcal/mol, respectively, with first excited states A (4)Sigma(-), A (5)Delta, A (6)Pi, and a (5)Sigma(+) about 2, 3, 23, and 19 kcal/mol higher. In essence all our numerical findings are in harmony with experimental results. For all molecules and states studied it is clear that the in situ metal atom (M) shows highly ionic character, therefore the binding is described realistically by M(+)F(-).     

MO theoretical studies of electron pair decorrelation processes. I. Pair correlation energy and single bond dissociation

The homolytic dissociation of a single bond involves the decorrelation of one electron pair. Thus, the contribution of electron correlation to dissociation energies is large. In the present paper a new procedure is presented which allows the computation of the (within the given basis) complete correlation energy of one optimized electron pair. The method which requires only modest computational effort has been applied to the calculation of dissociation energies of a number of bonds of different types. The results show that the correlation of the electron pair of the bond which is broken contributes about 50–80% to the change of the total correlation energy occuring during the dissociation process which amounts to 20–70 kcal/mol. The fraction of correlation contributed by the bond electron pair as well as the relative importance of the left-right correlation within the bond depend very much on the type of the bond. In the case of CC and CH single bonds our method yields dissociation energies which are low by only about 5 kcal/mol. Thus, the method seems to be well suited for the calculation of potential surfaces of non-concerted organic chemical reactions which involve diradicals as intermediates.     

No-pair bonding in coinage metal dimers

High-level ab initio calculations at the coupled cluster with single and double substitutions and perturbative treatment of triple substitutions, CCSD(T), level of theory have been carried out for the dimers of coinage metal atoms Cu, Ag, and Au in the ground 1Sigma(g)+ state and in the excited 3Sigma(u)+ state. All of the calculations have been carried out with the inclusion of scalar-relativistic effects via the normalized elimination of the small component (NESC) method. For the dimers in the triplet state, nonzero bond dissociation energies are obtained which vary from 1.3 kcal/mol for 3Cu2 to 4.6 kcal/mol for 3Au2. Taking into account that, in bulky high-spin copper clusters, the bond dissociation energy per atom increases steeply to the value of ca. 19 kcal/mol, the results obtained in the present paper suggest that the bond dissociation energy per atom in high-spin gold clusters may reach extremely high values exceeding 20 kcal/mol thus becoming comparable to the usual bonding due to the spin-pairing mechanism.     

Density functional study of chlorine–oxygen compounds related to the ClO self-reaction

Geometrical parameters, vibrational frequencies, relative stabilities, and dissociation energies of the three stable Cl₂O₂ isomers and the OClO and ClOO radicals were investigated by density functional theory (DFT). The present analysis shows that DFT using hybrid functionals is capable of describing these systems to at least the same degree of accuracy as ab initio methods. The average absolute bond-length deviation of ClClO₂, ClOOCl, and ClO₂ from experimental results is 0.024/0.027 Å, with a maximum deviation for the dichlorine peroxide O(SINGLE BOND)O bond equal to 0.072/0.063 Å, for the B3PW91 and B3LYP functionals, respectively. The average absolute bond-angle deviation for the hybrid functionals is 0.8°. Harmonic vibrational frequencies calculated with DFT give for all Cl(SINGLE BOND)O compounds good agreement with experiments. The dissociation energies of ClOOCl, OClO, and ClOO were found to be in good agreement with experiments, the average error being less than 1.2 kcal/mol. The two isomers chloryl chloride (ClClO₂) and dichlorine peroxide (ClOOCl) were found to be approximately 9 kcal/mol more stable than the chlorine chlorite (ClOClO) isomer. The ClOO isomer is predicted to be 3.0 kcal/mol more stable than OClO, in accordance with the experimental value of 4 kcal/mol. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 203–217, 1998     

Magnitude and nature of interactions in benzene-X (X=ethylene and acetylene) in the gas phase: significantly different CH/pi interaction of acetylene as compared with those of ethylene and methane

The accurate interaction energies of the CH/pi interaction in the benzene-X clusters (X = ethylene and acetylene) were experimentally and theoretically determined. Two-color multiphoton ionization spectroscopy was applied, and the binding energies in the neutral ground state of the clusters were evaluated from the dissociation threshold measurements of the cluster cations. The experimental binding energies of the clusters (D0) were 1.4+/-0.2 and 2.7+/-0.2 kcal/mol, respectively. Estimated CCSD(T) interaction energies for the clusters at the basis set limit (De) were 2.2 and 2.8 kcal/mol, respectively. Calculated D0 values (1.7 and 2.4 kcal/mol, respectively) are close to the experimental values. Large electron correlation contributions (Ecorr=-3.6 and -2.8 kcal/mol, respectively) show that dispersion is the major source of the attraction in both clusters. The electrostatic interaction in the ethylene cluster is very small (-0.38 kcal/mol), as in the case of the benzene-methane cluster, whereas the electrostatic interaction in the acetylene cluster is large (-1.70 kcal/mol). The shifts of the S1-S0 transition also suggest that the ethylene cluster is a van der Waals-type cluster, but the acetylene cluster is a pi-hydrogen-bonded cluster. The nature of the CH/pi interaction of the "activated" alkyne C-H bond is significantly different from that of the "nonactivated" (or typical) alkane and alkene C-H bonds.     

Probing the bent bonds in cyclopropane systems for gas storage and separation process: A computational study

The hydrogen, carbon dioxide, and carbon monoxide gas adsorption and storage capacity of lithium-decorated cyclopropane ring systems were examined with quantum chemical calculations at density functional theory, DFT M06-2X functional using 6-31G(d) and cc-pVDZ basis sets. To examine the reliability of M06-2X DFT functional, a few representative systems are also examined with complete basis set CBS-QB3 method and CCSD-aug-cc-pVTZ level of theory. The cyclopropane systems can bind to one Li⁺ ion; however, the corresponding the methylated systems can bind with two Li⁺ ions. The cyclopropane systems can adsorb six hydrogen molecules with an average binding energy of 3.8 kcal/mol. The binding free energy (ΔG) values suggest that the hydrogen adsorption process is feasible at 273.15 K. The calculation of desorption energies indicates the recyclable property of gas adsorbed complexes. The same number of CO₂ and CO gas molecules can also be adsorbed with an average binding energy of −14.4 kcal/mol and −10.7 kcal/mol, respectively. The carbon dioxide showed ~3–4 kcal/mol better binding energy as compared to carbon monoxide and hence such designed systems can function as a potential candidate for the separation of these flue gas molecules. The nature of interactions in complexes was examined with atoms in molecules analysis revealed the electrostatic nature for the interaction of Li⁺ ion with cyclopropane rings. The chemical hardness and electrophilicity calculations showed that the gas adsorbed complexes are rigid and therefore robust as gas storage materials.     

Continuum polarizable force field within the Poisson-Boltzmann framework

We have developed and tested a complete set of nonbonded parameters for a continuum polarizable force field. Our analysis shows that the new continuum polarizable model is consistent with B3LYP/cc-pVTZ in modeling electronic response upon variation of dielectric environment. Comparison with experiment also shows that the new continuum polarizable model is reasonable, with accuracy similar to that of B3LYP/cc-pVTZ in reproduction of dipole moments of selected organic molecules in the gas phase. We have further tested the validity to interchange the Amber van der Waals parameters between the explicit and continuum polarizable force fields with a series of dimers. It can be found that the continuum polarizable model agrees well with MP2/cc-pVTZ, with deviations in dimer binding energies less than 0.9 kcal/mol in the aqueous dielectric environment. Finally, we have optimized atomic cavity radii with respect to experimental solvation free energies of 177 training molecules. To validate the optimized cavity radii, we have tested these parameters against 176 test molecules. It is found that the optimized Poisson-Boltzmann atomic cavity radii transfer well from the training set to the test set, with an overall root-mean-square deviation of 1.30 kcal/mol, an unsigned average error of 1.07 kcal/mol, and a correlation coefficient of 92% for all 353 molecules in both the training and test sets. Given the development documented here, the next natural step is the construction of a full protein/nucleic acid force field within the new continuum polarization framework.     

Approximations to complete basis set-extrapolated, highly correlated non-covalent interaction energies

The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)∕aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)∕aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent absolute deviation of only 1.7%, relative to the (estimated) complete basis set CCSD(T) results. Use of this composite approach to an additional set of eight dimers gave binding energies to within 1% of previously published high-level data. It is also shown that binding within parallel and parallel-crossed conformations of naphthalene dimer is predicted by the composite approach to be 9% greater than that previously reported in the literature. The ability of some recently developed dispersion-corrected density-functional theory methods to predict the binding energies of the set of ten small dimers was also examined.     

Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H(2)O, potential energy curves of LiF, and valence excitation energies of H(2)CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H(2)O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H(2)CO, the maximum deviation from available experimental values is 0.28 eV.