Breaking bonds of open-shell species with the restricted open-shell size extensive left eigenstate completely renormalized coupled-cluster method

The recently developed restricted open-shell, size extensive, left eigenstate, completely renormalized (CR), coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as ROCCL, is compared with the unrestricted CCSD(T) [UCCSD(T)] and multireference second-order perturbation theory (MRMP2) methods to assess the accuracy of the calculated potential energy surfaces (PESs) of eight single bond-breaking reactions of open-shell species that consist of C, H, Si, and Cl; these types of reactions are interesting because they account for part of the gas-phase chemistry in the silicon carbide chemical vapor deposition. The full configuration interaction (FCI) and multireference configuration interaction with Davidson quadruples correction [MRCI(Q)] methods are used as benchmark methods to evaluate the accuracy of the ROCCL, UCCSD(T), and MRMP2 PESs. The ROCCL PESs are found to be in reasonable agreement with the corresponding FCI or MRCI(Q) PESs in the entire region R = 1-3Re for all of the studied bond-breaking reactions. The ROCCL PESs have smaller nonparallelity error (NPE) than the UCCSD(T) ones and are comparable to those obtained with MRMP2. Both the ROCCL and UCCSD(T) PESs have significantly smaller reaction energy errors (REE) than the MRMP2 ones. Finally, an efficient strategy is proposed to estimate the ROCCL/cc-pVTZ PESs using an additivity approximation for basis set effects and correlation corrections.     

The 1deltag dioxygen ene reaction with propene: a density functional and multireference perturbation theory mechanistic study

This study aims to determine whether a balance between concerted and non-concerted pathways exists, and in particular to ascertain the possible role of diradical/zwitterion or peroxirane intermediates. Three non-concerted pathways, via 1) diradical or 2) peroxirane intermediates, and 3) by means of hydrogen-abstraction/radical recoupling, plus one concerted pathway (4), are explored. The intermediates and transition structures (TS) are optimized at the DFT(MPW1K), DFT(B3LYP) and CASSCF levels of theory. The latter optimizations are followed by multireference perturbative CASPT2 energy calculations. (1) The polar diradical forms from the separate reactants by surmounting a barrier (deltaE(++)(MPW1K)=12, deltaE++(B3LYP)=14, and deltaE(++)(CASPT2)=16 kcal mol(-1) and can back-dissociate through the same TS, with barriers of 11 (MPW1K) and 8 kcal mol(-1) (B3LYP and CASPT2). The diradical to hydroperoxide transformation is easy at all levels (deltaE(++)(MPW1K)<4, deltaE(++)(B3LYP)=1 and deltaE(++)(CASPT2)=1 kcal mol(-1)). (2) Peroxirane is attainable only by passing through the diradical intermediate, and not directly, due to the nature of the critical points involved. It is located higher in energy than the diradical by 12 kcal mol(-1), at all theory levels. The energy barrier for the diradical to cis-peroxirane transformation (deltaE(++)=14-16 kcal mol(-1)) is much higher than that for the diradical transformation to the hydroperoxide. In addition, peroxirane can very easily back-transform to the diradical (deltaE(++)<3 kcal mol(-1)). Not only the energetics, but also the qualitative features of the energy hypersurface, prevent a pathway connecting the peroxirane to the hydroperoxide at all levels of theory. (3) The last two-step pathway (hydrogen-abstraction by (1)O(2), followed by HOO-allyl radical coupling) is not competitive with the diradical mechanism. (4) A concerted pathway is carefully investigated, and deemed an artifact of restricted DFT calculations. Finally, the possible ene/[pi2+pi2] competition is discussed.     

A multireference coupled-cluster potential energy surface of diazomethane, CH(2)N(2)

The intrinsically multireference dissociation of the C-N bond in ground-state diazomethane (CH(2)N(2)) at different angles has been studied with the multireference Brillouin-Wigner coupled-cluster singles and doubles (MRBWCCSD) method. The morphology of the calculated potential energy surface (PES) in C(s)() symmetry is similar to a multireference perturbational (CASPT3) PES. The MRBWCCSD/cc-pVTZ H(2)C-N(2) dissociation energy with respect to the asymptotic CH(2)(?(1)A(1)) + N(2)(X(1)Sigma(g)(+)) products is D(e) = 35.9 kcal/mol, or a zero-point corrected D(0) = 21.4 kcal/mol with respect to the ground-state CH(2)(X(3)B(1)) + N(2)(X(1)Sigma(g)(+)) fragments.     

High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems

For the first time high-order excitations (n>2) have been studied in three multireference couple cluster (MRCC) theories built on the wave operator formalism: (1) the state-universal (SU) method of Jeziorski and Monkhorst (JM) (2) the state-specific Brillouin-Wigner (BW) coupled cluster method, and (3) the state-specific MRCC approach of Mukherjee (Mk). For the H4, P4, BeH(2), and H8 models, multireference coupled cluster wave functions, with complete excitations ranging from doubles to hextuples, have been computed with a new arbitrary-order string-based code. Comparison is then made to corresponding single-reference coupled cluster and full configuration interaction (FCI) results. For the ground states the BW and Mk methods are found, in general, to provide more accurate results than the SU approach at all levels of truncation of the cluster operator. The inclusion of connected triple excitations reduces the nonparallelism error in singles and doubles MRCC energies by a factor of 2-10. In the BeH(2) and H8 models, the inclusion of all quadruple excitations yields absolute energies within 1 kcal mol(-1) of the FCI limit. While the MRCC methods are very effective in multireference regions of the potential energy surfaces, they are outperformed by single-reference CC when one electronic configuration dominates.     

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.     

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

The recently developed [P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 (2005)] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2Si[Double Bond]SiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R=1-3Re for all of the studied single bond-breaking reactions, where R and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R=1-3Re of the H-SiH3, H-Cl, H3Si-SiH3, Cl-CH3, H-CH3, and H3C-SiH3 bonds. The maximum errors are -2.1, 1.6, and 1.6 mhartree in the R=1-3Re region of the H3C-CH3, Cl-Cl, and H3Si-Cl bonds, respectively, while the discrepancy for the H2Si[Double Bond]SiH2 double bond-breaking reaction is 6.6 (8.5) mhartree at R=2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T).     

Reactions of 1,3-cyclohexadiene with singlet oxygen. A theoretical study.

A thorough study of the reaction of singlet oxygen with 1,3-cyclohexadiene has been made at the B3LYP/6-31G(d) and CASPT2(12e,10o) levels. The initial addition reaction follows a stepwise diradical pathway to form cyclohexadiene endoperoxide with an activation barrier of 6.5 kcal/mol (standard level = CASPT2(12e,10o)/6-31G(d); geometries and zero-point corrections at B3LYP/6-31G(d)), which is consistent with an experimental value of 5.5 kcal/mol. However, as the enthalpy of the transition structure for the second step is lower than the diradical intermediate, the reaction might also be viewed as a nonsynchronous concerted reaction. In fact, the concertedness of the reaction is temperature dependent since entropy differences create a free energy barrier for the second step of 1.8 kcal/mol at 298 K. There are two ene reactions; one is a concerted mechanism (DeltaH(double dagger) = 8.8 kcal/mol) to 1-hydroperoxy-2,5-cyclohexadiene (5), while the other, which forms 1-hydroperoxy-2,4-cyclohexadiene (18), passes through the same diradical intermediate (9) as found on the pathway to endoperoxide. The major pathway from the endoperoxide is O-O bond cleavage (22.0 kcal/mol barrier) to form a 1,4-diradical (25), which is 13.9 kcal/mol less stable than the endoperoxide. From the diradical, two low-energy pathways exist, one to epoxyketone (29) and the other to the diepoxide (27), where both products are known to be formed experimentally with a product ratio sensitive to the nature of substitutents. A significantly higher activation barrier leads to C-C bond cleavage and direct formation of maleic aldehyde plus ethylene.     

Structure and bonding in Hartwig stretched eta(3)-hydridoborate sigma-complex of niobium(III)

Ab initio calculations at the SCF, MP2, CASSCF, and CASPT2 levels of theory with basis sets using atomic pseudopotentials have been carried out for the stretched eta(3)-hydridoborate sigma-complex of niobium, [Cl2Nb(H2B(OH)2)], in order to investigate the nature and energetics of the interaction between the transition metal and the eta(3)-hydridoborate ligand. The geometry of the complex [Cl2Nb(H2B(OH)2] and its fragments [Cl2Nb](+) and [H2B(OH)2](-) were optimized at SCF and CASSCF levels. These results are consistent with [Cl2Nb(eta(3)-H2B(OH)2)] being a Nb(III) complex in which both hydrogen and boron of the [eta(3)-H2B(OH)2](-) ligand have a bonding interaction with the niobium preserving stretching B-H bond character. The calculated values of DEF (energy required to restore the fragment from the equilibrium structure to the structure it takes in the complex) for [Cl2Nb](+) are 5.35 kcal/mol at SCF, 3.27 kcal/mol at MP2, 4.80 kcal/mol at CASSCF, and 2.82 kcal/mol at CASPT2 and for [H2B(OH)2](-) 21.13 kcal/mol at SCF, 23.85 kcal/mol at MP2, 20.69 kcal/mol at CASSCF, and 23.48 kcal/mol at CASPT2. Values of INT (stabilization energy resulting from the coordination of distorted ligand to the metal fragment) for the complex [Cl2Nb(H2B(OH)2)] are -239.35 kcal/mol at SCF, -260.00 kcal/mol at MP2, -230.76 kcal/mol at CASSCF, and -252.60 kcal/mol at CASPT2. For the complex [(eta(5)-C5H5)2Nb(H2B(OH)2)], calculations at the SCF and MP2 levels were carried out. Values of INT for [(eta(5)-C5H5)2Nb(H2B(OH)2)] are -169.93 kcal/mol at SCF and -210.62 kcal/mol at MP2. The results indicate that the bonding of the [eta(3)-H2B(OH)2](-) ligand with niobium is substantially stable. The electronic structures of [Cl2Nb(H2B(OH)2)], [(eta(5)-C5H5)2Nb(H2B(OH)2)], and its fragments are analyzed in detail as measured by Mulliken charge distributions and orbital populations.     

Optimization of parameters for semiempirical methods II. Applications

MNDO/AM1-type parameters for twelve elements have been optimized using a newly developed method for optimizing parameters for semiempirical methods. With the new method, MNDO-PM3, the average difference between the predicted heats of formation and experimental values for 657 compounds is 7.8 kcal/mol, and for 106 hypervalent compounds, 13.6 kcal/mol. For MNDO the equivalent differences are 13.9 and 75.8 kcal/mol, while those for AM1, in which MNDO parameters are used for aluminum, phosphorus, and sulfur, are 12.7 and 83.1 kcal/mol, respectively. Average errors for ionization potentials, bond angles, and dipole moments are intermediate between those for MNDO and AM1, while errors in bond lengths are slightly reduced.     

Theoretical study of Ng--NiN(2) (Ng=Ar,Ne,He)

It is shown that NiN(2) and noble gas atoms, Ar, Ne, and He, combine with the binding energy of 11.52, 4.06, and 7.37 kcal/mol, respectively, by the multireference perturbational (CASPT2) method. By the density functional theory calculations using MPWPW91 functionals, the Ni-N-N bending frequency in NiN(2) and Ar-NiN(2) is estimated as 310.7 and 358.7 cm(-1), respectively, the latter of which is in good agreement with the corresponding experimental frequency, 357.0 cm(-1), determined for NiN(2) isolated in solid argon.     

On the stability of the elusive HO3 radical

The dissociation of HO(3) into OH + O(2) has been studied in a systematic and consistent way using the multireference configuration interaction method. Upon extrapolation of the calculated raw energies to the complete basis set limit and using jointly with a recent realistic estimate of the zero-point vibrational energy, the energy for OO-OH bond-breaking in the trans isomer is predicted to be of D(0) = (2.4 ± 0.1) kcal mol(-1), where the uncertainty reflects only the one inherent to the extrapolation. The average value so obtained falls short of the commonly accepted experimental counterpart by 0.5 kcal mol(-1). Reasons for the deviation are advanced, as well as an estimate of the binding energy for the cis-HO(3) isomer which is predicted to have a somewhat smaller binding energy than trans-HO(3), but likewise the latter dissociates without a barrier to the same products.     

Ab initio study of the electronic structure of manganese carbide

We report electronic structure calculations on 13 states of the experimentally unknown manganese carbide (MnC) using standard multireference configuration interaction (MRCI) methods coupled with high quality basis sets. For all states considered we have constructed full potential energy curves and calculated zero point energies. The X state, correlating to ground state atoms, is of 4sigma- symmetry featuring three bonds, with a recommended dissociation energy of D0 = 70.0 kcal/mol and r(e) = 1.640 angstroms. The first and second excited states, which also correlate to ground state atoms, are of 6sigma- and 8sigma- symmetry, respectively, and lie 17.7 and 28.2 kcal/mol above the X state at the MRCI level of theory.     

Phenyloxenium ions: more like phenylnitrenium ions than isoelectronic phenylnitrenes?

The geometries and energies of the electronic states of phenyloxenium ion 1 (Ph-O(+)) were computed at the multireference CASPT2/pVTZ level of theory. Despite being isoelectronic to phenylnitrene 4, the phenyloxenium ion 1 has remarkably different energetic orderings of its electronic states. The closed-shell singlet configuration ((1)A(1)) is the ground state of the phenyloxenium ion 1, with a computed adiabatic energy gap of 22.1 kcal/mol to the lowest-energy triplet state ((3)A(2)). Open-shell singlet configurations ((1)A(2), (1)B(1), (1)B(2), 2(1)A(1)) are significantly higher in energy (>30 kcal/mol) than the closed-shell singlet configuration. These values suggest a revision to the current assignments of the ultraviolet photoelectron spectroscopy bands for the phenoxy radical to generate the phenyloxenium ion 1. For para-substituted phenyloxenium ions, the adiabatic singlet-triplet energy gap (ΔE(ST)) is found to have a positive linear free energy relationship with the Hammett-like σ(+)(R)/σ(+) substituent parameters; for meta substituents, the relationship is nonlinear and negatively correlated. CASPT2 analyses of the excited states of p-aminophenyloxenium ion 5 and p-cyanophenyloxenium ion 10 indicate that the relative orderings of the electronic states remain largely unperturbed for these para substitutions. In contrast, meta-donor-substituted phenyloxenium ions have low-energy open-shell states (open-shell singlet, triplet) due to stabilization of a π,π* diradical state by the donor substituent. However, all of the other phenyloxenium ions and larger aryloxenium ions (naphthyl, anthryl) included in this study have closed-shell singlet ground states. Consequently, ground-state reactions of phenyloxenium ions are anticipated to be more closely related to closed-shell singlet arylnitrenium ions (Ar-NH(+)) than their isoelectronic arylnitrene (Ar-N) counterparts.     

Thermochemical kinetics of hydrogen-atom transfers between methyl, methane, ethynyl, ethyne, and hydrogen

Saddle point properties of three symmetric and one asymmetric hydrogen transfer and the energy of reaction of the asymmetric reactions are investigated in the present work. These reactions were calculated by various density functionals, many of which were developed in recent years, by coupled cluster theory, and by multicoefficient correlation methods based on wave function theory. Instead of comparing calculated results to "semi-experimental" values, we compared them to very accurate theoretical values (e.g., to values obtained by the Weizmann-1 method). Coupled cluster theory and the multicoefficient correlation methods MC-QCISD/3 and MCQCISD-MPW are very accurate for these reactions with mean unsigned errors below 0.94 kcal/mol. Diagnostics for multireference character add additional reliability to these results. The newly developed hybrid density functional M06-2X shows very good performance for these reactions with a mean unsigned error of only 0.77 kcal/mol; the BHandHLYP, MPW1K, and BB1K density functionals, can also predict these reactions well with mean unsigned errors less than 1.42 kcal/mol.     

Energetics, transition states, and intrinsic reaction coordinates for reactions associated with O(3P) processing of hydrocarbon materials

Electronic structure calculations based on multiconfiguration wave functions are used to investigate a set of archetypal reactions relevant to O(3P) processing of hydrocarbon molecules and surfaces. These include O(3P) reactions with methane and ethane to give OH plus methyl or ethyl radicals, O(3P) + ethane to give CH3O + CH3, and secondary reactions of the OH product radical with ethane and the ethyl radical. Geometry optimization is carried out with CASSCF/cc-pVTZ for all reactions, and with CASPT2/cc-pVTZ for O(3P) + methane/ethane. Single-point energy corrections are applied with CASPT2, CASPT3, and MRCI + Q with the cc-pVTZ and cc-pVQZ basis sets, and the energies extrapolated to the complete basis set limit (CBL). Where comparison of computed barriers and energies of reaction with experiment is possible, the agreement is good to excellent. The best agreement (within experimental error) is found for MRCI + Q/CBL applied to O(3P) + methane. For the other reactions, CASPT2/CBL and MRCI + Q/CBL predictions differ from experiment by 1-5 kcal/mol for 0 K enthalpies of reaction, and are within 1 kcal/mol of the best-estimate experimental range of 0 K barriers for O(3P) + ethane and OH + ethane. The accuracy of MRCI + Q/CBL is limited mainly by the quality of the active space. CASPT2/CBL barriers are consistently lower than MRCI + Q/CBL barriers with identical reference spaces.     

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.     

Ruthenocene and cyclopentadienyl pyrrolyl ruthenium as precursors for ruthenium atomic layer deposition: a comparative study of dissociation enthalpies

RuCp₂ (ruthenocene) and RuCpPy (cyclopentadienyl pyrrolyl ruthenium) complexes are used in ruthenium (Ru) atomic layer deposition (ALD) but exhibit a markedly different reactivity with respect to the substrate and co-reactant. In search of an explanation, we report here the results of a comparative study of the heterolytic and homolytic dissociation enthalpy of these two ruthenium complexes, making use of either density functional theory (DFT) or multiconfigurational perturbation theory (CASPT2). While both methods predict distinctly different absolute dissociation enthalpies, they agree on the relative values between both molecules. A reduced heterolytic dissociation enthalpy is obtained for RuCpPy compared to RuCp₂, although the difference obtained from CASPT2 (19.9?kcal/mol) is slightly larger than the one obtained with any of the DFT functionals (around 17?kcal/mol). Both methods also agree on the more pronounced stability of the Cp^? ligand in RuCpPy than in RuCp₂ (by around 9?kcal/mol with DFT and by 6?kcal/mol with CASPT2).     

Bond dissocation and conformational energetics of tetrasulfur: a quantum Monte Carlo study

Variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) calculations are performed for S4. The effect of single- and multireference trial functions, as well as choice of orbitals, is investigated for its effect on the quality of the Monte Carlo estimates. Estimates of symmetric (two S2 molecules) and asymmetric (S atom and S3 molecule) bond dissociation are reported. The conformational change of S4 from C2v to D2h defines a double-well potential and is also estimated. Multireference DMC with natural orbitals (DMC/NO) estimates the energy of the conformational change as 1.20(20) kcal/mol; the dissociation of the long S-S single bond is estimated at 21.1(1.3) kcal/mol, and the asymmetric bond energy is estimated as 53.2(2.4) kcal/mol. An estimate of the total atomization energy using multireference DMC/NO gives a value of 219.5(2.2) kcal/mol. The relative quality of result and implications for simplified trial function design are discussed.     

Theoretical studies on Myers-Saito and Schmittel cyclization mechanisms of hepta-1,2,4-triene-6-yne

The mechanisms of the Myers-Saito cyclization and the Schmittel cyclization of hepta-1,2,4-triene-6-yne are studied by ab initio multireference MO methods (CASSCF and MRMP2 methods). For the Myers-Saito cyclization, two transition states with C(s) and C? symmetries are located. The transition state with C1 symmetry is only 1.5 kcal/mol lower in energy than that with C(s) symmetry at the MRMP2 calculation level. The obtained activation energy at the transition state with C? symmetry and the reaction energy are 16.6 and 16.2 kcal/mol exothermic, respectively. For the Schmittel cyclization, two transition states with C(s) and C? symmetry are also obtained. The transition state with C? symmetry is 7.9 kcal/mol lower in energy than that with C(s) symmetry. The transition state with C? symmetry for Schmittel cyclization is 6.7 kcal/mol higher in energy than that for the Myers-Saito cyclization. The reaction mechanisms are analyzed by a CiLC-IRC method. The interactions of orbitals for the Myers-Saito and Schmittel cyclizations can be distinguished.     

First principles investigation of chromium carbide, CrC

We have investigated the electronic structure of 14 states of the experimentally unknown diatomic molecule chromium carbide, CrC, using standard multireference configuration interaction methods and high quality basis sets. We report potential curves, binding energies, and a number of spectroscopic parameters. The ground state of CrC, X 3Sigma-, displays triple-bond character with a binding energy of D(e)=89 kcal/mol and an internuclear separation of r(e)=1.63 A. The first excited state (1 5Sigma-) lies 9.2 kcal/mol higher. All the states studied are fairly ionic, featuring an electron transfer of 0.3-0.5e- from the metal atom to the carbon atom.