Modified Coupled Pair Functional Research Articles

ChemInform Abstract: Binding Energies and Bond Distances of Ni(CO)x, x = 1-4: An Application of Coupled-Cluster Theory.

The accuracy of the single and double excitation coupled‐cluster (CCSD) method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), has been tested for some representative transition metal complexes. For both the binding energy and metal to ligand bond distance of NiCO and Ni(CO)2, the CCSD(T) method yields results in very good agreement with multireference averaged coupled‐pair functional (ACPF) calculations. The results are much better than those obtained using either the coupled‐pair functional (CPF) or modified CPF (MCPF) methods. The contribution of connected triples to the binding energy is significant for all Ni(CO)x, x=1–4 ranging from 15 kcal/mol for NiCO to 30 kcal/mol for Ni(CO)4. In contrast, for the geometries the connected triples are only of minor importance. In this case, the correct treatment of disconnected quadruple excitations appears to be more important. For Ni(CO)4, the calculated binding energy is 125 kcal/mol (expt. 140 kcal/mol) and the bond d...

The Different Nature of Bonding in Cu+-Glycine and Cu2+-Glycine

A comparative study of the metal−glycine bonding for the biologically relevant Cu+ and Cu2+ pair is presented. The structure and vibrational frequencies for several coordination modes of Cu+ and Cu2+ to glycine have been determined using the hybrid three-parameter B3LYP density functional approach. Single-point calculations have also been carried out at the modified coupled pair functional (MCPF) and single- and double- (triple) excitation coupled cluster (CCSD(T)) levels of theory and using larger basis sets. Calculations have shown that the metal−glycine bonding and the energy ordering of the different conformers are very different in Cu+-glycine than in Cu2+-glycine. Whereas for Cu+-glycine, the ground state structure is found to have a bidentated η2-N,O coordination in which Cu+ interacts with the nitrogen of the amino group and the carbonyl oxygen, the ground state structure of Cu2+-glycine is the η2-O,O (CO2-) one, derived from the interaction of the metal cation with the CO2- terminus of the zwitterionic glycine. In this case, the results seem to indicate that glycine acquires an important radical character that changes the relative metal affinities of the different basic sites, which favors the interaction of the metal cation with the CO2 group compared with other coordinations.

Comparisons of results from parametrized configuration interaction (PCI-80) and from hybrid density functional theory with experiments for first row transition metal compounds

Different methods and schemes have been tested for the difficult class of first row transition metal complexes. The systems investigated are the M+, MH+, MCH+3, and MCH+2 systems for the entire row and the Ni(CO)x systems with x=1–4. In general quite satisfactory results are obtained both at the PCI-80 and hybrid density functional levels. In particular, for the MH+ and MCH+3 systems the PCI-80 average deviation to experiments is of the same size as the uncertainty in the experiments. The MCH+2 systems are somewhat more difficult to describe and a rather large error is found for chromium at the PCI-80 level, due to a large coupling of exchange energy loss and change of correlation energy resulting from the formation of two covalent d-bonds. Scaling at the modified coupled pair functional (MCPF) level is also compared to scaling at the coupled cluster singles and doubles (CCSD) level. In most cases very similar results are obtained, but classes of systems can be identified where scaling works better at the MCPF level and other classes where it works better at the CCSD level.

What is the structure of FeC 5H 6+?

Calculations performed using both density functional theory (DFT) and the modified coupled-pair functional (MCPF) approach show that FeC 5H 6 + is more stable than HFeC 5H 5 + by about 10 kcal/mol. The ground state of FeC 5H 6 + is a quartet state derived from the 3d 7 occupation of Fe +. For HFeC 5H 5 +, the MCPF approach yields a sextet ground state while DFT yields a quartet; however, these two states are close in energy at both levels of theory.

On the accuracy of gradient corrected density functional methods for transition metal complexes

Density functional theory with gradient corrections (DFTG) is applied to a series of second-row transition metal compounds. The mean absolute deviations from experiment for the atomic excitation energies and ionization potential are in the range 0.2–0.4 eV. In comparison with accurate multireference configuration interaction (MR-CI) and parametrized CI with parameter 80 (PCI-80) results for the binding energies of the MCH+2 cations, the mean absolute deviation is 6.7 kcal/mol to be compared with 17.8 kcal/mol at the modified coupled pair functional (MCPF) level. The DFTG result is more sensitive to the choice of asymptote with a mean deviation of 14 kcal/mol if the bonding atomic state is not used as asymptote. Product energies and transition states for the addition of methane to RhXL (X=H, Cl, L=H2O, NH3, PH3, and CO) also show the same trends as the PCI-80 comparison and represent an improvement over the MCPF results.

A theoretical study of CO/Cu(100)

The convergence of the binding energy, geometry, and vibrational frequencies for CO/Cu(100) is studied using a cluster model containing up to 38 Cu atoms. A large basis set is used for the Cu atom at the adsorption site and for the CO molecule. Electron correlation, which is included at the modified coupled-pair functional (MCPF) level, is found to increase the binding energy by about 1 eV. The binding energy and geometry are in very good agreement with experiment for the largest Cu clusters considered. The MCPF binding energies for the smaller clusters can be either larger or smaller than experiment. Unlike the binding energies, the shift in the CO vibrational frequency, relative to free CO, is quite independent of the cluster size or even the inclusion of electron correlation.

An ab initio study of CuCO

Modified coupled-pair functional (MCPF) calculations and coupled cluster singles and doubles calculations, which include a perturbational estimate of the connected triples [CCSD(T)], yield a bent structure for CuCO, thus, supporting the prediction of a nonlinear structure based on density functional (DF) calculations. Our best estimate for the binding energy is 4.9±1.4 kcal/mol; this is in better agreement with experiment (6.0±1.2 kcal/mol) than the DF approach which yields a value (19.6 kcal/mol) significantly larger than experiment.

Structure and energetics of Cr(CO)6 and Cr(CO)5

The geometric structure of Cr(CO)6 is optimized at the modified coupled-pair functional (MCPF), single and double excitation coupled-cluster (CCSD), and CCSD(T) levels of theory (including a perturbational estimate for connected triple excitations), and the force constants for the totally symmetric representation are determined. The geometry of Cr(CO)5 is partially optimized at the MCPF, CCSD, and CCSD(T) levels of theory. Comparison with experimental data shows that the CCSD(T) method gives the best results for the structures and force constants, and that remaining errors are probably due to deficiencies in the one-particle basis sets used for CO. The total binding energies of Cr(CO)6 and Cr(CO)5 are also determined at the MCPF, CCSD, and CCSD(T) levels of theory. The CCSD(T) method gives a much larger total binding energy than either the MCPF or CCSD methods. An analysis of the basis set superposition error (BSSE) at the MCPF level of treatment points out limitations in the one-particle basis used here and in a previous study. Calculations using larger basis sets reduce the BSSE, but the total binding energy of Cr(CO)6 is still significantly smaller than the experimental value, although the first CO bond dissociation energy of Cr(CO)6 is well described. An investigation of 3s3p correlation reveals only a small effect. In the largest basis set, the total CO binding energy of Cr(CO)6 is estimated to be 140 kcal/mol at the CCSD(T) level of theory, or about 86% of the experimental value. The remaining discrepancy between the experimental and theoretical value is probably due to limitations in the one-particle basis, rather than limitations in the correlation treatment. In particular, an additional d function and an f function on each C and O are needed to obtain quantitative results. This is underscored by the fact that even using a very large primitive set (1042 primitive functions contracted to 300 basis functions), the superposition error for the total binding energy of Cr(CO)6 is 22 kcal/mol at the MCPF level of treatment.

Tungsten hexahydride (WH6). An equilibrium geometry far from octahedral

Ab initio all-electron quantum mechanical methods were applied to the tungsten hexahydride (WH6) molecule using very large basis sets. Seven distinct structures were investigated with full geometry optimizations at the self-consistent field (SCF) level of theory. The effects of electron correlation were estimated with second-order Mo/ller–Plesset perturbation theory (MP2), modified coupled pair functional (MCPF) method, and the coupled cluster with single and double excitations (CCSD) method, and relativistic effects estimated using the Cowan–Griffin (mass–velocity and Darwin) corrections. Our results suggest that the ground state of the tungsten hexahydride (WH6) molecule is a closed-shell triangular prism belonging to the C3v point group, with a set of three hydrogens stacked on top of another set of three hydrogens. From the perspective of inorganic chemistry, it is truly remarkable that the octahedral structure lies 130 kcal/mol above the C3v ground state. Furthermore, these results imply major qualitative differences between WH6 and the well-known W(CH3)6 molecule. Another C3v structure, with one set of three hydrogens staggered with respect to the other set, is energetically nearby. With MCPF and relativistic corrections at the SCF optimized geometry, a third low-lying structure belonging to the C5v point group is virtually degenerate with the triangular prism C3v structure.

Theoretical study of the bond dissociation energies of methanol

We present a theoretical study of the bond dissociation energies (D0) for H2O and CH3OH. The C–H and O–H bond energies are computed accurately with the modified coupled-pair functional (MCPF) method using a large basis set. For these bonds, an accuracy of ±2 kcal/mol is achieved, which is consistent with the C–H and C–C single bond energies of other molecules. The C–O bond is much more difficult to compute accurately because it requires higher levels of correlation treatment and more extensive one-particle basis sets.

Binding energies and bond distances of Ni(CO)x, x=1–4: An application of coupled-cluster theory

The accuracy of the single and double excitation coupled-cluster (CCSD) method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), has been tested for some representative transition metal complexes. For both the binding energy and metal to ligand bond distance of NiCO and Ni(CO)2, the CCSD(T) method yields results in very good agreement with multireference averaged coupled-pair functional (ACPF) calculations. The results are much better than those obtained using either the coupled-pair functional (CPF) or modified CPF (MCPF) methods. The contribution of connected triples to the binding energy is significant for all Ni(CO)x, x=1–4 ranging from 15 kcal/mol for NiCO to 30 kcal/mol for Ni(CO)4. In contrast, for the geometries the connected triples are only of minor importance. In this case, the correct treatment of disconnected quadruple excitations appears to be more important. For Ni(CO)4, the calculated binding energy is 125 kcal/mol (expt. 140 kcal/mol) and the bond distance is 3.46 a0 (exp. 3.45 a0). Virtually all of the remaining discrepancy, relative to experiment, should be due to limitations in the one-particle basis set. In addition, some test calculations were performed for Ni(C2H4), where near degeneracy effects are even more severe than for the nickel carbonyls and the CCSD(T) method gives very accurate results in this case also.

The electronic and molecular structure of ferrocene

The metal–ligand distance in ferrocene has been calculated with several different electronic structure methods. The only correlation treatment able to reproduce the experimental value is the MCPF (modified coupled-pair functional) approach with all 66 valence electrons correlated. Large basis sets are necessary to account for the dispersion interaction between the rings.

A theoretical study of the low-lying states of Ti2 and Zr2

The 1Σ+g, 3Δg, 3Σ+u, and 7Σ+u states of Ti2 and Zr2 have been studied using a multireference configuration-interaction (MRCI) approach. Although our best calculation produces a 1Σ+g ground state for Zr2, the 3Σ+u and 3Δg states are found to be very low lying. Additional support for a 1Σ+g ground state assignment comes from the fact that the resulting vertical excitation spectrum is consistent with the optical spectrum of Zr2 observed in noble gas matrices. For Ti2, it proved more difficult to make a definitive assignment of the ground state, because of the many low-lying states and the large effect of inner-shell (3s and 3p) correlation. With only valence correlation included, the ground state is predicted to be 7Σ+u at both the MRCI and averaged coupled-pair functional (ACPF) levels of correlation treatment. However, inner-shell correlation effects, estimated based on modified coupled-pair functional (MCPF) and contracted configuration-interaction (CCI) calculations, preferentially lower the 1Σ+g and 3Δg states, resulting in a 3Δg ground state and a very low-lying 1Σ+g state. Since the 3Δg state lies below the 1Σ+g state at all levels of correlation treatment and both states are derived from the same atomic asymptote, we prefer a 3Δg assignment for the ground state of Ti2. This is consistent with the failure to observe an electron-spin resonance (ESR) signal, but such an assignment requires an explanation for the absence of subcomponents on the lines observed in the resonance Raman spectrum of Ti2.

An ab initio study of the low-lying doublet states of AgO and AgS

Spectroscopic constants ( D o, r e, μ e, T e) are determined for the doublet states of AgO and AgS below ≈ 30000 cm −1. valence basis sets are employed in conjunction with relativistic effective core potentials (RECPs). Electron correlation is included using the modified coupled-pair functional (MCPF) and multireferenceconfiguration interaction (MRCI) methods. The A 2Σ +-X 2Π band system is found to occur in the near infrared ( ≈ 9000 cm −1) and to be relatively weak with a radiative lifetime of 900 μs for A 2Σ + (ν = 0). The weakly bound C 2Π state (our notation), the upper state of the blue system, is found to require high levels of theoretical treatment to determine a quantitatively accurate potential. The red system is assigned as a transition from the C 2Π state to the previously unobserved A 2Σ + state. Several additional transitions are identified that should be detectable experiment A more limited study is performed for the vertical excitation spectrum of AgS. In addition, a detailed all-electron study of the X 2Π and A 2Σ + states of AgO is carried out using large atomic natural orbital (ANO) basis sets. Our best calculated D o value for AgO is significantly less than the experimental value, which suggests that there may be some systematic error in the experimental determination.

Theoretical study of polarizabilities and hyperpolarizabilities of Ne, HF, F−, and OH−

Theoretical calculations are presented for the polarizability parameters through the fourth power of an applied static electric field for Ne and HF and through the second power in the field for the negative ions F− and OH−. Large Gaussian basis sets are employed and electron correlation is incorporated using the modified coupled pair functional (MCPF) method and for Ne and HF using coupled-cluster single- and double-excitation (CCSD) methods with two approaches of including the effect of triple excitations. The MCPF method is found to perform well in relation to the more rigorous CCSD method. Our theoretical values for Ne are in good accord with the recent experimental value of Shelton, as well as with recent theoretical studies. Our best results for the first and second hyperpolarizability of HF are in slightly better agreement with experiment than previous theoretical studies, but still show a very large disparity.

Theoretical confirmation of a 4Δ ground state for FeH

Large CAS SCF/multireference configuration interaction (MRCI) and modified coupled pair functional (MCPF) calculations are carried out for the 4Δ and 6Δ states of FeH using very large Gaussian basis sets. At the MCPF level, 3s and 3p correlation preferentially lowers the 4Δ state by 0.10 eV. Adding this inner-shell correlation effect to our best CAS SCF/MRCI+Q valence treatment results in a 4Δ- 6Δ separation of 0.16 eV. This supports the interpretation of the photodetachment spectra of Stevens et al. that places the 6Δ state about 0.25 eV above the 4Δ ground state.

Theoretical study of the electron affinities of Cu, Cu2, and Cu3

Modified coupled pair functional (MCPF) calculations are shown to yield the electron affinities of Cu, Cu2, and Cu3 to nearly equal accuracy. The structural results for Cu−3, together with the experimental negative ion photoelectron results, show conclusively that Cu−3 is linear in its (1Σ+g) ground state. The weak feature in the Cu−3 photoelectron spectrum at an electron binding energy of 1.5 eV is due to ionization from the 3A′2 (equilateral triangle) excited state of Cu−3.

Theoretical dipole moments for the first-row transition metal hydrides

Spectroscopic parameters (De, re, μ) are determined for the first-row transition metal hydrides using better than DZP basis sets at the modified coupled pair functional (MCPF) level. Extensive comparisons between MCPF and complete-active space self-consistent field (CASSCF)/MRCI calculations with natural orbital iterations, and studies with more extensive basis sets, show this level of treatment to supply an accurate and cost-effective treatment of these systems. For the transition metal hydrides, the bonding can arise from either the 3dn4s2 or 3dn+14s1 atomic asymptotes, or a mixture of both. Since the dipole moment arising from these two bonding mechanisms is very different, the dipole moment is found to be directly related to the 3d population. Thus, the magnitude of the dipole moments provide a sensitive test of the wave function, and gives insight into the nature of the bonding.

A modified coupled pair functional approach

A modified coupled pair functional (MCPF) method is presented that dramatically improves properties for cases where the Hartree–Fock reference configuration is not a good zeroth-order description of the wave function. This new methodology is compared to singles-plus-doubles configuration interaction and the CPF method of Ahlrichs et al. for the ground states of NiH, CuH, and ZnH.