Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

Self-consistent correlation potentials for H(2) and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the improved total energy in the dissociation limit.     

The Chemical Bond: When Atom Size Instead of Electronegativity Difference Determines Trend in Bond Strength

We have quantum chemically analyzed element−element bonds of archetypal H_nX−YH_n molecules (X, Y=C, N, O, F, Si, P, S, Cl, Br, I), using density functional theory. One purpose is to obtain a set of consistent homolytic bond dissociation energies (BDE) for establishing accurate trends across the periodic table. The main objective is to elucidate the underlying physical factors behind these chemical bonding trends. On one hand, we confirm that, along a period (e. g., from C−C to C−F), bonds strengthen because the electronegativity difference across the bond increases. But, down a period, our findings constitute a paradigm shift. From C−F to C−I, for example, bonds do become weaker, however, not because of the decreasing electronegativity difference. Instead, we show that the effective atom size (via steric Pauli repulsion) is the causal factor behind bond weakening in this series, and behind the weakening in orbital interactions at the equilibrium distance. We discuss the actual bonding mechanism and the importance of analyzing this mechanism as a function of the bond distance.     

Theory of late-transition-metal alkyl and heteroatom bonding: analysis of Pt, Ru, Ir, and Rh complexes

Density functional and correlated ab initio methods were used to calculate, compare, and analyze bonding interactions in late-transition-metal alkyl and heteroatom complexes (M-X). The complexes studied include: (DMPE)Pt(CH(3))(X) (DMPE = 1,2-bis(dimethylphosphino)ethane), Cp*Ru(PMe(3))(2)(X) (Cp* = pentamethylcyclopentadienyl), (DMPE)(2)Ru(H)(X), (Tp)(CO)Ru(Py)(X) (Tp = trispyrazolylborate), (PMe(3))(2)Rh(C(2)H(4))(X), and cis-(acac)(2)Ir(Py)(X) (acac = acetylacetonate). Seventeen X ligands were analyzed that include alkyl (CR(3)), amido (NR(2)), alkoxo (OR), and fluoride. Energy decomposition analysis of these M-X bonds revealed that orbital charge transfer stabilization provides a straightforward model for trends in bonding along the alkyl to heteroatom ligand series (X = CH(3), NH(2), OH, F). Pauli repulsion (exchange repulsion), which includes contributions from closed-shell d(π)-p(π) repulsion, generally decreases along the alkyl to heteroatom ligand series but depends on the exact M-X complexes. It was also revealed that stabilizing electrostatic interactions generally decrease along this ligand series. Correlation between M-X and H-X bond dissociation energies is good with R(2) values between 0.7 and 0.9. This correlation exists because for both M-X and H-X bonds the orbital stabilization energies are a function of the orbital electronegativity of the X group. The greater than 1 slope when correlating M-X and H-X bond dissociation energies was traced back to differences in Pauli repulsion and electrostatic stabilization.     

Excitation energies from range-separated time-dependent density and density matrix functional theory

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.     

Chemical bonding in phosphane and amine complexes of main group elements and transition metals

The geometries and bond dissociation energies of the main group complexes X3B-NX3, X3B-PX3, X3Al-NX3, and X3Al-PX3 (X = H, Me, Cl) and the transition metal complexes (CO)5M-NX3 and (CO)5M-PX3 (M = Cr, Mo, W) have been calculated using gradient-corrected density functional theory at the BP86/TZ2P level. The nature of the donor-acceptor bonds was investigated with an energy decomposition analysis. It is found that the bond dissociation energy is not a good measure for the intrinsic strength of Lewis acidity and basicity because the preparation energies of the fragments may significantly change the trend of the bond strength. The interaction energies between the frozen fragments of the borane complexes are in most cases larger than the interaction energies of the alane complexes. The bond dissociation energy of the alane complexes is sometimes higher than that of the borane analogues because the energy for distorting the planar equilibrium geometry of BX3 to the pyramidal from in the complexes is higher than for AlX3. Inspection of the three energy terms, DeltaE(Pauli), DeltaE(orb), and DeltaE(elstat), shows that all three of them must be considered to understand the trends of the Lewis acid and base strength. The orbital term of the donor-acceptor bonds with the Lewis bases NCl3 and PCl3 have a higher pi character than the bonds of EH3 and EMe3, but NCl3 and PCl3 are weaker Lewis bases because the lone-pair orbital at the donor atoms N and P has a high percent s character. The calculated DeltaE(int) values suggest that the trends of the intrinsic Lewis bases' strengths in the main-group complexes with BX3 and AlX3 are NMe3 > NH3 > NCl3 and PMe3 > PH3 > PCl3. The transition metal complexes exhibit a somewhat different order with NH3 > NMe3 > NCl3 and PMe3 > PH3 > PCl3. The slightly weaker bonding of NMe3 than that of NH3 comes from stronger Pauli repulsion. The bond length does not always correlate with the bond dissociation energy, nor does it always correlate with the intrinsic interaction energy.     

Low-energy electron attachment to 5'-thymidine monophosphate: modeling single strand breaks through dissociative electron attachment

Mechanisms of low-energy electron (LEE) attachment and subsequent single-strand break (SSB) formation are investigated by density functional theory treatment of a simple model for DNA, i.e., the nucleotide, 5'-thymidine monophosphate (5'-dTMPH). In the present study, the C5'-O5' bond dissociation due to LEE attachment has been followed along the adiabatic as well as on the vertical (electron attached to the optimized geometry of the neutral molecule) anionic surfaces using B3LYP functional and 6-31G* and 6-31++G** basis sets. Surprisingly, it is found that the PES of C5'-O5' bond dissociation in the anion radicals have approximately the same barrier for both adiabatic and vertical pathways. These results provide support for the hypothesis that transiently bound electrons (shape resonances) to the virtual molecular orbitals of the neutral molecule likely play a key role in the cleavage of the sugar-phosphate C5'-O5' bond in DNA resulting in the direct formation of single strand breaks without significant molecular relaxation. To take into account the solvation effects, we considered the neutral and anion radical of 5'-dTMP surrounded by 5 or 11 water molecules with Na+ as a counterion. These structures were optimized using the B3LYP/6-31G** level of theory. We find the barrier height for adiabatic C5'-O5' bond dissociation of 5'-dTMP anion radical in aqueous environment is so substantially higher than in the gas phase that the adiabatic route will not contribute to DNA strand cleavage in aqueous systems. This result is in agreement with experiment.     

Low-lying electronic states and Cl-loss photodissociation of the C2H3Cl+ ion studied using multiconfiguration second-order perturbation theory

We studied the 1(2)A' '(X2A' '), 1(2)A' (A2A'), 2(2)A' ' (B2A' '), and 2(2)A' (C2A') states of the C2H3Cl+ ion using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods. For the four ionic states, we calculated the equilibrium geometries, adiabatic (T0) and vertical (Tv) excitation energies, and relative energies (Tv') at the geometry of the molecule at the CASPT2 level and the Cl-loss dissociation potential energy curves (PECs) at the CASPT2//CASSCF level. The computed oscillator strength f value for the X2A' ' <-- A2A' transition is very small, which is in line with the experimental fact that the A state has a long lifetime. The CASPT2 geometry and T0 value for the A2A' state are in good agreement with experiment. The CASPT2 Tv' values for the A2A', B2A' ', and C2A' states are in good agreement with experiment. The Cl-loss PEC calculations predict that the X2A' ', A2A', and C2A' states correlate to C2H3+ (XA1) and the BA' ' state to C2H3+ (1A' ') (the B2A' ' and C2A' PECs cross at R(C-Cl) approximately 2.24 A). Our calculations indicate that at 357 nm the X2A' ' state can undergo a transition to B2A' ' followed by a predissociation of B2A' ' by the repulsive C2A' state (via the B/C crossing), leading to C2H3+ (X1A1), and therefore confirm the experimentally proposed pathway for the photodissociation of X2A' ' at 357 nm. Our CASPT2 D0 calculations support the experimental fact that the X state does not undergo dissociation in the visible spectral region and imply that a direct dissociation of the A state to C2H3+ (X1A1) is energetically feasible.     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

Assessment of new meta and hybrid meta density functionals for predicting the geometry and binding energy of a challenging system: the dimer of H2S and benzene

Noncovalent interactions of a hydrogen bond donor with an aromatic pi system present a challenge for density functional theory, and most density functionals do not perform well for this kind of interaction. Here we test seven recent density functionals from our research group, along with the popular B3LYP functional, for the dimer of H 2S with benzene. The functionals considered include the four new meta and hybrid meta density functionals of the M06 suite, three slightly older hybrid meta functionals, and the B3LYP hybrid functional, and they were tested for their abilities to predict the dissociation energies of three conformations of the H 2S-benzene dimer and to reproduce the key geometric parameters of the equilibrium conformation of this dimer. All of the functionals tested except B3LYP correctly predict which of the three conformations of the dimer is the most stable. The functionals that are best able to reproduce the geometry of the equilibrium conformation of the dimer with a polarized triple-zeta basis set are M06-L, PWB6K, and MPWB1K, each having a mean unsigned relative error across the two experimentally verifiable geometric parameters of only 8%. The success of M06-L is very encouraging because it is a local functional, which reduces the cost for large simulations. The M05-2X functional yields the most accurate binding energy of a conformation of the dimer for which a binding energy calculated at the CCSD(T) level of theory is available; M05-2X gives a binding energy for the system with a difference of merely 0.02 kcal/mol from that obtained by the CCSD(T) calculation. The M06 functional performs well in both categories by yielding a good representation of the geometry of the equilibrium structure and by giving a binding energy that is only 0.19 kcal/mol different from that calculated by CCSD(T). We conclude that the new generation of density functionals should be useful for a variety of problems in biochemistry and materials where aromatic functional groups can serve as hydrogen bond acceptors.     

Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.     

Bonding analysis using localized relativistic orbitals: water, the ultrarelativistic case and the heavy homologues H2X (X = Te, Po, eka-Po)

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).     

Sigma- and pi-bond strengths in main group 3-5 compounds

The sigma- and pi-bond strengths for the molecules BH2NH2, BH2PH2, AlH2NH2, and AlH2PH2 have been calculated by using ab initio molecular electronic structure theory at the CCSD(T)/CBS level. The adiabatic pi-bond energy is defined as the rotation barrier between the equilibrium ground-state configuration and the C(s)symmetry transition state for torsion about the A-X bond. We also report intrinsic pi-bond energies corresponding to the adiabatic rotation barrier corrected for the inversion barrier at N or P. The adiabatic sigma-bond energy is defined as the dissociation energy of AH2XH2 to AH2 + XH2 in their ground states minus the adiabatic pi-bond energy. The adiabatic sigma-bond strengths for the molecules BH2NH2, BH2PH2, AlH2NH2, and AlH2PH2 are 109.8, 98.8, 77.6, and 68.3 kcal/mol, respectively, and the corresponding adiabatic pi-bond strengths are 29.9, 10.5, 9.2, and 2.7 kcal/mol, respectively.     

The short N [bond] F bond in N(2)F(+) and how Pauli repulsion influences bond lengths. Theoretical study of N(2)X(+), NF(3)X(+), and NH(3)X(+) (X [double bond] F, H)

Exceptionally short N [bond] F bond distances of only 1.217 A (crystal) and 1.246 A (gas phase) have been reported for N(2)F(+), making it the shortest N [bond] F bond ever observed. To trace the origin of this structural phenomenon, we have analyzed the model systems N(2)X(+), NF(3)X(+), and NH(3)X(+) (X [double bond] F, H) using generalized gradient approximation density functional theory at BP86/TZ2P. In good agreement with experiment, the computations yield an extremely short N [bond] F bond for N(2)F(+): we find N [bond] F bond distances in N(2)F(+), NF(4)(+), and NH(3)F(+) of 1.245, 1.339, and 1.375 A, respectively. The N [bond] X bonding mechanisms are quantitatively analyzed in the framework of Kohn-Sham MO theory. At variance with the current hypothesis, reduced steric and other Pauli repulsion (of substituents or lone pairs at N with F) rather than the extent of s [bond] p hybridization of N (i.e., sp versus sp(3)) are responsible for the much shorter N [bond] F distance in N(2)F(+) compared to NF(4)(+). The results for our nitrogen compounds are furthermore discussed in the more general context of how bond lengths are determined by both bonding and repulsive orbital interactions.     

Molecular structure of the octatetranyl anion, C8H-: a computational study

The equilibrium molecular structure of the octatetranyl anion, C8H(-), which has been recently detected in two astronomical environments, is investigated with the aid of both ab initio post-Hartree-Fock and density functional theory (DFT) calculations. The model chemistry adopted in this study was selected after a series of benchmark calculations performed on molecular acetylene for which accurate gas-phase structural data are available. Geometry optimizations performed at the CCSD/6-311+G(2d,p), QCISD/6-311+G(2d,p), and MP4(SDQ)/6-311+G(2d,p) levels of theory yield for C8H(-) an interesting polyyne-type structure that defies the chemical formula displaying a simple alternation of triple and single carbon-carbon bonds, [:C[triple bond]C-C[triple bond]C-C[triple bond]C-C[triple bond]CH](1-). In the optimized geometry of C8H(-), as one proceeds from the naked carbon atom on one side of the chain to the CH unit on the opposite side of the chain, the short (formally triple) carbon-carbon bonds decrease in length from 1.255 to 1.213 A whereas the long (formally single) carbon-carbon bonds increase (albeit only slightly) in length from 1.362 to 1.378 A (CCSD results). In striking contrast, both MP2 and DFT (B3LYP and PBE0) calculations fail in reproducing the pattern of the carbon-carbon bond lengths obtained with the CCSD, QCISD, and MP4 methods. The structures of three shorter n-even chains, C(n)H(-) (n = 2, 4, and 6), along with those of four n-odd compounds (n = 3, 5, 7, and 9) are also investigated at the CCSD/6-311+G(2d,p) level of theory.     

An extended hybrid density functional (X3LYP) with improved descriptions of nonbond interactions and thermodynamic properties of molecular systems

We derive here the form for the exact exchange energy density for a density that decays with Gaussian-type behavior at long range. This functional is intermediate between the B88 and the PW91 exchange functionals. Using this modified functional to match the form expected for Gaussian densities, we propose the X3LYP extended functional. We find that X3LYP significantly outperforms Becke three parameter Lee-Yang-Parr (B3LYP) for describing van der Waals and hydrogen bond interactions, while performing slightly better than B3LYP for predicting heats of formation, ionization potentials, electron affinities, proton affinities, and total atomic energies as validated with the extended G2 set of atoms and molecules. Thus X3LYP greatly enlarges the field of applications for density functional theory. In particular the success of X3LYP in describing the water dimer (with R(e) and D(e) within the error bars of the most accurate determinations) makes it an excellent candidate for predicting accurate ligand-protein and ligand-DNA interactions.     

C−X Bond Activation by Palladium: Steric Shielding versus Steric Attraction

The C−X bond activation (X = H, C) of a series of substituted C(n°)−H and C(n°)−C(m°) bonds with C(n°) and C(m°) = H₃C− (methyl, 0°), CH₃H₂C− (primary, 1°), (CH₃)₂HC− (secondary, 2°), (CH₃)₃C− (tertiary, 3°) by palladium were investigated using relativistic dispersion-corrected density functional theory at ZORA-BLYP-D3(BJ)/TZ2P. The effect of the stepwise introduction of substituents was pinpointed at the C−X bond on the bond activation process. The C(n°)−X bonds become substantially weaker going from C(0°)−X, to C(1°)−X, to C(2°)−X, to C(3°)−X because of the increasing steric repulsion between the C(n°)- and X-group. Interestingly, this often does not lead to a lower barrier for the C(n°)−X bond activation. The C−H activation barrier, for example, decreases from C(0°)−X, to C(1°)−X, to C(2°)−X and then increases again for the very crowded C(3°)−X bond. For the more congested C−C bond, in contrast, the activation barrier always increases as the degree of substitution is increased. Our activation strain and matching energy decomposition analyses reveal that these differences in C−H and C−C bond activation can be traced back to the opposing interplay between steric repulsion across the C−X bond versus that between the catalyst and substrate.     

Electronic structure of cobalt carbide, CoC

The ground and 18 low lying excited states of the diatomic molecule cobalt carbide, CoC, have been examined by multireference variational methods (MRCI) combined with quantitative basis sets. All calculated states are bound and correlate adiabatically to the ground-state atoms, Co(a4F) + C(3P). We report complete potential energy curves, equilibrium bond distances, dissociation energies (De), spectroscopic constants, electric dipole moments and spin-orbit splittings. The bonding character of certain states is also discussed with the help of Mulliken distributions and valence-bond-Lewis diagrams. We are practically certain that the ground state is of 2Sigma+ symmetry with a state of 2Delta symmetry lying less than 3 kcal/mol higher, in agreement with the relevant experimental findings. Our best estimate of the X 2Sigma+ dissociation energy is De(D0) = 83(82) kcal/mol at r(e) = 1.541 A, 0.02 A shorter than the experimental bond length.     

BDE261: a comprehensive set of high-level theoretical bond dissociation enthalpies

We have used the high-level W1w protocol to compile a comprehensive collection of 261 bond dissociation enthalpies (BDEs) for bonds connecting hydrogen, first-row and second-row p-block elements. Together they cover 45 bond types, and we term this the BDE261 set. We have used these benchmark values to assess the performance of computationally less demanding theoretical procedures, including density functional theory (DFT), double-hybrid DFT (DHDFT), and high-level composite procedures. We find that the M06-2X (DFT), ROB2-PLYP and DuT-D3 (DHDFT), and G3X(MP2)-RAD and G4(MP2)-6X (composite) procedures yield absolute BDEs with satisfactory to excellent accuracy. Overall, we recommend G4(MP2)-6X as an accurate and relatively cost-effective procedure for the direct computation of BDEs. One important finding is that the deviations for DFT and (especially) DHDFT procedures are often quite systematic. This allows an alternative approach to obtaining accurate absolute BDEs, namely, to evaluate accurate relative BDEs (RBDEs) using a computationally less demanding procedure, and to use these RBDEs in combination with appropriate and accurate reference BDEs to give accurate absolute BDEs. We recommend DuT-D3 for this purpose. For a still less computationally demanding approach, we introduce the deviation from additivity of the RBDE (DARBDE), and demonstrate that the combination of lower-level DARBDEs for larger systems and higher-level (W1w) reference RBDEs and BDEs for small systems can be utilized to obtain improved RBDEs for multiply substituted systems at low cost.     

Ligand effects in bimetallic high oxidation state palladium systems

Ligand effects in bimetallic high oxidation state systems containing a X-Pd-Pd-Y framework have been explored with density functional theory (DFT). The ligand X has a strong effect on the dissociation reaction of Y to form [X-Pd-Pd](+) + Y(-). In the model system examined where Y is a weak σ-donor ligand and a good leaving group, we find that dissociation of Y is facilitated by greater σ-donor character of X relative to Y. We find that there is a linear correlation of the Pd-Y and Pd-Pd bond lengths with Pd-Y bond dissociation energy, and with the σ-donating ability of X. These results can be explained by the observation that the Pd d(z(2)) population in the PdY fragment increases as the donor ability of X increases. In these systems, the Pd(III)-Pd(III) arrangement is favored when X is a weak σ-donor ligand, while the Pd(IV)-Pd(II) arrangement is favored when X is a strong σ-donor ligand. Finally, we demonstrate that ligand exchange to form a bimetallic cationic species in which each Pd is six-coordinate should be feasible in a high polarity solvent.