On the convergence of Z-averaged perturbation theory

Very high order open-shell Z-averaged perturbation theory (ZAPT) energies, equilibrium bond lengths, and harmonic vibrational frequencies have been computed for a suite of small molecules using a determinantal algorithm. The convergence of ZAPTn energies is compared to alternative Moller-Plesset (MP) perturbation theories built on restricted open-shell Hartree-Fock (ROMP, RMP, OPT1, and OPT2) and unrestricted Hartree-Fock (UMP) reference wave functions for NH(2) at three N-H bond lengths and for CN. The ZAPTn energy series closely parallel those of RMPn and ROMPn theories for these systems. Further, we examine the convergence of ZAPTn energies, equilibrium bond lengths (r(e)), and harmonic vibrational frequencies (omega(e)) for X (2)Sigma(g)(+) CN, X (4)Sigma(g) (-) C(2)(+), and b (2)Delta(g) C(2)(+), tracking oscillations in the energy series for the challenging latter system to order 1000. Finally, we obtain r(e) and omega(e) values from explicit ZAPT2 and ZAPT4 computations with a triple-zeta plus double polarization basis set. The ensuing results are very close to those from second- and fourth-order RMP and ROMP for the NO and CN molecules but are significantly closer to experiment in the case of (3)Sigma(g)(-) O(2). The ZAPTn series exhibit all the fascinating diversity of behavior previously observed for closed-shell MPn theory. Particularly encouraging is the ability of Feenberg transformations to remove erratic, strongly oscillatory, and divergent behavior that may occur in ZAPTn series and provide systematic improvements toward the full configuration interaction limit. In light of the appealing mathematical properties of ZAPT and similarity of results to those from the oft-applied RMP theory, coupled with the reductions in computational cost inherent in the ZAPT method relative to theories requiring different orbitals for different spins, we recommend low-order ZAPT for general applications to open-shell systems, particularly in cases where spin contamination is of concern.     

Binuclear iron carbonyl nitrosyls: bridging nitrosyls versus bridging carbonyls

The iron carbonyl nitrosyls Fe 2(NO) 2(CO) n ( n = 7, 6, 5, 4, 3) have been studied by density functional theory (DFT) using the B3LYP and BP86 methods, for comparison of their predicted structures with those of isoelectronic cobalt carbonyl derivatives. The lowest energy structures for Fe 2(NO) 2(CO) 7 and Fe 2(NO) 2(CO) 6 have two NO bridges, and the lowest energy structure for Fe 2(NO) 2(CO) 5 has a single NO bridge with metal-metal distances (BP86) of 3.161, 2.598, and 2.426 A, respectively, corresponding to the formal metal-metal bond orders of zero, one, and two, respectively, required for the favored 18-electron configuration for the iron atoms. The heptacarbonyl Fe 2(NO) 2(CO) 7 is thermodynamically unstable with respect to CO loss to give Fe 2(NO) 2(CO) 6. The favored structures for the more highly unsaturated Fe 2(NO) 2(CO) 4 and Fe 2(NO) 2(CO) 3 also have bridging NO groups but avoid iron-iron bond orders higher than two by formal donation of five electrons from bridging NO groups with relatively short Fe-O distances. The lowest energy structures of the unsaturated Fe 2(NO) 2(CO) n derivatives ( n = 5, 4, 3) are significantly different from the isoelectronic cobalt carbonyls Co 2(CO) n +2 owing to the tendency for Fe 2(NO) 2(CO) n to form structures with bridging NO groups and metal-metal formal bond orders no higher than two.     

Toward the observation of quartet states of the ozone radical cation: insights from coupled cluster theory

Since the discovery of ozone depletion, the doublet electronic states of the ozone radical cation have received much attention in experimental and theoretical investigations, while the low-lying quartet states have not. In the present research, viable pathways to the quartet states from the lowest three triplet states of ozone, (3)A(2), (3)B(2), and (3)B(1), and excitations from the (2)A(1) and (2)B(2) states of the ozone radical cation have been studied in detail. The potential energy surfaces, structural optimizations, and vibrational frequencies for several states of ozone and its radical cation have been thoroughly investigated using the complete active space self-consistent field, unrestricted coupled cluster theory from a restricted open-shell Hartree-Fock reference including all single and double excitations (UCCSD), UCCSD method with the effects of connected triple excitations included perturbatively, and unrestricted coupled cluster including all single, double, and triple excitations with the effects of connected quadruple excitations included perturbatively. These methods used Dunning's correlation-consistent polarized core-valence basis sets, cc-pCVXZ (X = D, T, Q, and 5). The most feasible pathways (symmetry and spin allowed transitions) to the quartet states are (4)A(1)<--(3)A(2), (4)A(2)<--(3)A(2), (4)A(1)<--(3)B(2), (4)A(2)<--(3)B(1), (4)B(2)<--(3)B(1), (4)A(2)<--(1)A(1), (4)B(2)<--(1)A(1), and (4)A(1)<--(1)A(1) with vertical ionization potentials of 12.46, 12.85, 12.82, 12.46, 12.65, 13.43, 13.93, and 14.90 eV, respectively.     

Spectroscopic detection and theoretical confirmation of the role of Cr2(CO)5(C5R5)2 and .Cr(CO)2(ketene)(C5R5) as intermediates in carbonylation of N=N=CHSiMe3 to O=C=CHSiMe3 by .Cr(CO)3(C5R5) (R = H, CH3)

Conversion of N=N=CHSiMe3 to O=C=CHSiMe3 by the radical complexes .Cr(CO)3C5R5 (R = H, CH3) derived from dissociation of [Cr(CO)3(C5R5)]2 have been investigated under CO, Ar, and N2 atmospheres. Under an Ar or N2 atmosphere the reaction is stoichiometric and produces the Cr[triple bond]Cr triply bonded complex [Cr(CO)2(C5R5)]2. Under a CO atmosphere regeneration of [Cr(CO)3(C5R5)]2 (R = H, CH3) occurs competitively and conversion of diazo to ketene occurs catalytically as well as stoichiometrically. Two key intermediates in the reaction, .Cr(CO)2(ketene)(C5R5) and Cr2(CO)5(C5R5)2 have been detected spectroscopically. The complex .Cr(13CO)2(O=13C=CHSiMe3)(C5Me5) has been studied by electron spin resonance spectroscopy in toluene solution: g(iso) = 2.007; A(53Cr) = 125 MHz; A(13CO) = 22.5 MHz; A(O=13C=CHSiMe3) = 12.0 MHz. The complex Cr2(CO)5(C5H5)2, generated in situ, does not show a signal in its 1H NMR and reacts relatively slowly with CO. It is proposed to be a ground-state triplet in keeping with predictions based on high level density functional theory (DFT) studies. Computed vibrational frequencies are also in good agreement with experimental data. The rates of CO loss from 3Cr2(CO)5(C5H5)2 producing 1[Cr(CO)2(C5H5)]2 and CO addition to 3Cr2(CO)5(C5H5)2 producing 1[Cr(CO)3(C5H5)]2 have been measured by kinetics and show DeltaH approximately equal 23 kcal mol(-1) for both processes. Enthalpies of reduction by Na/Hg under CO atmosphere of [Cr(CO)n(C5H5)]2 (n = 2,3) have been measured by solution calorimetry and provide data for estimation of the Cr[triple bond]Cr bond strength in [Cr(CO)2(C5H5)]2 as 72 kcal mol(-1). The complex [Cr(CO)2(C5H5)]2 does not readily undergo 13CO exchange at room temperature or 50 degrees C implying that 3Cr2(CO)5(C5H5)2 is not readily accessed from the thermodynamically stable complex [Cr(CO)2(C5H5)]2. A detailed mechanism for metalloradical based conversion of diazo and CO to ketene and N2 is proposed on the basis of a combination of experimental and theoretical data.     

Model systems for probing metal cation hydration: the V+(H2O) and ArV+(H2O) complexes

In support of mass-selected infrared photodissociation (IRPD) spectroscopy experiments, coupled-cluster methods including all single and double excitations (CCSD) and a perturbative contribution from connected triple excitations [CCSD(T)] have been used to study the V+(H2O) and ArV+(H2O) complexes. Equilibrium geometries, harmonic vibrational frequencies, and dissociation energies were computed for the four lowest-lying quintet states (5A1, 5A2, 5B1, and 5B2), all of which appear within a 6 kcal mol(-1) energy range. Moreover, anharmonic vibrational analyses with complete quartic force fields were executed for the 5A1 states of V+(H2O) and ArV+(H2O). Two different basis sets were used: a Wachters+f V[8s6p4d1f] basis with triple-zeta plus polarization (TZP) for O, H, and Ar; and an Ahlrichs QZVPP V[11s6p5d3f2g] and Ar[9s6p4d2f1g] basis with aug-cc-pVQZ for O and H. The ground state is predicted to be 5A1 for V+(H2O), but argon tagging changes the lowest-lying state to 5B1 for ArV+(H2O). Our computations show an opening of 2 degrees -3 degrees in the equilibrium bond angle of H2O due to its interaction with the metal ion. Zero-point vibrational averaging increases the effective bond angle further by 2.0 degrees -2.5 degrees, mostly because of off-axis motion of the heavy vanadium atom rather than changes in the water bending potential. The total theoretical shift in the bond angle of about +4 degrees is significantly less than the widening near 9 degrees deduced from IRPD experiments. The binding energies (D0) for the successive addition of H2O and Ar to the vanadium cation are 36.2 and 9.4 kcal mol(-1), respectively.     

Hydrogen-atom abstraction from the adenine-uracil base pair

The hydrogen-abstracted radicals from the adenine-uracil (AU) base pair have been studied at the B3LYP/DZP++ level of theory. The A(N9)-U and A-U(N1) radicals, which correspond to hydrogen-atom abstraction at the adenine N9 and uracil N1 atoms, respectively, were predicted to be the two lowest-lying among the nine (AU-H) radicals studied in this study. The removal of the amino hydrogen of the adenine moiety that forms a hydrogen bond with the uracil O4 atom in the AU pair resulted in radical A(N6a)-U, which has the smallest base-pair dissociation energy, 5.9 kcal mol(-1). This radical is more likely to dissociate into the two isolated bases than to recover the hydrogen bond with the O4 atom through N6-H bond rotation along the C6-N6 bond. In general, the radicals generated by C-H bond breaking were higher in energy than those arising from N-H bond cleavage, because the unpaired electrons in the carbon-centered radicals were mainly localized on the carbon atom from which the hydrogen atom was removed. However, the highest-lying radical was found to arise from removal of the N3 hydrogen of uracil. The most remarkable structural feature of this radical is a very short C-H...O distance of 2.094 A, consistent with a substantial hydrogen bond. Although this radical lost the N1...H-N3 hydrogen bond between the two bases, its dissociation energy was predicted to be 12.9 kcal mol(-1), similar to that of the intact AU base pair. This is due to the transfer of electron density from the adenine N1 atom to the uracil N3 atom.     

Observation of a mixed-metal transition in heterobimetallic Au/Ag dicyanide systems

Crystals of the mixed-metal heterobimetallic Au/Ag dicyanide complex, K[AuxAg1-x(CN)2] (x = 0-->1), were obtained by slow evaporation. The mixed-metal complex K[Au0.44Ag0.56(CN)2] crystallizes in a rhombohedral crystal system, space group R. The crystal structure consists of layers of linear chains of Au(CN)2- and Ag(CN)2- ions and K+ ions that connect the layers through the N atoms. The excitation and emission spectra of single crystals of K[AuxAg1-x(CN)2] were recorded at 4.2-180 K using excitation wavelengths between 230 and 260 nm. Two emission bands due to Ag-Au interactions were observed at 343 and 372 nm. Lifetime measurements indicate the shorter-wavelength emission corresponds to fluorescence and the longer-wavelength band is phosphorescence. These new emission bands are not seen in the pure K[Ag(CN)2] or pure K[Au(CN)2] crystals. Extended Hückel calculations show that the LUMO of the mixed-metal system is bonding while the HOMO is antibonding or very weakly bonding. Moreover, excited-state extended Hückel calculations indicate the formation of exciplexes with shorter metal-metal distances and higher metal-metal overlap populations than the corresponding ground-state oligomers. The luminescence is assigned to a mixed-metal transition from a molecular orbital with Au character to a molecular orbital with Ag character.     

Electron attachment induced proton transfer in a DNA nucleoside pair: 2'-deoxyguanosine-2'-deoxycytidine

To elucidate electron attachment induced damage in the DNA double helix, electron attachment to the 2'-deoxyribonucleoside pair dG:dC has been studied with the reliably calibrated B3LYP/DZP++ theoretical approach. The exploration of the potential energy surface of the neutral and anionic dG:dC pairs predicts a positive electron affinity for dG:dC [0.83 eV for adiabatic electron affinity (EAad) and 0.16 eV for vertical electron affinity (VEA)]. The substantial increases in the electron affinity of dG:dC (by 0.50 eV for EAad and 0.23 eV for VEA) compared to those of the dC nucleoside suggest that electron attachment to DNA double helices should be energetically favored with respect to the single strands. Most importantly, electron attachment to the dC moiety in the dG:dC pair is found to be able to trigger the proton transfer in the dG:dC- pair, surprisingly resulting in the lower energy distonic anionic complex d(G-H)-:d(C+H).. The negative charge for the latter system is located on the base of dC in the dG:dC- pair, while it is transferred to d(G-H) in d(G-H)-:d(C+H)., accompanied by the proton transfer from N1(dG) to N3(dC). The low energy barrier (2.4 kcal/mol) for proton transfer from dG to dC- suggests that the distonic d(G-H)-:d(C+H). pair should be one of the important intermediates in the process of electron attachment to DNA double helices. The formation of the neutral nucleoside radical d(C+H). is predicted to be the direct result of electron attachment to the DNA double helices. Since the neutral radical d(C+H). nucleotide is the key element in the formation of this DNA lesion, electron attachment might be one of the important factors that trigger the formation of abasic sites in DNA double helices.     

Dipolar double-quantum filtered rotational-echo double resonance

The homonuclear dipolar coupling of a directly bonded (13)C-(13)C pair has been used to create a dipolar double-quantum filter (D-DQF) to remove the natural-abundance (13)C background in (13)C[(2)H] rotational-echo double-resonance (REDOR) experiments. The most efficient version of this experiment has the D-DQF excitation and reconversion preceding the REDOR evolution period. Calculated and observed (13)C[(2)H]D-DQF-REDOR dephasings were in agreement for a test sample of mixed recrystallized labeled alanines.     

Adaptive umbrella sampling of the potential energy: modified updating procedure of the umbrella potential and application to peptide folding

Adaptive umbrella sampling of the potential energy is used as a search method to determine the structures and thermodynamics of peptides in solution. It leads to uniform sampling of the potential energy, so as to combine sampling of low-energy conformations that dominate the properties of the system at room temperature with sampling of high-energy conformations that are important for transitions between different minima. A modification of the procedure for updating the umbrella potential is introduced to increase the number of transitions between folded and unfolded conformations. The method does not depend on assumptions about the geometry of the native state. Two peptides with 12 and 13 residues, respectively, are studied using the CHARMM polar-hydrogen energy function and the analytical continuum solvent potential for treatment of solvation. In the original adaptive umbrella sampling simulations of the two peptides, two and six transitions occur between folded and unfolded conformations, respectively, over a simulation time of 10 ns. The modification increases the number of transitions to 6 and 12, respectively, in the same simulation time. The precision of estimates of the average effective energy of the system as a function of temperature and of the contributions to the average effective energy of folded conformations obtained with the adaptive methods is discussed. Received: 11 July 1998 / Accepted: 22 September 1998 / Published online: 17 December 1998