Ab initio spectroscopic characterization of the HNNO and ONHN radicals

A composite coupled cluster methodology is used with systematic sequences of correlation consistent basis sets to accurately determine the structure, vibrational frequencies, and isotopic shifts for trans-HNNO ((2)A'), cis-HNNO ((2)A'), and ONHN ((2)A'). Anharmonic corrections to the vibrational frequencies and rotational constants are obtained using density functional theory. With basis sets larger than double-zeta, large differences between restricted open-shell Hartree-Fock (ROHF)-based and unrestricted Hartree-Fock (UHF)-based coupled cluster harmonic frequencies are calculated, with the UHF-based ones judged to be more reliable based on an analysis of the orbital hessian eigenvalues. The final calculated anharmonic vibrational band origins are generally in good agreement with the experimental values measured in rare gas matrices. The calculation of the vibrational band origins of the isovalent NO(2) molecule at similar levels of theory exhibits an agreement with experiment to within a few wavenumbers. In the latter case, however, a ROHF treatment was required since the UHF approach failed to provide realistic frequencies for the antisymmetric stretching mode. The heat of formation at 0 K of trans-HNNO is calculated to be 50.5 ± 0.5 kcal∕mol using a very similar composite coupled cluster methodology as in the structure and harmonic frequency determinations.     

Communication: ROHF theory made simple

Restricted open-shell Hartree-Fock (ROHF) theory is formulated as a projected self-consistent unrestricted HF (UHF) model by mathematically constraining spin density eigenvalues. This constrained UHF (CUHF) wave function is identical to that obtained from Roothaan's effective Fock operator. The α and β CUHF Fock operators are parameter-free and have eigenvalues (orbital energies) that are physically meaningful as in UHF, except for eliminating spin contamination. This new way of solving ROHF leads to orbitals that turn out to be identical to semicanonical orbitals. The present approach removes ambiguities in ROHF orbital energies.     

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).     

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method.     

Infrared spectra of C(3)H(3)(+)-N(2) dimers: identification of proton-bound c-C(3)H(3)(+)-N(2) and H(2)CCCH(+)-N(2) isomers.

Mid-infrared photodissociation spectra of mass selected C(3)H(3)(+)-N(2) ionic complexes are obtained in the vicinity of the C-H stretch fundamentals (2970-3370 cm(-1)). The C(3)H(3)(+)-N(2) dimers are produced in an electron impact cluster ion source by supersonically expanding a gas mixture of allene, N(2), and Ar. Rovibrational analysis of the spectra demonstrates that (at least) two C(3)H(3)(+) isomers are produced in the employed ion source, namely the cyclopropenyl (c-C(3)H(3)(+)) and the propargyl (H(2)CCCH(+)) cations. This observation is the first spectroscopic detection of the important c-C(3)H(3)(+) ion in the gas phase. Both C(3)H(3)(+) cations form intermolecular proton bonds to the N(2) ligand with a linear -C-H...N-N configuration, leading to planar C(3)H(3)(+)-N(2) structures with C(2v) symmetry. The strongest absorption of the H(2)CCCH(+)-N(2) dimer in the spectral range investigated corresponds to the acetylenic C-H stretch fundamental (v(1) = 3139 cm(-1)), which experiences a large red shift upon N(2) complexation (Delta(v1) approximately -180 cm(-1)). For c-C(3)H(3)(+)-N(2), the strongly IR active degenerate antisymmetric stretch vibration (v4)) of c-C(3)H(3)(+) is split into two components upon complexation with N(2): v4)(a(1)) = 3094 cm(-1) and v4)(b(2)) = 3129 cm(-1). These values bracket the yet unknown v4) frequency of free c-C(3)H(3)(+) in the gas phase, which is estimated as 3125 +/- 4 cm(-1) by comparison with theoretical data. Analysis of the nuclear spin statistical weights and A rotational constants of H(2)CCCH(+)-N(2) and c-C(3)H(3)(+)-N(2) provide for the first time high-resolution spectroscopic evidence that H(2)CCCH(+) and c-C(3)H(3)(+) are planar ions with C(2v) and D(3h) symmetry, respectively. Ab initio calculations at the MP2(full)/6-311G(2df,2pd) level confirm the given assignments and predict intermolecular separations of R(e) = 2.1772 and 2.0916 A and binding energies of D(e) = 1227 and 1373 cm(-1) for the H-bound c-C(3)H(3)(+)-N(2) and H(2)CCCH(+)-N(2) dimers, respectively.     

Structures of tetrafluorocyclopropene, hexafluorocyclobutene, octafluorocyclopentene and related perfluoroalkene radical anions revealed by electron spin resonance spectroscopic and computational studies

Isotropic and anisotropic ESR spectra were observed for the radical anions of hexafluorocyclobutene (c-C(4)F(6)(-)), octafluorocyclopentene (c-C(5)F(8)(-)) and perfluoro-2-butene (CF(3)CF=CFCF(3)(-)) in gamma-irradiated plastically crystalline neopentane, tetramethylsilane (TMS) and TMS-d(12) matrices, or the rigid 2-methyltetrahydrofuran (MTHF) matrix. The isotropic spectra of c-C(4)F(6)(-) and c-C(5)F(8)(-) are characterized by three different sets of pairs of (19)F nuclei with the isotropic hyperfine (hf) splittings of 15.2 (2F), 6.5 (2F), 1.1 (2F) mT for c-C(4)F(6)(-) and 14.7 (2F), 7.4 (2F), 1.0 (2F) mT for c-C(5)F(8)(-). By comparison with the results of ab initio quantum chemical computations, the large triplet (19)F hf splittings of ca. 15 mT are assigned to the two fluorines attached to the C=C bond. The UHF, B3LYP and MP2 computations predict that the geometrical structures of the perfluoroalkenes are strongly distorted by one-electron reduction to form their radical anions; c-C(3)F(4)(-): C(2) symmetry ((2)A state) <-- C(2)(v) ((1)A(1)), c-C(4)F(6)(-): C(1) ((2)A) <-- C(2)(v) ((1)A(1)) and c-C(5)F(8)(-): C(1) ((2)A) <-- C(s) ((1)A'). The structural distortion arises from a mixing of the pi* and higher-lying sigma* orbitals at the C=C carbons similar to that previously found for CF(2)=CF(2)(-) with a C(2)(h) distortion. The isotropic (19)F hf splittings computed with the B3LYP method with 6-311+G(2df,p) basis set for the geometry optimized by the UHF and/or MP2 methods are within 6% error of the experimental values. The experimental anisotropic spectra of c-C(4)F(6)(-), c-C(5)F(8)(-) and CF(2)=CF(2)(-) were satisfactorily reproduced by the ESR spectral simulation method using the computed hf principal values and orientation of (19)F nuclei. In addition, the electronic excitation energies and oscillator strengths for the CF(2)=CF(2)(-), c-C(3)F(4)(-), c-C(4)F(6)(-) and c-C(5)F(8)(-) radical anions were computed for the first time by TD-DFT methods.     

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.     

Variational spaces of electronic calculations in quantum chemistry

The exterior algebra formalism is presented, then used to obtain, in a very simple way, Brillouin's theorem, and to derive the general algebraic equations of the various variational spaces explored by RHF, ROHF, UHF, CASSCF, UCASSCF, CI methods. When a given basis set of one-electron orbitals (not necessarily orthogonal) is fixed, these equations lead to analytical equations for the CI coefficients only. The important algebraic concepts (i.e. concepts that do not refer to any particular basis set) of internal space, length and factorization of a multi-configuration are also introduced.     

Method of local increments for the calculation of adsorption energies of atoms and small molecules on solid surfaces. 2. CO/MgO(001)

The method of local increments is used in connection with an embedded cluster approach and wave function based quantum chemical ab initio methods to describe the adsorption of a single CO molecule on the MgO(001) surface. The first step in this approach is a conventional Hartree-Fock calculation. The occupied orbitals are then localized by means of the Foster-Boys localization procedure, and the full system is decomposed into several "subunits" that consist of the orbitals localized at the CO molecule and at the Mg and O atoms of the MgO cluster. The correlation energy is expanded into a series of local n-body increments that are evaluated separately and independently. In this way, big savings in computer time can be achieved because (a) the treatment of a large system is replaced with a series of much faster calculations for small subsystems and (b) the big basis sets necessary for describing dispersion effects are only needed for the atoms in the respective subsystem while all other atoms can be treated by medium size Hartree-Fock type basis sets. The coupled electron pair approach, CEPA, an approximate coupled cluster method, is used to calculate the correlation energies of the various subsystems. For the vertical adsorption of CO on top a Mg atom of the MgO(001) surface with the C atom toward Mg, the individual one- and two-body increments are calculated as functions of the CO-MgO separation and a full potential energy curve is constructed from them. A very shallow minimum with an adsorption energy of 0.016 eV at a Mg-C distance of 3.04 ? is found at the Hartree-Fock level, while inclusion of correlation (dispersion) effects shortens the Mg-C distance to 2.59 ? and yields a much larger adsorption energy of 0.124 eV. This is in very good agreement with the best experimental value of 0.14 eV. The basis set superposition error, BSSE, was fully corrected for by the counterpoise method and the bonding mechanism was analyzed at the Hartree-Fock level by means of the constrained space orbital variation, CSOV, analysis.     

Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone

To assess the separation of dynamic and nondynamic correlations and orbital choice, we calculate the molecular structure and harmonic vibrational frequencies of ozone with the recently developed tailored coupled cluster singles and doubles method (TCCSD). We employ the Hartree-Fock and complete active space (CAS) self-consistent field (SCF) orbitals to perform TCCSD calculations. When using the Hartree-Fock orbitals, it is difficult to reproduce the experimental vibrational frequency of the asymmetric stretching mode. On the other hand, the TCCSD based on the CASSCF orbitals in a correlation consistent polarized valence triple zeta basis yields excellent results with the two symmetric vibrations differing from the experimental harmonic values by 2 cm(-1) and the asymmetric vibration differing by 9 cm(-1).     

Coupled cluster methods including triple excitations for excited states of radicals

We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N(7)) computational steps and avoids storage of the triple-excitation amplitudes for both the ground- and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence (2)B(1) state of the allyl radical, low-lying states of the CH and CO(+) diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the (2)Sigma(+) state of CH, significant errors of more than 0.4 eV remain.     

Ab initio study of the cyclooctatetraenyl radical

Ab initio calculations have been carried out on the 1,3,5,7- and 1,2,4,7-tetraene configurations of the cyclooctatetraenyl radical at UHF, ROHF, MCSCF, ROCISD, QCISD, and CCSD(T) levels of theory with 6-311G(d,p) and cc-pVDZ basis sets. Although spin contamination is present, the ROCISD calculations support the energies obtained from less intensive, UHF-based coupled cluster calculations over the energies obtained from MCSCF analysis of the pi-electron orbitals. The 1,3,5,7-form is a local minimum at the coupled cluster levels, higher in energy than the resonance-stabilized 1,2,4,7-form by 10-13 kJ/mol, but bounded by a barrier of less than 0.5 kJ/mol. The isomerization surface connecting these two structures is described and results reported from integration of the vibrational Schr?dinger equation on that surface. Excited vibrational states at energies just above the isomerization barrier are dominated by the character of the 1,3,5,7-tetraenyl radical, which suggests that chemistry involving this intermediate at typical combustion temperatures may branch at this juncture.     

Hybrid correlation models based on active-space partitioning: seeking accurate O(N5) ab initio methods for bond breaking

Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.     

Structures of the hexafluorocyclopropane, octafluorocyclobutane, and decafluorocyclopentane radical anions probed by experimental and computational studies of anisotropic electron spin resonance (ESR) spectra

Anisotropic electron spin resonance (ESR) spectra are reported for the radical anions of hexafluorocyclopropane (c-C(3)F(6)(-)), octafluorocyclobutane (c-C(4)F(8)(-)), and decafluorocyclopentane (c-C(5)F(10)(-)) generated via gamma-irradiation in plastically crystalline tetramethylsilane (TMS) and rigid 2-methyltetrahydrofuran (MTHF) matrices. By combining the analysis of these experimental ESR spectra involving anisotropic hyperfine (hf) couplings with a series of quantum chemical computations, the geometrical and electronic structure of these unusual perfluorocycloalkane radical anions have been characterized more fully than in previous studies that considered only the isotropic couplings. Unrestricted Hartree-Fock (UHF) computations with the 6-311+G(d,p) basis set predict planar ring structures for all three radical anions, the ground electronic states being (2)A(2)(") for c-C(3)F(6)(-) (D(3h) symmetry), (2)A(2u) for c-C(4)F(8)(-) (D(4h)), and (2)A(2)(") for c-C(5)F(10)(-) (D(5h)), in which the respective six, eight, and ten 19F-atoms are equivalent by symmetry. A successful test of the theoretical computation is indicated by the fact that the isotropic 19F hf couplings computed by the B3LYP method with the 6-311+G(2df,p) basis set for the optimized geometries are in almost perfect agreement with the experimental values: viz., 19.8 mT (exp) vs 19.78 mT (calc) for c-C(3)F(6)(-); 14.85 mT (exp) vs 14.84 mT (calc) for c-C(4)F(8)(-); 11.6 mT (exp) vs 11.65 mT (calc) for c-C(5)F(10)(-). Consequently, the same computation method has been applied to calculate the almost axially symmetric anisotropic 19F hf couplings for the magnetically equivalent 19F atoms: (-4.90 mT, -4.84 mT, 9.75 mT) for c-C(3)F(6), (-3.54 mT, -3.48 mT, 7.02 mT) for c-C(4)F(8)(-), and (-2.62 mT, -2.56 mT, 5.18 mT) for c-C(5)F(10)(-). ESR spectral simulations performed using the computed principal values of the hf couplings and the spatial orientations of the 19F nuclei as input parameters reveal an excellent fit to the experimental anisotropic ESR spectra of c-C(3)F(6)(-), c-C(4)F(8)(-), and c-C(5)F(10)(-), thereby providing a convincing proof of the highly symmetric D(nh) structures that are predicted for these negative ions. Furthermore, using the computed 19F principal values and their orientations, the effective 19F anisotropic hf couplings along the molecular symmetry axes were evaluated for c-C(3)F(6)(-) and c-C(4)F(8)(-) and successfully correlated with the positions of the characteristic outermost features in both the experimental and calculated anisotropic spectra. In addition, the electronic excitation energies and oscillator strengths for the c-C(3)F(6)(-) , c-C(4)F(8)(-), and c-C(5)F(10)(-) radical anions were computed for the first time using time-dependent density functional theory (TD-DFT) methods.     

New coupled cluster approaches based on the unrestricted Hartree-Fock reference for treating molecules with multireference character

Here we review the basic formalism, implementation details, and performance of two newly developed coupled cluster (CC) methods based on the unrestricted Hartree-Fock (UHF) reference for treating molecules with multireference character. These two approaches can be considered to be approximations to the CC singles, doubles, and triples (CCSDT) method. The key concept of these two approaches is the corresponding orbitals, which are unitary transformations of canonical UHF molecular orbitals so that all spin orbitals are grouped into unique orbital pairs. In one approach called CCSDT(5P), a subset of triple excitations involving up to five-pair indices is included. In another approach called CCSD(T)-h, the contribution of connected triple excitations is treated in a hybrid way. With the concept of active corresponding orbitals, triple excitations can be automatically partitioned into two subsets, and the amplitudes of these two subsets are determined via solving different equations. Both CCSD(T)-h and CCSDT(5P) computationally scale as the seventh power of the system size. A survey of a number of applications demonstrates that CCSD(T)-h is an excellent approximation to the full CCSDT method, and CCSDT(5P) provides a good approximation to CCSDT for single-bond breaking processes. The overall performance of CCSDT(5P) is less accurate than that of CCSD(T)-h, but significantly better than that of the widely used CCSD(T).     

Spin-Adapted restricted Hartree–Fock reference coupled-cluster theory for open-shell systems: Noniterative triples for noncanonical orbitals

The coupled clusters singles and doubles (CCSD ) method for calculations of open-shell systems with the single restricted Hartree–Fock (ROHF ) reference determinant is extended by the noniterative triples to give CCSD(T) . Our approach profits from the fact that (a) single- and double-excitation amplitudes are spin-adapted, which directly leads to a computationally less demanding algorithm than are nonadapted procedures and produces the spin-adapted CCSD wave function and (b) triple excitations calculated from converged spin-adapted (SA ) CCSD amplitudes are also obtained more effectively. Altogether, computer demands of our SA CCSD(T) approach, applicable to high-spin open-shell cases which are well represented by a single-determinant reference is comparable to that for closed-shell systems. Our approach is not based on semicanonical orbitals, applied by Bartlett's group. However, we compare some other possible choices of ROHF orbitals to this “standard.” Numerical results for a series of atoms and molecules demonstrate little sensitivity to this selection. © 1995 John Wiley & Sons, Inc.     

Theoretical study of the energetics of the reactions of triplet dioxygen with hydroquinone, semiquinone, and their protonated forms: relation to the mechanism of superoxide generation in the respiratory chain

One-electron reduction of the dioxygen molecule by the reduced form of mitochondrial ubiquinones (Q) of the NADH dehydrogenase (complex I) and mitochondrial cytochrome bc1 (complex III) is believed to be the main source of the superoxide anion radical O2*- and the hydroperoxide radical OOH*. In this work, we modeled the energetics of four possible reactions of the triplet ((3)Sigma(g)) dioxygen-molecule reduction by fully reduced and protonated ubiquinone (QH2; reaction 1), its deprotonated form (QH-; reaction 2), the semiquinone radical (QH*; reaction 3), and the semiquinone anion radical (Q*-; reaction 4), by means of ab initio calculations with the 6-31G(d) and 6-31+G(d) basis set in the restricted open-shell Hartree-Fock (ROHF), unrestricted Hartree-Fock (UHF), and complete active space self-consistent field (CASSCF) with dynamic correlation [at the second-order M?ller-Plesset (MP2) or multiple reference M?ller-Plesset (MRMP), respectively] schemes and the basis set superposition error (BSSE) correction included, as well as semiempirical AM1 and PM3 calculations in the UHF and ROHF schemes. 2-Butene-1,4-dione and p-benzoquinone were selected as model compounds. For the reduced forms of both compounds, reaction 1 turned out to be energetically unfavorable at all levels of theory, this agreeing with the experimentally observed diminished reductive properties of hydroquinone derivatives at low pH. For 2-butene-1,4-dione treated at the most advanced MRMP/CASSCF/6-31+G(d) level, the energies of reactions 1-4 are 4.7, -34.3, -15.0, and -4.1 kcal/mol, respectively. This finding suggests that reactions 2 and 3 are the most likely mechanisms of electron transfer to molecular oxygen in aprotic environments and that proton transfer is involved in this process. Nearly the same energies of reactions 2 and 3 were calculated at the MRMP/CASSCF/6-31+G(d) level for reduced forms of p-benzoquinone. Inclusion of diffuse functions in the basis set and dynamic correlation at the CASSCF level appears essential. Because deprotonated ubiquinol is unlikely to exist in physiological environments, reaction 3 appears to be the most likely mechanism of one-electron reduction of oxygen; however, if oxygen can penetrate cytochrome bc1 as far as the Q(o) center where ubiquinol can be deprotonated, reaction 2 can also come into play. The energies of reactions 2 and 3 calculated at the MRMP/CASSCF/6-31+G(d) level are most closely reproduced in the ab initio and semiempirical UHF PM3 calculations. Additional semiempirical calculations on more realistic models of ubiquinone, 2,3-dimethoxy-6-methyl-p-benzoquinone and 2,3-dimethoxy-5-isoprenyl-6-methyl-p-benzoquinone, gave qualitatively the same relations between the energies of reactions 2 and 3 as those carried out for p-benzoquinone species, thereby suggesting that this method could be used in studying electron-transfer reactions from reduced quinone derivatives to molecular oxygen in more complex systems, such as a model of the Q(o) site of cytochrome bc1, where applying ab initio methods is unfeasible.     

Singlet�Ctriplet energy gap for trimethylenemethane, oxyallyl diradical, and related species: single- and multireference computational results

We have investigated the through-bond exchange interactions in three non-Kekulé hydrocarbon diradicals on the basis of single- and multireference coupled cluster and related broken-symmetry (BS) methods. The singlet?Ctriplet energy gap (S-T gap) and diradical characters for these species are evaluated. It is found that the spin contamination involved in the BS solutions is non-negligible and the approximate spin-projection method greatly improves the usual BS solutions. As for Mukherjee??s state-specific multireference coupled cluster (MkMRCC) computations, the size-consistent correction with the UHF localized natural orbitals (ULO) is useful to obtain the qualitatively correct 2J values.     

丙烷分子的价轨道(2b2)电子的动量分布测量

电子动量谱学（EMS）是在原子、分子和固体物理中研究电子结构的一种强有力的工具，它基于运动学条件完全确定的（e，2e）碰撞电离反应[1-3]．本文报告用高分辨电子动量谱仪首次测量得到丙烷门3H8）分子的价轨道电子（252）的动量分布·丙烷（C3Hs）价轨道电子的动量分布实验是     

Extraordinary cluster formation and intramolecular ligand-ligand interactions in cyanoacetylene [corrected] mediated by Mg+*: implications for the atmospheric chemistry of titan and for circumstellar chemistry

Experimental results are reported that track the kinetics of gas-phase reactions initiated by Mg+*, (c-C5H5)Mg+ and (c-C5H5)2Mg+* in hydrogen cyanide and cyanoacetylene. The experiments were performed with a selected-ion flow tube (SIFT) tandem mass spectrometer at a helium buffer-gas pressure of 0.35 +/- 0.01 Torr and at 294 +/- 3 K. The observed chemistries of Mg+* and (c-C5H5)Mg+ are dominated by sequential ligation, while that of (c-C5H5)2Mg+* is by ligand switching. The rate-coefficient measurements for sequential addition of cyanoacetylene to Mg+* indicate an extraordinary pattern in alternating chemical reactivity while multiple-collision induced dissociation experiments revealed an extraordinary stability for the Mg(HC3N)4+* cluster ion. Molecular orbital calculations with density functional theory (DFT) at the B3LYP level, Hartree-Fock (HF) and second-order Mphiller-Plesset (MP2) levels, all performed with a 6-31+G(d) basis set, have been used to calculate structures and energies for the observed Mg(HC3N)1-4(+)* cations. These calculations indicate that the path of formation of Mg(HC3N)4+* involves ligand-ligand interactions leading to two cyclic (HC3N)2 ligands which then interact to form 2,4,6,8-tetracyanosemibullvalene-Mg+ or 1,2,5,6-tetracyano-1,3,5,7-cyclooctatetraene-Mg+ cations. A case is made for the formation of similar complex organomagnesium ions in the upper atmosphere of Titan where subsequent electron-ion recombination may produce cyano derivatives of large unsaturated hydrocarbons. In contrast, circumstellar environments with their much higher relative content of free electrons are less likely to give rise to such chemistry.