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The minimum energy path for the reaction O(\(^3\)P\(_g\)) + C\(_2\)H\(_4\)(\(^1\)A\(_g\)) has been calculated by optimizing all relevant geometrical parameters along the approach of oxygen to ethene. A barrier of 4.7 kcal/mol in the \(^3\)A"( ... 9a'\(^2\)- 10a'3a") potential energy surface and an energy difference of 14.4 kcal/mol between the product and the fragments is found at the multireference-configuration interaction level. The corresponding values at the lower-level treatment CASSCF are 9 kcal/mol for the barrier and 9 kcal/mol for the depth of the potential; this shows the importance of inclusion of electron correlation. The barrier for CH\(_2\) rotation for the lowestenergy structure (asymmetric OC\(_2\)H\(_4\)) is around 5 kcal/mol. The energy gap to the first excited state \(^3\)A'( ... 9a'l0a'3a'12) is found tobe 3.6 kcal/mol in MRD-CI calculations at the ground-state minimum. Comparison with \(^3\)CH\(_2\) + C\(_2\)H\(_4\) shows that in this system the lowest-energy surface is \(^3\)A', i.e., the state which is the excited state in 0 + C\(_2\)H\(_4\). This difference in energy ordering of \(^3\)A' and \(^3\)A" states results from the fact that the p\(_x\), p\(_y\), p\(_z\) degeneracy of oxygen orbitals is lifted in \(^3\)CH\(_2\)leading to b\(_1\), b\(_2\). and a\(_1\) MOs whereby the lowest b\(_2\) (a") remains doubly occupied; as a consequence, the reaction pattem between the oxygen and \(^3\)CH\(_2\) approach is different, which is also quite apparent in the calculated charge transfer.

Large-scale multireference configuration interaction calculations in a double·t·type AO basis including polarization functions are carried out for the potential surface of the ClC\(_2\)H\(_4\9 system. The charge distribution for various extreme points of the surface is discussed. The absolute minimum is found for an asymmetric ClC2H4 structure. The symmetrical bridged nuclear conformation is also found to be stable with respect to dissociation into Cl + C\(_2\)H\(_4\)• The activation energy for rotation about the C-C axis is calculated tobe around 18 kJ/mol, which is comparable tothat for the 1,2 migration {around 26 kJ/mol). The stereochemistry is governed by the fact that addition of CI to C\(_2\)H\(_4\) (or dissociation) is a two-step reaction proceeding through a symmetrica1 intermediate. The direct addition pathway possesses a small barrier of about 8 kJ jmol.

In the present work the dimethylamino radical ( ( CH\(_3\)) \(_2\)N) and its protonated cation ( ( CH\(_3\))\(_2\)NH\(^+\)) are investigated by means of ab initio methods. The geometries of various conformations of both compounds are obtained with UMP2/6·31 G** calculations, while the hyperfine structure and its dependence on the geometry is studied using the MRD-Cl/B\(_K\) method. The two molecules are compared to study the inftuence of the protonation on geometry and hyperfine structure. The effects of the rotational barriers on the hyperfine structures of (CH\(_3\))\(_2\)N, (CH\(_3\)CH\(_2\))\(_2\)N and ( (CH\(_3\))\(_2\)CH)\(_2\)N will be discussed.

Large-acale multi-reference configuration interaction (MRD-CI) calculations in a quite flexible AO basis are employed to study the energy hypersurface for the reaction intermediates XC\(_3\)H\(_4\) with X = Cl, Br and F. Particular emphasis is therby placed on determining the equilibrium conformations, the CH\(_2\) rotation barrier and the energy surface for a possible bridging (shuttling motion (1a] of X between the two carbon centers). The absolute minimum in the potential energy surface is found in all three cases for the asymmetric ß-halo radical in general agreement with ESR data at an XCC angle of ca. 110°, a c-c separation somewhat shorter than a single bond and an approximate sp3 type hybridization (\(\alpha _2 \approx \) 135-140°). In FC\(_2\)H\(_4\) the energy difference between the minimum in the symmetric conformation and the absolute minimum is found to be more than 30 kcal so that shuttling seems impossible in agreement with experimental findings. In BrC\(_2\)H\(_4\) the difference between these two potential minima is only between 1-2 kcal, i.e., smaller than the barrier to CH\(_2\), rotation, so that· shuttling is favored, while ClC\(_2\)H\(_4\) takes an intermediate position between these extremes. The use of correlated wavefunctions is found to be quite important for such a study; the results are related to various kinetic studies of these radicals.

Large-scale multireference configuration interaction (MRD-CI) calculations in a quite flexible AO basis are employed to study the energy hypersurface for the reaction intermediate FC\(_2\)H\(_4\) • The reaction F + C\(_2\)H\(_4\) -> FC\(_2\)H\(_4\) as weil as the 1,2 migration of the fluorine atom in FC\(_2\)H\(_4\) is investigated. In addition the rotation around the CC bond in the optimum conformation is studied. The absolute minimum in the potential energy is found for the asymmetric structure but the symmetric structure is also found to be stable with respect to the dissociation, so that a shuttling of the fluorine atom is in principle possible but highly unlikely because ( l) the activation energy is high ( II 5-130 kJ fmol) and the saddle point lies only 4(}-50 kJ jmol below the dissociation Iimit of F + C\(_2\)H\(_4\) and (2) the competitive motion, i.e., rotation around the CC axis, is nearly free (I 1-17 kJ/mol).

The hyperfine structure of the two isoelectronic molecules H\(_2\)CN and H\(_2\)CO\(^+\) in their electronic ground state (X\(^2\)B\(_2\)) is studied. The influence of the atomic orbital (AO), basis sets, of the correlation treatment, and of the. equilibrium geometry on the obtained hyperfine propertles 1s - investigated. It is found that the multireference double excitation-configuration interaction (MRD-CI)/ BK treatment in which an MRD-CI wave function is corrected by a modified B\(_K\) method yields equivalent results to quadratic CI [QCISD(T)], coupled cluster single doubles [CCSD(T)), or Brueckner doubled [BD(T)]. Uncertainties in the equilibrium geometries are found to be the major source for discrepancies between theoretically and experimentally determined isotropic hyperfine coupling constants (hfccs). For the heavier centers, the calculated values of the isotropic hfccs agrees nearly perfectly with experimental values (\(\approx\) 1%-2%). The calculated values for the hydrogens are too low, but using the equilibrium structure suggested by Yamamoto and Sato [J. Chem. Phys. 96, 4157 ( 1992)], the best estimate deviates by less than 3%.

Large-scale multireference configuration interaction (MRD-CI) calculations in a flexible atomic orbital (AO) basis are employed to study the reaction of C\(_2\)H\(_4\) with CH\(_2\) in its firSt triplet and singlet state. The minimum energy path (MEP) of both reactions is calculated, and different mechanisms are discussed. To examine the possible participation of the singlet state in the overall reaction starting from the triplet channel and terminating in the singlet-state c-C\(_3\)H\(_6\), various cuts through both hypersurfaces are calculated. lt is found that favorable interconversion from the trip1et to the singlet surface can only occur at !arge separations of the two fragments of CH2 and C\(_2\)H\(_4\). Experimental data considering the vibrational motion of CH\(_2\) in connection with the relative position of both surfaces are used to obtain an estimate for the overall barrier of the reaction. The height of the barrier is about 6 kcal/mol, while the barrier of the pure triplet reaction is calculated to be 7-9 kcal/mol.

The hyperfine coupling constants for the \(^3\)Σ\(-\) ground state of the NH molecule are determined by configuration interaction calculations whereby the infl.uence of polarization functions as weil as of the configuration space on the spin polarization mechanism is analysed. The dipolar part Au(N) and Au(H) can be obtained very reliably without much computational effort (A .. (N) == -45·3 MHz and A"(H) = -62·3 MHz). The value for the isotropic contribution a1.., in the best AO basis and MRD-CI treatment is - 64·5 MHz for H and 16·6 MHz for nitrogen compared to the corresponding experimental quantities of -66 MHz and 19 MHz respectively. Their determination depends on a subtle balance of the lu, 2u and 3u shell correlation description, whereby the dominant contribution to a1..,(H) results from the 2u shell. It is shown that the often good agreement of a110 values with experiment in a small basis singledouble configuration interaction treatment results from a cancellation of two errors.

The isotropic (a\(_{iso}\)) and dipolar (A\(_{dip}\)) hyperfine coupling constants of 19F2 were obtained from MRD-CI wave functions using a variety of basis sets. In series I, increasing numbers of d functions were added to a 5s4p contracted Huzinaga!Dunning basis. In series II, the 5s3p basis set was uncontracted in several steps until 9s5p was reached, to which were added from one to three d-polarization functions. Cl parameters (selectioo threshoids and the number of reference coofiguratioos) were also varied. A study of the R dependence of aiso and Adip was perfonned. The best values obtained at R\(_e\) are 260 G for a\(_{iso}\) and 308 G for A\(_{dip}\)• compared with experimental values of about 280 G for a;10 and 320 G for A\(_{dip}\)·

Study of the hyperfine coupling constants of the moleculs NH<sub>2</sub>, NHD and ND<sub>2</sub>
(1990)

In the present paper we c:alculate tbe magnetic hyperfine couplina constants (hfcc) ai.ID and A11 of the ground states of the isotopes NH2, NHD and ND2 using truncated MR..CI methods. Differences from other theoretical methocls and shortoominp of the truncated Cl approach in calculating tlj10 are studied. Polarization effects wbich detennirae ailo. as weU as a simple model to describe the dipolar hfcc's, are discussed. All results are in. excellent aareement with experimental data. lt is shown that ab initio methods are able to obtain reliable values for otf-diaaonal values of A41 which are difficult to measure experimentaDy.

The hyperfine coupling constants (hfcc) A\(_{iso}\) and A\(_{ij}\) are calculated for the atoms of NH\(_2\) in its, two lowest-lying electronk states at various molecular geometries by means of the ab initio multireference configuration interaction .method. The vibronically averaged values of the hfccs for the K = 0 and 1 levels in \(^{14}\)N \(^1\)H\(_2\) in the energy range up to 20 000 cm\(^{-1}\) are computed. Polarization elfects which determine A\(_{iso}\) as well as a simple model to describe the dipolar hfccs are discussed. All resrilts are in excellent agreement with experimental data.

Study of the 1s and 2s shell contributions to the isotropic hyperfine coupling constant in nitrogen
(1988)

The istropic part of the hyperfine coupling constant is investigated by means of multireference configuration interaction calculations employing Gaussian basis sets. A detailed study of the 1s and 2s spin polarisation in the nitrogen atom and the NH molecule shows that the structure of the lower-energy space of the unoccupied orbitals is essential for the results. A contraction of the Gaussian basis is possible without loss of accuracy if enough flexibility is retained to describe the main features of the original space of unoccupied functions. Higher than double excitations are found to be non-negligible for the description of α\(_{iso}\).

Multi-reference configuration interaction calculations employing various orbital transformations are undertaken to obtain the isotropic hyperfine coupling constant a\(_{iso\) in nitrogen and a\(_{iso\) (H) in the CH molecule. The natural orbital (NO) basis is found to be more effective than the simple RHF-MO basis; the most obvious is a basis of spin natural orbitals (SNO). It is found that a\(_{iso\) is approached from opposite sides in the NO and 2s shell SNO basis if the CI expansion is increased. Both results are within a few percent of the full CI Iimit for the nitrogen atorn (in the given AO basis) and the experimental value for Hin the CH radical. Various features ofthe SNO are discussed.

Reliable prediction of the isotropic hyperfine coupling constant A\(_{iso}\) is still a difficult task for ab initio calculations. Strang dependence on the method employed for its ca1culation has been found. Within a CI ansatz A\(_{iso}\) is considerably affected by the excitation classes taken into account within the CI calculation. In the present work the influence of various excitation classes on A\(_{iso}\) is examined. Calculations including all single, double, triple and a large part of the quadruple excitations are performed and the individual effects of the excitation classes are studied. It is found that the surprisingly good agreement found for S-CI treatments is due to large error cancellations. The importance of higher than double excitations arises from their indirect influence on the single excitations.

We have investigated theoretically the importance of the O(\(^3\)P)+CH(a\(^4\sum^-\)) and the O(\(^3\)P)+CH(X\(^2\Pi\)) channels in the collinear chemi-ionization reaction O+CH->HCO\(^+\) +e\(^-\). We have found that both channels may lead to chemi-ionization via favorable Franck-Condon overlaps with the states ofthe ionic species.

Molecules containing multiple bonds between atoms—most often in the form of olefins—are ubiquitous in nature, commerce, and science, and as such have a huge impact on everyday life. Given their prominence, over the last few decades, frequent attempts have been made to perturb the structure and reactivity of multiply-bound species through bending and twisting. However, only modest success has been achieved in the quest to completely twist double bonds in order to homolytically cleave the associated π bond. Here, we present the isolation of double-bond-containing species based on boron, as well as their fully twisted diradical congeners, by the incorporation of attached groups with different electronic properties. The compounds comprise a structurally authenticated set of diamagnetic multiply-bound and diradical singly-bound congeners of the same class of compound.

Background: Cyclic aminals are core features of natural products, drug molecules and important synthetic intermediates. Despite their relevance, systematic investigations into their stability towards hydrolysis depending on the pH value are lacking.
Results: A set of cyclic aminals was synthesized and their stability quantified by kinetic measurements. Steric and electronic effects were investigated by choosing appropriate groups. Both molecular mechanics (MM) and density functional theory (DFT) based studies were applied to support and explain the results obtained. Rapid decomposition is observed in acidic aqueous media for all cyclic aminals which occurs as a reversible reaction. Electronic effects do not seem relevant with regard to stability, but the magnitude of the conformational energy of the ring system and pK a values of the N-3 nitrogen atom.
Conclusion: Cyclic aminals are stable compounds when not exposed to acidic media and their stability is mainly dependent on the conformational energy of the ring system. Therefore, for the preparation and work-up of these valuable synthetic intermediates and natural products, appropriate conditions have to be chosen and for application as drug molecules their sensitivity towards hydrolysis has to be taken into account.

Reliable prediction of the isotropic hyperfine coupling constant, a\(_{iso}\), is still a difficult task for ab initio calculations. Strong dependence on the method used for its calculation is found. Within a truncated multi-referencc ansatz a\(_{iso}\) is strongly affected by the size ofthe reference space and the nurober of terms in the truncated Cl expansion. In the present paperdifferent effects of the neglected Cl space are discussed. Modified B\(_K\) and A\(_K\) methods are used to estimate the contributions ofthe neglected configurations. lt can be shown that a combination of both methods is able to recover about 90-9 S% of the total error in a\(_{iso}\)· Furthermore, it was found that to obtain about 90% of the B\(_K\) correction only about I 0-20% ofthe configurations within H0 have to be corrected.

Density functional theory is applied to the calculation ofthe isotropic byperfine coupJing constants in some small molecules. Various functionals are tested. The agreement of the calculated values to experimental data and values obtained from sophisticated ab initio methods depends on the functionals used and the system under consideration. With respect to spin density calculations the functional of Lee, Yang and Parr with Becke's excbange functional (BLYP) is found to give good results for tbe heavier center of the CH and the NH molecule, while the spin densities of other molecules such as OH, H\(_2\)CN, H\(_2\)CO\(^+\), NO and O\(_2\) deviate considerably from experimental and/or other theoretical results (30%-60%). In cases where the singly occupied orbital can contribute to the isotropic hyperfine coupling constants, accurate results are obtained. The reason fortbis is analyzed.

A reliable prediction of the isotropic hyperfine coupling constant A\(_{iso}\) is still a difficult task for ab initio calculations. In previous studies, the configuration selected multireference configuration interaction method in combination with perturbation theory to correct the wave function (MRCI/ B\(_K\)) yielded accurate isotropic hyperfine coupling constants very economically. The present study gives a detailed analysis of the MRCI/ B\(_K\) method based on the X\(^2 \pi\) state of CH as a test case. Furthermore, a comparison to various other methods such as Maller-Ptesset perturbation theory and the coupled cluster approach is made. The success of the MRCI/ B\(_K\) method in predicting isotropic hyperfine coupling constants is explained in terms of the inßuence of higher than double excitations.

The hyperfine coupling constant for the nitrogen atom is evaluated by large-scale MRD-CI calculations. A detailed analysis of the charge density at the nucleus and the spin polarization in the ls and 2s shell as a function of various technical parameters is undertaken. Various (s, p) AO basis sets and the inftuence of correlation orbitals is investigated as weil as selection threshold and other properlies in CI calculations. The best value, obtained for the isotropic hyperfine coupling constant in an s, p, d basis, based on theoretical judgment of' best' quantities, is 9·9 MHz compared to 10·4509 MHz.

Dipole moments and various spectroscopic constants of some low-lying electronic states of the CaF molecule have been calculated using the multireference single· and double-excitation configuration-interaction (MRD-CI) method. The electronic structure of the highly ionic molecule in various excited states can be explained in tenns of different polarisations of the mainly Cacentered valence electron in the field of the F\(^-\) anion. Plots of natural orbitals occupied by the valence electron in the different states give a qualitative picture of the charge distribution and provide a visualisation of the different polarisations of the valence electron in the various states. Comparisons with the electrostatic polarisation model ofTörring, Ernstand Kändler (TEK model) are made. The unknown A' \(^2 \Delta\) state is predicted to lie about 21200 cm\(^{-1}\) above the ground state.

The energy difference between the three lowest-lying isomers of C\(_6\) the linear \(^3 \sum ^-\) state and the two ring forms,the benzene structure (\(^1\)A\(_{18}\)) possessing D\(_{6h}\) symmetry and a distorted cyclic form ( \(^1\)A'\(_1\), D\(_{3h}\) symmetry) have been calculated using various ab initio methods. Variational methods such as multireference configuration interaction (MR-CI) and complete active space second order perturbatiOn treatment (CASPT2) have been applied, as weil as perturbational treatments and coupled cluster calculations (CCD). The correlation of all valence shell electrons is found to be important for a balanced description of the isomers of C\(_6\) . Methods which do not account for higher-order effects appropriately proved to be unsuitable for calculating the energy difference correctly. The results from multireference configuration interaction methods show that the isomers are close in energy with the cyclic forms somewhat lower than the linear form. The ring form possessing D\(_{3h}\) symmetry (\(^1\)A'\(_1\)} is found tobe the lowest-lying structure.

The vibronically averaged values for tbe hyperfine coupling constants in the X\(^2 \sum\)-A\(^2 \Pi\) system of the ethynyl radical are computed by means of tbe ab initio metbod calculations. The results point at tbe importance of taking into account the coupling of a1l tbree electronic states in question ( I\(^2\)A', 2\(^2\)A', and 1\(^2\)A") for a reliable explanation of the available experimental findings. The mean values of the hfcc's for K = 0 and 1 levels in \(^{13}\)C\(_2\)H and \(^{13}\)C\(_2\)D in the energy range up to 6000 cm\(^{-1}\) are predicted.

The hyperfine coupling constants (isotropic hfcc and four Cartesian components of the ani~ tropic tensor) are calculated for all three atoms of C\(_2\)H in its three lowest-lying electronic states at various molecu)ar geometries by means of the ab initio configuration interaction ( MRO.CI) method. The off-diagonal electronic matrix elements involving the two species ofthe A' symmetry are also computed. A diabatic transforrnation is perforrned Jeading to simple geometrical depen· dences of the hyperline coupling constants.

Results ofan ab initio study ofthe hyperfine structure of the X\(^2\)A', A\(^2\) A" ( 1\(^2 \Pi\)) system ofthe formyl radical are presented. Special attention is paid to the analysis of the interplay between the vibronic and magnetic hyperfine etfects. The results of computations are in very good agreement with the available experimental findings. The values for the hyperfine coupling constants in lower bending Ievels of both electronic species are predicted.

Various structural possibilities for Si\(_3\)C\(_3\) clusters are investigated by ab initio calculations employing basis sets of double- and triple-zeta quality augmented by d polarization functions. Correlation effects are included by a second-order Moeller Piesset perturbation treatment. For the two lowest-lying structures higher-order correlation corrections and multi-reference effects are also included. Bonding features are investigated by two different types of population analyses to obtain insight into the nature of chemical bonding. A total of 17 stationary points were investigated, 14 of which correspond to local minima and three being transition states. The energetically lowest-lying structures are: A "pyramidlike" structure with various multicenter bonds, followed by a es symmetric isomer closely related to the ground state Si6 structure. Planar structures, favoured in small carbon clusters, lie higher in energy and are transition states. The lowest-lying triplet system is found to be the linear nonsymmetric Si - C-C-C-Si -Si structure, which is calculated to lie about 38 kcalfmole above the singlet ground state. A building-up principle based on bonding criteria is suggested for the occurence of the various structural possibilities.

Potential energy and spectroscopic constants for the X\(^2 \sum^+ _\mu\) ground state of a;, were calculated by configuration-interaction (Cl) methods, using large basis sets with polarization and diffuse functions. From these CI wavefunctions, the isotropic (a\(_{iso}\)) and dipolar (A\(_{dip}\)) components of the hyperfine coupling constant were obtained. The effects of various s, p basis sets, polarization and diffuse functions, as well as the influence of reference configurations and configuration selection thresholds were investigated. The best values obtained are 35·31 G for a\(_{iso}\) and 29·440 for A\(_{dip}\)• tobe compared with experimental values of 37 ± 1 G and 32 ± 1 G, respectively. It is shown that the contributions to a1so of the K and L shells are opposite in sign, differing by about 4 G. Upon vibrational averaging, both a\(_{iso}\) and A\(_{dip}\) move towards smaller values as v increases. An adiabatic electron affinity of 2·46eV was obtained for CL\(_2\) , and a vertical electron detachment energy of 3·71 eV for Cl;.

Vibronically averaged values for K =0 and K = 1 bending levels in the energy range between 0 and 25 000 cm\(^{-1}\) are computed for the \(^{14}\)N, H, and D atoms in NH\(_2\), NHD, and ND\(_2\) The pure ab initio electronic potentials, as well as those derived by fitting of experimentally observed band positions are employed. Effects of vibronic coupling and local perturbations of close-lying levels belanging to different electronic states are discussed.

The hyperfine structures of the isoelectronic molecules CCO. CNN, and NCN in their triplet ground states (X\(^3 \sum ^-\)) are investigated by means of ab initio methods. The infrared frequencies and geometries are detennined and compared with experiment. Configuration selected multireference configuration interaction calculations in combination with perturbation theory to correct the wave function (MRD-CI/B\(_K\)) employing extended atomic orbital (AO) basis sets yielded very accurate hyperfine properties. The theoretical values for CCO are in excellent agreement with the experimental values determined by Smith and Weltner [J. Chem. Phys. 62,4592 (1975)]. For CNN, the first assignment of Smith and Weltner for the two nitrogen atoms has to be changed. A qualitative discussion of the electronic structure discloses no simple relation between the structure of the singly occupied orbitals and the measured hyperfine coupling constants. Vibrational effects were found to be of little importance.

A comparative ab initio study of the Si\(_2\)C\(_4\), Si\(_3\)C\(_3\), Si\(_4\)C\(_2\) clusters
(1994)

Various structural possibilities for the Si\(_2\)C\(_4\) and Si\(_4\)C\(_2\) clusters are investigated by employing a basis set of triple-zeta plus polarization quality; electron correlation is generally accounted for by second-order M0ller-Plesset and, in certain instances, by higher-order perturbation (CASPT2) approaches. The building-up principle recently suggested from an analysis of Si\(_3\)C\(_3\) clusters is found to be fully operative for Si\(_2\)C\(_4\) and Si\(_4\)C\(_2\) clusters. A comparison of the structure and stability of various geometrical arrangements in the series C\(_6\) , Si\(_2\)C\(_4\) , Si\(_3\)C\(_3\) , Si\(_4\)C\(_2\), and Si\(_6\) shows that linear and planar structures become rapidly less stable if carbons are replaced by silicons and that the three-dimensional bipyramidal forms become less favorable as soon as silicons are exchanged by carbons in the parent Si\(_6\) structure. The effects can be rationalized in qualitative terms based on differences in silicon and carbon bonding.