Localized molecular orbital studies in momentum space. II. Correspondence between coordinate and momentum space properties of various electron pairs

The momentum space properties of the ten-electron systems Ne, HF, H₂O, NH₃ and CH₄ as well as those of CH₃CH₃, CH₃NH₂, CH₃OH and FCH₂OH were investigated using localized molecular orbitals (LMO) obtained from ab initio self-consistent-field (SCF) wavefunctions constructed from double zeta quality gaussain basis sets.Compton profiles of various LMO electron pairs (CC, CN, CO, CF; CH, NH, OH, FH bond pairs and C, N, O, F lone pairs) are tabulated. In order to understand the correspondence between the momentum and the coordinate space properties of those electron pairs, the concept of the size and the shape of an LMO electron pair charge distribution has been utilized. The use of the intermediate expectation values of pⁿ is introduced for the purpose of interpreting the momentum space properties.The dependence of molecular property partitioning on different localization schemes and on different basis sets is also studied by using the H₂O profile as an example.     

Ab-Initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H₃C? NO₂ bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H₃C? NO₂ bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H₃C? NO₂ bond dissociation energies.     

Localized molecular orbitals for aromatic molecules

Localized molecular orbitals are calculated using the method of Boys for the aromatic molecules C₆H₆, C₆H₅X and the p-, m-, and o-forms of C₆H₄XY, where X,Y = CN,OH,F. The calculations are performed both with and without the constraint of σ, π-separation in the localization. The localized π-orbitals are multicenter bonds. If the σ- and π-orbitals are localized together, two different structures are found, Kekulé-type structures and structures with a set of six two center and a set of three three center bonds. The C-X bond turns out to be a single bond if X = CN and a double bond, if X = OH or F.     

Bildung siliciumorganischer Verbindungen. LXI. Die Kristall- und MolekülStruktur des 1,1,3,3,5,5,7,7-Octamethyl-1,3,5,7-tetrasila-cyclooctans Si4C12H32

Formation of Organosilicon Compounds. LXI. Crystal and Molecular Structure of 1.1.3.3.5.5.7.7-Octamethyl-1.3.5.7-tetrasila-cyclooctane Si₄C₁₂H₃₂ Octamethyl-tetrasila-cyclooctan Si₄C₁₂H₃₂ crystallizes in the monoclinic space group C2 with a = 17.807, b = 6.121, c = 10.856 Å, β = 126.09° und 2 molecules in the unit cell. The molecule has a C₂-conformation which deviates slightly from C_2v symmetry. The mean Si? C bond length is 1.879 ± 0.011 Å. The mean Si? CH₂ bond length is greater than the Si? CH₃ bond length (1.897(15) Å and 1.861(10) Å respectively).     

A chain of π‐stacked molecules in 4‐(2‐chlorophenyl)pyrrolo[1,2‐a]quinoxaline and a hydrogen‐bonded sheet in (4RS)‐4‐(1,3‐1,3‐benzodioxol‐6‐yl)‐4,5‐dihydropyrrolo[1,2‐a]quinoxaline

In the molecule of 4‐(2‐chlorophenyl)pyrrolo[1,2‐a]quinoxaline, C₁₇H₁₁ClN₂, (I), the bond lengths are consistent with electron delocalization in the two outer rings of the fused tricyclic system, with a localized double bond in the central ring. The molecules of (I) are linked into chains by a π–π stacking interaction. In (4RS)‐4‐(1,3‐benzodioxol‐6‐yl)‐4,5‐dihydropyrrolo[1,2‐a]quinoxaline, C₁₈H₁₄N₂O₂, (II), the central ring of the fused tricyclic system adopts a conformation intermediate between screw‐boat and half‐chair forms. A combination of N—H...O and C—H...π(arene) hydrogen bonds links the molecules of (II) into a sheet. Comparisons are made with related compounds.     

Seeking new metalloligands: Synthesis and reactivity of palladacycles with pyridine and pyrimidine rings

Treatment of the Schiff base ligands 4-(NC₅H₄)C₆H₄C(H)N[2′-(OH)C₆H₄] (a), 3,5-(N₂C₄H₃)C₆H₄C(H)N[2′-(OH)-C₆H₄] (b) and 3,5-(N₂C₄H₃)C₆H₄C(H) N[2′-(OH)-5′-^tBuC₆H₃] (c) with palladium (II) acetate in toluene gave the poly-nuclear cyclometallated complexes [Pd{4-(NC₅H₄)C₆H₃C(H)N[2′-(O)C₆H₄]}]₄ (1a), [Pd{3,5-(N₂C₄H₃)C₆H₃C(H)N[2′-(O)-C₆H₄]}]₄ (1b) and [Pd{3,5-(N₂C₄H₃)C₆H₃C(H)N[2′-(O)-5′-^tBuC₆H₃]}]₄ (1c) respectively, as air stable solids, with the ligand acting as a terdentate [C,N,O] moiety after deprotonation of the –OH group. Reaction of the cyclometallated complexes with triphenylphosphine gave the mononuclear species [Pd{4-(NC₅H₄)C₆H₃C(H) N[2′-(O)C₆H₄]}(PPh₃)], (2a), [Pd{3,5-(N₂C₄H₃)C₆H₃C(H) N[2′-(O)C₆H₄]}(PPh₃)], (2b) and [Pd{3,5-(N₂C₄H₃)C₆H₃C(H)N[2′-(O)-5′-^tBuC₆H₃)}(PPh₃)], (2c) in which the polynuclear structure has been cleaved and the coordination of the ligand has not changed [C,N,O]. When the cyclometallated complexes 1b and 1c were treated with the diphosphines Ph₂P(CH₂)₄PPh₂ (dppb), Ph₂PC₅H₄FeC₅H₄PPh₂ (dppf) and Ph₂P(CH₂)₂PPh₂ (t-dppe) in a 1:2 molar ratio the dinuclear cyclometallated complexes [{Pd[3,5-(N₂C₄H₃)C₆H₃C(H)N{2′-(O)C₆H₄}]}₂(μ-Ph₂P(CH₂)₄PPh₂)], (3b), [{Pd[3,5-(N₂C₄H₃)C₆H₃C(H) N{2′-(O)-5′-^tBuC₆H₃}]}₂(μ-Ph₂P(CH₂)₄PPh₂)], (3c), [{Pd[3,5-(N₂C₄H₃)C₆H₃C(H)N{2′-(O)C₆H₄}]}₂(μ-Ph₂P(η⁵-C₅H₄)Fe(η⁵-C₅H₄)PPh₂)], (4b), [{Pd[3,5-(N₂C₄H₃)C₆H₃C(H) N{2′-(O)-5′-^tBuC₆H₃}]}₂(μ-Ph₂P(η⁵C₅H₄)Fe(η⁵C₅H₄)P-Ph₂)], (4c) and [{Pd[3,5-(N₂C₄H₃)C₆H₃C(H)N{2′-(O)-5′-^tBuC₆H₃}]}₂(μ-Ph₂P(CHCH)PPh₂)], (5c) were obtained as air stable solids.     

DFT study on second-order nonlinear optical properties of the derivatives of 7-vertex cobalt–carborane metallocenyl

Density functional theory (DFT) B3LYP method was employed to calculate electron properties and the second-order nonlinear optical (NLO) responses of the derivatives which were formed by (C₅H₅)Co(C₂B₄H₆) and CHCHC₆H₄NO₂, CHCHC₆H₄NH₂. The results show: when H atom of (C₅H₅)Co(C₂B₄H₆) is substituted by CHCHC₆H₄NO₂, the β_tot values of isomers are all slightly smaller than that of ferrocene (Fc) derivative (FcCHCHC₆H₄NO₂). However, when H atom of (C₅H₅)Co(C₂B₄H₆) is substituted by CHCHC₆H₄NH₂, the β_tot values of isomers are close to that of ferrocene (Fc) derivative (FcCHCHC₆H₄NH₂). It indicates that (C₅H₅)Co(C₂B₄H₆) can be either a donator or an acceptor.     

Can a Single Molecule of Water be Completely Isolated Within the Subnano‐Space Inside the Fullerene C60 Cage? A Quantum Chemical Prospective

Based on an experimental observation, it has been controversially suggested in a study (Kurotobi et al., Science 2011 , 33, 613) that a single molecule of water can completely be localized within the subnano‐space inside the fullerene C₆₀ cage and, that neither the H atoms nor the O lone‐pairs are linked, either via hydrogen bonding or through dative bonding, with the interior C‐framework of the C₆₀ cage. To resolve the controversy, electronic structure calculations were performed by using the density functional theory, together with the quantum theory of atoms in molecules, the natural population and bond orbital analyses, and the results were analyzed by using varieties of recommended diagnostics often used to interpret noncovalent interactions. The present results reveal that the mechanically entrapped H₂O molecule is not electronically innocent of the presence of the cage; each H atom of H₂O is weakly O? H???C₆₀ bonded, whereas the O lone‐pairs are O???C₆₀ bonded regardless of the conformations investigated. Exploration of various featured properties suggests that H₂O@C₆₀ may be regarded as a unique system composed of both inter‐ and intramolecular interactions.     

Diaquatetrakis(tert‐butyl isocyanide)cobalt(II) bis(perchlorate): an example of cobalt(II) coordinated by only four alkyl isocyanide ligands

The title compound, [Co(C₅H₉N)₄(H₂O)₂](ClO₄)₂, crystallizes in the monoclinic space group C2/m. The cation has space‐group‐imposed 2/m symmetry, while the perchlorate ion is disordered about a mirror plane. The two slightly non‐equivalent Co—C bonds [1.900 (3) and 1.911 (3) Å] form a rectangular plane, with a C—Co—C bond angle of 86.83 (11)°, and the linear O—Co—O C₂ axis is perpendicular to this plane. The C[triple‐bond]N bond lengths are 1.141 (4) Å and the Co—C[triple‐bond]N and C[triple‐bond]N—C angles average 175.5 (4)°. The perchlorate counter‐ions are hydrogen bonded to the water molecules. The title compound is the first example of four alkyl isocyanide ligands coordinating Co^II upon initial reaction of Co(ClO₄)₂·6H₂O/EtOH with alkyl isocyanide. In all other known examples, five alkyl isocyanide molecules are coordinated, as in [(RNC)₅Co—Co(CNR)₅](ClO₄)₄ (R = Me, Et, CHMe₂, CH₂Ph, C₄H₉‐n or C₆H₁₁) or [Co(CNC₈H₁₇‐t)₅](ClO₄)₂. This complex, therefore, is unique and somewhat unexpected.     

Four related diethyl [(arylamino)(4‐ethynylphenyl)methyl]phosphonates

Crystal structures are reported for four related diethyl [(arylamino)(4‐ethynylphenyl)lmethyl]phosphonate derivatives, namely diethyl [(4‐bromoanilino)(4‐ethynylphenyl)methyl]phosphonate, C₁₉H₂₁BrNO₃P, (I), diethyl ((4‐chloro‐2‐methylanilino){4‐[2‐(trimethylsilyl)ethynyl]phenyl}methyl)phosphonate, C₂₃H₃₁ClNO₃PSi, (II), diethyl ((4‐fluoroanilino){4‐[2‐(trimethylsilyl)ethynyl]phenyl}methyl)phosphonate, C₂₂H₂₉FNO₃PSi, (III), and diethyl [(4‐ethynylphenyl)(naphthalen‐2‐ylamino)methyl]phosphonate, C₂₃H₂₄NO₃P, (IV). The conformation of the anilinobenzyl group is very similar in all four compounds. The P—C bond has an approximately staggered conformation, with the aniline and ethynylphenyl groups in gauche positions with respect to the P=O double bond. The two six‐membered rings are almost perpendicular. The sums of the valence angles about the N atoms vary from 344 (2) to 351 (2)°. In the crystal structures, molecules of (I), (III) and (IV) are arranged as centrosymmetric or pseudocentrosymmetric dimers connected by two N—H...O=P hydrogen bonds. The molecules of (II) are arranged as centrosymmetric dimers connected by C_methyl—H...O=P hydrogen bonds. The N—H bond of (II) is not involved in hydrogen bonding.     

Analysis of bonding properties in molecular ground and excited states by a Cohen-type bond order

We propose a Cohen-type bond order analysis in terms of orthogonalized atomic basis functions which can be used to analyze NDO wave functions of large organic and metal–organic molecules. It is shown that for small molecules the results gained with this method are in excellent agreement with the same analysis based on ab initio STO -3G wavefunctions. For large planar aromatic systems these all-valence electron bond orders are found to be a consistent generalization of the π-bond order. A simple relation between these bond orders and the corresponding covalent bond energies is established. The method can be easily extended to study excited state multiconfiguration wave functions. We present calculations for C₂H₂, C₂H₄, C₂H₆, and Mn₂(CO)₁₀. The results indicate that the method can be used to discuss the photochemistry of organic and metal–organic compounds.     

Looking at orbitals in the laboratory: The experimental investigation of molecular wavefunctions and binding energies by electron momentum spectroscopy

The experimental technique of electron momentum spectroscopy (EMS ) (i.e., binary (e, 2e) spectroscopy) is discussed together with typical examples of its applications over the past decade in the area of experimental quantum chemistry. Results interpreted within the framework of the plane wave impulse and the target Hartree—Fock approximations provide direct measurements of, spherically averaged, orbital electron momentum distributions. Results for a variety of atoms and small molecules are compared with calculations using a range of Fourier transformed SCF position space wavefunctions of varying sophistication. Measured momentum distributions (MD ) provide a “direct” view of orbitals. In addition to offering a sensitive experimental diagnostic for semiempirical molecular wavefunctions, the MD's provide a chemically significant, additional experimental constraint to the usual variational optimization of wavefunctions. The measured MD's clearly reflect well known characteristics of various chemical and physical properties. It appears that EMS and momentum space chemistry offer the promise of supplementary perspectives and new vistas in quantum chemistry, as suggested by Coulson more than 40 years ago. Binding energy spectra in the inner valence region reveal, in many cases, a major breakdown of the simple MO model for ionization in accord with the predictions of many-body calculations. Results are considered for atomic targets, including H and the noble gases. The measured momentum distribution for H₂ is also compared with results from Compton scattering. Results for H₂ and H are combined to provide a direct experimental assessment of the bond density in H₂, which is compared with calculations. The behavior of the outer valence MD ''s for small row two and row three hydride molecules such as H₂O and H₂S, NH₃, HF, and HCl are consistent with well known differences in chemical and physical behavior such as ligand-donor activity and hydrogen bonding. MD measurements for the outermost valence orbitals of HF, H₂O and NH₃ show significant differences from those calculated using even very high-quality wavefunctions. Measurements of MD's for outer σ_g orbitals of small polyatomic molecules such as CO₂, COS, CS₂, and CF₄ show clear evidence of mixed s and p character. It is apparent that EMS is a sensitive probe of details of electronic structure and electron motion in atoms and molecules.     

Higher hydrogen uptake capacity of C2H4Ti+ than C2H4Ti: a quantum chemical study

Using density functionals theory, we show that gravimetric hydrogen uptake of C₂H₄Ti complex and its cation, C₂H₄Ti⁺, differ by about 2 wt%. Six and five hydrogen molecules are found to be adsorbed on C₂H₄Ti⁺ and C₂H₄Ti complexes thereby showing a hydrogen-uptake capacity of 13.74 and 11.72 wt%, respectively. All hydrogen molecules are adsorbed in molecular form on C₂H₄Ti⁺ ion with an increase in metal bond strength, whereas in some cases, the hydrogen molecules are found to be dissociated on C₂H₄Ti neutral complex. The uptake capacity of neutral C₂H₄Ti complex shown in this work is in excellent agreement with that reported experimentally, Phillips and Shivaram (Phys Rev Lett 100:105505, 2008). The H₂ adsorption energy and its dependence on exchange and correlation functions in density functionals method were illustrated. Even after the adsorption of maximum number of hydrogen molecules on C₂H₄Ti and C₂H₄Ti⁺ complexes, Ti and Ti⁺ remain strongly bound to C₂H₄ substrate.     

(5Z)‐4‐Amino‐2‐(4‐hydroxyphenyl)‐1H‐imidazol‐5(2H)‐one oxime 3‐oxide

The title molecule, C₉H₁₀N₄O₃, consists of benzene and imidazole rings which are almost perpendicular to each other. A hydroxyimino group is directly linked to the imidazole ring with a double C=N bond, which is the first example in this type of compound. The double bond may be a good location for the initiation of various reactions with a wide range of potential applications. In the crystal structure, there are π–π interactions between molecules related by a centre of symmetry, with the imidazole and benzene rings almost completely overlapped. The molecules are hydrogen bonded in each direction and form a three‐dimensional hydrogen‐bond network.     

Dibenzylammonium hydrogen maleate and a redetermination at 120 K of bis(dibenzylamino)methane

In dibenzylammonium hydrogen maleate [or dibenzylammonium (2Z)‐3‐carboxyprop‐2‐enoate], C₁₄H₁₆N⁺·C₄H₃O₄⁻, (I), the anion contains a fairly short and nearly linear O—H...O hydrogen bond, with an O...·O distance of 2.4603 (16) Å, but with the H atom clearly offset from the mid‐point of the O...O vector. The counter‐ions in (I) are linked by two N—H...O hydrogen bonds to form C₂²(6) chains and these chains are weakly linked into sheets by a C—H...O hydrogen bond. Bis(dibenzylamino)methane, C₂₉H₃₀N₂, (II), crystallizes with two independent molecules lying across twofold rotation axes in the space group C2/c, and the molecules are conformationally chiral; there are no direction‐specific intermolecular interactions in the crystal structure of (II).     

Ab initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. III. Me2N?NO2 decomposition of dimethylnitramine in a large crystalline environment

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations, based on localized/local orbitals and an “effective” CI Hamiltonian, for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystalline or other solid environment. Our technique begins with an explicit quantum chemical SCF calculation for a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized, and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general in that the space treated explicitly, as well as the surrounding space, may contain voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. Dimethylnitramine is the smallest prototype of the energetic R₂N—NO₂ nitramines, such as the 6-member ring RDX or the 8-member ring HMX. Decomposition of energetic compounds is initiated in the solid by a breaking of the target bond. Thus, it is crucial to know the difference in energy between breaking a bond in an isolated energetic molecule versus in the molecule in a solid. In the present study, we have carried out MRD-CI calculations for the Me₂N—NO₂ dissociation of dimethylnitramine in a dimethylnitramine crystal. The cases we investigated were one dimethylnitramine molecule (surrounded by 53 and 685 neighboring dimethylnitramine molecules represented by multipoles), three dimethylnitramine molecules, and three dimethylnitramine molecules (surrounded by 683 neighbors). All multipoles were cumulative atomic multipoles up through quadrupoles. The MRD-CI calculations on dimethylnitramine required large numbers of reference configurations from which were allowed all single and double excitations.     

Heterobimetallic aluminium and zinc complex with N-arylanilido-imine ligand: Synthesis, structure and catalytic property for ring-opening polymerization of ε-caprolactone

Treatment of a N-arylanilido-imine ligand [ortho-C₆H₄(NHAr)CHN]₂CH₂CH₂ (Ar = 2,6-Me₂C₆H₃) (LH₂) with one equiv. of AlMe₃ affords a monometallic complex [C₆H₄(NHAr)–CHN)]CH₂CH₂(C₆H₄(NAr)CHNAlMe₂) (1). The monometallic complex 1 reacts with one equiv. of ZnEt₂ to give a heterobimetallic complex [C₆H₄(NAr)–CHNZnEt]CH₂CH₂[C₆H₄(NAr)–CHNAlMe₂] (2). Both complexes were characterized by ¹H and ¹³C NMR spectroscopy and elemental analyses, and the molecular structures of 1 and 2 were determined by X-ray diffraction analysis. The complexes 1 and 2 both are efficient catalysts for ring-opening polymerization of ε-caprolactone in the presence of benzyl alcohol yielding polymers with narrow polydispersity values and complex 2 initiates the polymerization in a controllable manner.     

Bildung siliciumorganischer Verbindungen. 94. Die Kristallstruktur des Hexaphenyltrisilacyclohexans Si3C39H36

Formation of Organosilicon Compounds. 94. Crystal Structure of Hexaphenyltrisilacyclohexane Si₃C₃₉H₃₆ 1.1.3.3.5.5-Hexaphenyl-1.3.5-trisilacyclohexane crystallizes monoclinically in the space group P2₁/n (No. 14) with a = 1718.3 pm, b = 1769.2 pm, c = 1091.4 pm, β = 90.72° and Z = 4 molecules per unit cell. The trisilacyclohexane sceleton is present in a flattened twist boat conformation with mean bond angles of 110.0° at the Si atoms and 117.9° at the C atoms, respectively. The mean bond lengths are d(Si? C) = 187.1 pm in the six membered ring and 187.9 pm to the substituents.     

Calculation of the magnetic properties of C-H bonds and their contribution to the magnetic susceptibility of saturated hydrocarbons

The magnetic susceptibility tensors of the C-H bonds in the CH₄, C₂H₆, C₃H₈, n-C₅H₁₂, iso-C₅H₁₂, and neo-C₅H₁₂ molecules have been calculated by the method of varying the vector potential with the use of a multiparameteric gradient-transformation function, which was constructed in the form of a polynomial in spherical coordinates and takes into account the electron correlation. The influence of the electron correlation on the magnetic properties of C-H bonds is greater than that in homonuclear molecules (H₂) and bonds (C-C) and increases strongly with enhancement of the electron correlation in the wave function not perturbed by an external magnetic field. In contrast to the previously established identity of the magnetic properties of C-C bonds, the magnetic properties of C-H bonds depend both on the structure and geometry of the molecule as a whole and on the location of the bond itself in the molecule. The values of the mean susceptibility of the molecules considered calculated in the additive approximation are in good agreement with the experimental values.