3,17‐Dioxoandrost‐4‐en‐4‐yl acetate

The title compound, C₂₁H₂₈O₄, has a 4‐acetoxy substituent positioned on the steroid α face. The six‐membered ring A assumes a conformation intermediate between 1α,2β‐half chair and 1α‐sofa. A long Csp³—Csp³ bond is observed in ring B and reproduced in quantum‐mechanical ab initio calculations of the isolated molecule using a molecular‐orbital Hartree–Fock method. Cohesion of the crystal can be attributed to van der Waals interactions and weak C—H...O hydrogen bonds.     

2,2,4,4‐Tetra‐tert‐butyl‐1,3,5,2,4‐benzotrioxadisilepine‐7‐carbaldehyde

The mol­ecule of the title compound, C₂₃H₄₀O₄Si₂, features an approximate non‐crystallographic C₂ symmetry axis. The aldehyde group is disordered over two positions with similar occupancies. The geometry of the isolated mol­ecule was studied by ab initio quantum mechanical calculations employing a mol­ecular orbital Hartree–Fock method. The calculations reproduce well the equilibrium geometry but slightly overestimate the value of the Si—O bond lengths of the trioxadisilepine ring.     

3‐Hydro­xy­benz­aldehyde

The title compound, C₇H₆O₂, forms infinite chains where the mol­ecules are hydrogen bonded via the hydroxyl and aldehyde groups, with an O?O distance of 2.719 (3) Å. Interchain interactions are weak. The geometry of the ring differs from the ideal form due to the effect of the substituents. Abinitio (Hartree–Fock self‐consistent field–molecular orbital and density functional theory) calculations for the free mol­ecule reproduce well the observed small distortions of the ring. In the crystal, the geometry deviates from the ideal C_s symmetry of the free mol­ecule, as given by the ab initio calculations. The aldehyde and hydroxyl groups are twisted around the single bonds which join them to the ring as a result of the intermolecular hydrogen‐bond interactions. These are also responsible for an elongation of the hydroxy C—OH bond compared with that calculated for the free mol­ecule.     

5β,6β‐Epoxy‐17‐oxoandrostan‐3β‐yl acetate and 5β,6β‐epoxy‐20‐oxopregnan‐3β‐yl acetate

In the title compounds, C₂₁H₃₀O₄, (I), and C₂₃H₃₄O₄, (II), respectively, which are valuable intermediates in the synthesis of important steroid derivatives, rings A and B are cis‐(5β,10β)‐fused. The two molecules have similar conformations of rings A, B and C. The presence of the 5β,6β‐epoxide group induces a significant twist of the steroid nucleus and a strong flattening of the B ring. The different C17 substituents result in different conformations for ring D. Cohesion of the molecular packing is achieved in both compounds only by weak intermolecular interactions. The geometries of the molecules in the crystalline environment are compared with those of the free molecules as given by ab initio Roothan Hartree–Fock calculations. We show in this work that quantum mechanical ab initio methods reproduce well the details of the conformation of these molecules, including a large twist of the steroid nucleus. The calculated twist values are comparable, but are larger than the observed values, indicating a possible small effect of the crystal packing on the twist angles.     

6β‐Hydroxy‐5β‐methyl‐20‐oxo‐19‐norpregn‐9(10)‐en‐3β‐yl acetate

In the title compound, C₂₃H₃₄O₄, which is an intermediate in the synthesis of pregnane derivatives with a modified skeleton that show potent abortion‐inducing activity, the conformation of ring B is close to half‐chair due to the presence of both the C=C double bond and the axial 5β‐methyl group. Rings A and C have conformations close to chair, while ring D has a twisted conformation around the bridgehead C—C bond. Molecules are hydrogen bonded via the hydroxyl and acetoxy groups into infinite chains. Quantum‐mechanical ab initio Roothan Hartree–Fock calculations show that crystal packing might be responsible for the low values of the angles between rings A and B, and between ring A and rings C and D, as well as for a different steric position of the methyl ketone side chain compared to the geometry of the free molecule.     

1H‐Indazole and 2H‐indazole derivatives of androsta‐5,16‐dien‐3β‐ol

The title compounds, 17‐(1H‐indazol‐1‐yl)androsta‐5,16‐dien‐3β‐ol, (I), and 17‐(2H‐indazol‐2‐yl)androsta‐5,16‐dien‐3β‐ol, (II), both C₂₆H₃₂N₂O, have an indazole substituent at the C17 position. The six‐membered B ring of each compound assumes a half‐chair conformation. A twist of the steroid skeleton is observed and reproduced in quantum‐mechanical ab initio calculations of the isolated molecule using a molecular orbital Hartree–Fock method. In the 1H‐indazole derivative, (I), the molecules are joined in a head‐to‐head fashion via O—H...O hydrogen bonds, forming chains along the a axis. In the 2H‐indazole derivative, (II), the molecules are joined in a head‐to‐tail fashion with one of the N atoms of the indazole ring system acting as the acceptor. The hydrogen‐bond pattern consists of zigzag chains running along the b axis. Substituted steroids have proven to be effective in inhibiting androgen biosynthesis through coordination of the Fe atoms of some enzymes, and this study shows that indazole‐substituted steroids adopt twisted conformations that restrict their intermolecular interactions.     

Ab initio quantum chemical calculations of a cluster C8H12

Using unrestricted Hartree–Fock–Roothaan approximation and density functional theory on 6‐31G* basis, ab initio calculation cluster C₈H₁₂ has been carried out. It was shown as a result of calculations that a ground state for the conformation given is a septet state. This cluster can be used for investigation of the kinematic mechanism of magnetic exchange and magnetic ordering in polyradicals. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

6‐[(4‐Fluorophenyl)(1H‐imidazol‐1‐yl)methyl]‐1,3‐benzodioxol‐5‐ol and 6‐[(4‐methoxyphenyl)(1H‐imidazol‐1‐yl)methyl]‐1,3‐benzodioxol‐5‐ol

The title compounds, C₁₇H₁₃FN₂O₃ and C₁₈H₁₆N₂O₄, are new potent aromatase inhibitors combining the common features of second‐ and third‐generation nonsteroid anti‐aromatase compounds. The molecules have a propeller shape, with dihedral angles between adjacent planes in the range 49–86°. A quantum mechanical ab initio Roothaan–Hartree–Fock calculation for the isolated molecules shows values for these angles close to the ideal value of 90°. Docking studies of the molecules in the aromatase substrate show that their strong inhibitor potency can be attributed to molecular flexibility, hydrophobic interactions, heme Fe coordination and hydrogen bonding.     

2‐Bromo‐5‐hydroxy­benz­aldehyde

The mol­ecules of the title compound, C₇H₅BrO₂, form zigzag chains running along the b axis and are stacked in layers perpendicular to the a axis. Intermolecular bonding occurs through hydrogen bonds linking the hydroxyl and carbonyl groups, with an O?O distance of 2.804 (4) Å. The Br atom deviates significantly from the plane of the ring and the aldehyde group is twisted by 7.1 (5)° around the Csp²—C_aryl bond. The geometry of the mol­ecule in the crystal is compared to that given by ab initio quantum mechanical calculations for the isolated mol­ecule, using a molecular orbital Hartree–Fock method and density functional theory.     

Conformation of cationic N,N‐di­methyl­glycine in di­methyl­glycinium tri­fluoro­acetate

In the title compound, C₄H₁₀NO₂⁺·C₂F₃O₂^?, the main N—C—COOH skeleton of the protonated amino acid is nearly planar. The C=O/C—N and C=O/O—H bonds are syn and the two methyl groups are gauche to the methyl­ene H atoms. The conformation of the cation in the crystal is compared to that given by ab initio calculations (Hartree–Fock, self‐consistent field molecular‐orbital theory). The tri­fluoro­acetate anion has the typical staggered conformation with usual bond distances and angles. The cation and anion form dimers through a strong O—H?O hydrogen bond which are further interconnected in infinite zigzag chains running parallel to the a axis by N—H?O bonds. Weaker C—H?O interactions involving the methyl groups and the carboxy O atoms of the cation occur between the chains.     

Interaction between polymers: Dispersion energy of two infinite linear chains

Using the newly developed discrete variant of the k · p perturbation theory for linear chains an expression is derived for the dispersion interaction between two infinite chains valid for both insulating and metallic polymers. It is shown that the formally divergent dispersion energy is also finite for metallic systems, but it may be considerably enhanced in polymers with partly filled bands as compared with insulting ones. The accuracy of the proposed k · p expansion is investigated on model chains through comparisons with direct ab initio Hartree–Fock crystal orbital calculations. Applying second order perturbation theory an explicit formula in terms of band parameters is given for the numerical calculation of the dispersion energy.     

Multiplicity,instability, and SCF convergence problems in Hartree–Fock solutions

We present a study of the instability and convergence of Hartree–Fock (HF) ab initio solutions for the diatomic systems H₂, LiH, CH, C₂, and N₂. In our study, we consider real molecular orbitals (MOs) and analyze the classes of single‐determinant functions associated to Hartree–Fock–Roothaan (HFR) and Hartree–Fock–Pople–Nesbet (HFPN) equations. To determine the multiple HF solutions, we used either an SCF iterative procedure with aufbau and non‐aufbau ordering rules or the algebraic method (AM). Stability conditions were determined using TICS and ASDW stability matrices, derived from the maximum and minimum method of functions (MMF). We examined the relationship between pure SCF convergence criterion with the aufbau ordering rule, and the classification of the HF solution as an extremum point in its respective class of functions. Our results show that (i) in a pure converged SCF calculation, with the aufbau ordering rule, the solutions are not necessarily classified as a minimum of the HF functional with respect to the TICS or ASDW classes of solutions, and (ii) for all studied systems, we obtained local minimum points associated only with the aufbau rule and the solutions of lower energies. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 600–610, 2000     

Ab initio study of the π–π interactions between CO2 and benzene,pyridine, and pyrrole

The π–π interactions between CO₂ and three aromatic molecules, namely benzene (C₆H₆), pyridine (C₅H₅N), and pyrrole (C₄H₅N), which represent common functional groups in metal‐organic/zeoliticimidazolate framework materials, were characterized using high‐level ab initio methods. The coupled‐cluster with single and double excitations and perturbative treatment of triple excitations (CCSD(T)) method with a complete basis set (CBS) was used to calibrate Hartree–Fock, density functional theory, and second‐order M?ller–Plesset (MP2) with resolution of the identity approximation calculations. Results at the MP2/def2‐QZVPP level showed the smallest deviations (only about 1 kJ/mol) compared with those at the CCSD(T)/CBS level of theory. The strength of π–π binding energies (BEs) followed the order C₄H₅N > C₆H₆ ～ C₅H₅N and was roughly correlated with the aromaticity and the charge transfer between CO₂ and aromatic molecule in clusters. Compared with hydrogen‐bond or electron donor–acceptor interactions observed during BE calculations at the MP2/def2‐QZVPP level of theory, π–π interactions significantly contribute to the total interactions between CO₂ and aromatic molecules. © 2013 Wiley Periodicals, Inc.     

Ethyl 3,5‐dimethyl‐4‐phenyl‐1H‐pyrrole‐2‐carboxylate

In the title compound, C₁₅H₁₇NO₂, the ethoxy­carbonyl group is anti with respect to the pyrrole N atom. The angle between the planes of the phenyl and pyrrole rings is 48.26 (9)°. The mol­ecules are joined into dimeric units by a strong hydrogen bonds between pyrrole N—H groups and carbonyl O atoms. The geometry of the isolated mol­ecule was studied by ab initio quantum mechanical calculations, employing both molecular orbital Hartree–Fock (MO–HF) and density functional theory (DFT) methods. The minimum energy was achieved for a conformation where the angle between the planes of the phenyl and pyrrole rings is larger, and that between the ethoxy­carbonyl and pyrrole planes is smaller than in the solid‐state mol­ecule.     

Evaluation of the electron momentum density of crystalline systems from ab initio linear combination of atomic orbitals calculations

Alternative techniques are presented for the evaluation of the electron momentum density (EMD) of crystalline systems from ab initio linear combination of atomic‐orbitals calculations performed in the frame of one‐electron self‐consistent‐field Hamiltonians. Their respective merits and drawbacks are analyzed with reference to two periodic systems with very different electronic features: the fully covalent crystalline silicon and the ionic lithium fluoride. Beyond one‐electron Hamiltonians, a post‐Hartree–Fock correction to the EMD of crystalline materials is also illustrated in the case of lithium fluoride. © 2012 Wiley Periodicals, Inc.     

3‐Amino‐1,2,4‐triazine

In the crystal structure of 3‐amino‐1,2,4‐triazine, C₃H₄N₄, the mol­ecules form hydrogen‐bonded chains that are almost parallel to the b axis (3.2°), and which are inclined to the a and c axes by ～21 and ～69°, respectively. The distortion of the 1,2,4‐triazine ring in the crystal is compared with gas‐phase ab initio molecular‐orbital calculations.     

Bis­(melaminium) dl‐malate tetrahydrate

The crystal structure of the title melaminium salt, bis(2,4,6‐tri­amino‐1,3,5‐triazin‐1‐ium) dl ‐malate tetrahydrate, 2C₃H₇N₆⁺·C₄H₄O₅²⁻·4H₂O, consists of singly protonated melaminium residues, dl ‐malate dianions and water mol­ecules. The melaminium residues are connected into chains by four N—H⃛N hydrogen bonds, and these chains form a stacking structure along the c axis. The dl ‐malate dianions form hydrogen‐bonded chains and, together with hydrogen‐bonded water mol­ecules, form a layer parallel to the (100) plane. The conformation of the malate ion is compared with an ab initio molecular‐orbital calculation. The oppositely charged moieties, i.e. the stacks of melaminium chains and hydrogen‐bonded dl ‐malate anions and water mol­ecules, form a three‐dimensional polymeric structure, in which N—H⃛O hydrogen bonds stabilize the stacking.     

Electronic structure of long cumulene chains

The analysis of the equations of the unrestricted Hartree–Fock (UHF) method for polyenes C_NH_N+2 with even and odd N » 1 is carried out. The equations of the UHF method are shown to be the same in both cases. The comparison of the UHF method with the extended Hartree–Fock (EHF) method applied to large systems is performed. The ground state and π-electron spectra of long cumulene chains C_NH₄ are treated by the EHF Method. The end effects are taken into consideration. It is shown that the EHF method gives a finite value of the first optical transition frequency and, at the same time, zero value of torsion barrier of end CH₂–groups in long cumulene chains (N → ) in contrast to previous calculations of cumulenes by the Huckel method and the restricted Hartree–Fock method.     

Ab initio Hartree–Fock approach to the study of polymers: Application to polyacetylenes

An ab initio Hartree–Fock method devoted to the study of polymers is presented, truncation criteria for the exchange and the Coulomb series are discussed, and it is shown that the error in the total energy evaluation can be reduced to below 0.0001 a.u./cell with little computational effort. Results for six polyacetylene isomers are presented and compared with previous ab initio data obtained using the same basis set. In agreement with the experimental findings, the alternating all-trans structure is the most stable.