Discrete spatial symmetries in energy derivatives

Based upon the invariance of N-particle systems under discrete operations of reflection, inversion, and rotation by 2π/n, a method for obtaining complete sets of relations among energy derivatives of all orders has been presented. The method is based on the criterion that, for a discrete symmetry operation such as reflection across a plane; the change in energy due to simultaneous arbitrary displacements of each particle is equal to another set of “conjugate” displacements of all particles. Applications of the above relations for particular molecular systems possessing a combination of symmetry operations is also presented. Here, via the row echelon analysis, the number of independent derivatives are found, and simple symmetry relations that allow determination of the remaining derivatives are presented. For example, for a homonuclear diatomic molecule with D_2h symmetry only 1 of the 6 first derivatives and 1 of the 21 second derivatives need to be independently calculated.     

Normal coordinate analysis of H8Si8O12

Normal coordinate analysis of the fundamental vibrations of H₈Si₈O₁₂ has been carried out. Because of the octahedral symmetry, the 78 vibrational degrees of freedom lead to 33 different vibrations, six of which are infrared active, 13 are Raman active and 14 are inactive. From the internal coordinates one gets 116 symmetry coordinates. We describe a straightforward method for determining the internal symmetry coordinates of any molecular system. Internal coordinates, symmetry force constants, the full set of orthonormal symmetry coordinates as well as the 38 redundant orthonormal symmetry coordinates of H₈Si₈O₁₂ are tabulated. The potential energy distribution analysis shows that most of the fundamental vibrations can be very well interpreted in terms of the internal vibrations ν(SiH), ν(SiO), δ(SiH), δ(OSiO) and δ(SiOSi) which makes it easy to compare them with vibrations observed in other silsesquioxanes and similar silicon compounds.     

Exact and efficient calculation of Lagrange multipliers in biological polymers with constrained bond lengths and bond angles: proteins and nucleic acids as example cases

To accelerate molecular dynamics simulations, it is common to impose holonomic constraints on the hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thereby allowing longer total simulation times. The imposition of such constraints results in an aditional set of N_c equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), whose solution is closely related to any algorithm implementing the constraints in Euclidean coordinates. In this work, it is shown that, due to the essentially linear structure of typical biological polymers the algebraic equations that need to be solved involve a matrix which is not only sparse, but also banded if the constraints are indexed in a skilful way. This allows the Lagrange multipliers to be obtained through a noniterative procedure, which can be considered exact up to machine precision, and which takes O(N_c) operations, instead of the usual O(N) for generic molecular systems. We develop the formalism, and describe the appropriate indexing for a number of model molecules. Finally, we provide a numerical example of the technique in a series of polyalanine peptides of different lengths. Although a use of the Lagrange multipliers without any modification in the solution of the underlying ordinary differential equations yields unstable integration algorithms, the central role of these quantities makes their efficient calculation useful for the improvement of methods that correctly enforce the exact satisfaction of the constraints at each time step. We provide several examples of this. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Catalytic Enantioselective Reactions. Part VIII. Catalytic Enantioselective Addition of Diethylzinc to Aldehydes Using (2S,3S)-(-)-1,4-Diamino-2,3-Butanediol Derivatives as Chiral Catalysts

A series of new chiral β-N,N-dialkylaminoalcohol derivatives with an axis of C₂ symmetry was prepared from diethyl L-tartrate and their enantioselectivities as chiral catalysts for enantioselective addition of diethylzinc to aldehydes were compared.     

Treatment of redundancies among internal coordinates in optimizing molecular mechanics force constants

The use of redundant coordinate bases in the construction of molecular mechanics force fields is discussed. It is shown that the intrinsic indeterminacy in a force field in redundant coordinates in general stems from the squares of the first-order redundancy relations. The necessity to use constraints in such a force field is pointed out, and a method to check whether or not a set of constraints makes the force field determinate is described. It is also explained how force fields corresponding to different sets of constraints can be transformed into one another. To facilitate the utilization of ab initio or other spectroscopic force fields, a procedure is given by which force constants pertaining to a nonredundant coordinate basis can be optimized in molecular mechanics calculations where redundant coordinates are used. © 1992 by John Wiley & Sons, Inc.     

Determining symmetry changes during a chemical reaction: the case of diazene isomerization

Analysis of reaction paths in terms of the Continuous Symmetry Measure (CSM) provides an alternative way to analyze the geometrical changes that take place during a reaction. Unique symmetry-profiles, describing the symmetry changes along the internal reaction coordinate were calculated for the cis-trans isomerization reaction of N₂H₂ and for its halogeno derivatives. A “symmetry transition point” is identified at the extremum point along the symmetry-profiles. At this point, the deviation of the molecule from the rotational symmetry of the reactant is the same as its deviation from the rotational symmetry of the product. In a second application we show that the CSM can be used as an alternative reaction coordinate. Calculations at the MP2 and DFT levels result in similar symmetry profiles.     

Transferability of intensity parameters

The transferability of different kinds of intensity parameters is discussed. In order to transfer dipole moment derivatives with respect to internal or symmetry coordinates (dmd's) among similar modes in different molecules they must be split up into a mode-specific part (the dmd with respect to rotation-free reference coordinates) and a molecule-specific part (the rotational contribution). The calculation of reference coordinates and rotational contributions is discussed. The dmd's with respect to reference coordinates can be expressed in terms of first-order intensity parameters (bcp's or aop's). Expressions are given for CH₃X, propyne, butyne-2 and acetylene. The transferability of bcp's (or eop's) is tested by searching for a common set of bcp's for the following molecules: C₂H₂, C₂D₂, CH₃CCH, CD₃CCH, CH₃CCCH₃, CD₃CCCD₃. The final results are discussed in relation to the basic assumptions and the adopted constraints.     

Synthesis and Crystal Structure Determination of [H2‐cryptand 222](Br3)2: A Unique Tribromide Catalyst for the Catalytic Chemoselective N‐Boc Protection of Amines

The organic tribromide, [H₂‐cryptand 222](Br₃)₂ was synthesized and characterized by X‐ray crystallography, and was utilized as an active catalyst for the N‐boc protection of amines. The method is general for the preparation of N‐boc derivatives of aliphatic (acyclic and cyclic), aromatic, primary and secondary amines. We also applied our new reaction protocols for the N‐boc protection of some new amines and spectral and physical data for the obtained products are reported.     

Energy levels of paramagnetic ions: Algebra. III. The case of dN ions in cubical symmetry

The formalism developed in the first two papers of this series is applied to the investigation of a new weak-field model. This crystal-field model lies on the use of a symmetry-adapted weak-field basis and an effective Hamiltonian involving in a symmetrical way both spin- and orbit-dependent contributions. Some general properties of this Hamiltonian are studied and complete calculation of its matrix elements is conducted in a symmetry-adapted weak-field basis in the case of an arbitrary configuration nl^N in any symmetry. The case of a configuration nd^N in octahedral symmetry is fully explored. In this case, the proposed weak-field model is restricted to a 12-parameter model which accounts for isotropic and anisotropic Coulomb interactions, isotropic and anisotropic spin-orbit interactions, and crystal-field interactions. A comparison between this 12-parameter weak-field model and the 14-parameter strong-field model is established. Equivalence between the latter two models requires two constraint relations to be satisfied for some strong-field parameters. These two relations are examined with various viewpoints.     

Spin-Dependent operators in the spin-free quantum chemistry

The two-particle spatial density matrix components introduced by McWeeny are expressed in terms of the Fock coordinate wave function, which is constructed from an arbitrary function of N spatial coordinates. The integral relations for these components are verified. The necessary matrix elements of a standard representation of the S_N group are calculated.     

Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I. Three-electron integrals

A method to evaluate the nonrelativistic electron-repulsion, nuclear attraction and kinetic energy three-electron integrals over Slater orbitals appearing in Hylleraas-CI (Hy-CI) electron structure calculations on atoms is shown. It consists on the direct integration over the interelectronic coordinate r _ij and the sucessive integration over the coordinates of one of the electrons. All the integrals are expressed as linear combinations of basic two-electron integrals. These last are solved in terms of auxiliary two-electron integrals which are easy to compute and have high accuracy. The use of auxiliary three-electron ones is avoided, with great saving of storage memory. Therefore this method can be used for Hy-CI calculations on atoms with number of electrons N ≥ 5. It has been possible to calculate the kinetic energy also in terms of basic two-electron integrals by using the Hamiltonian in Hylleraas coordinates, for this purpose some mathematical aspects like derivatives of the spherical harmonics with respect to the polar angles and recursion relations are treated and some new relations are given.     

Dinuclear Zinc Hydride Supported by an Anionic Bis(N‐Heterocyclic Carbene) Ligand

Methylene‐linked bis(N,N′‐di‐tert‐butylimidazol‐2‐ylidene) 1 reacted with diethylzinc to give dinuclear zinc ethyl compound 2 , which contains a formally anionic bis(carbene) ligand as a result of deprotonation of the methylene bridge. The reaction of 2 with PhSiH₃ gave the phenylsilyl compound 3 . The zinc hydride 4 was obtained by the reaction of 2 with LiAlH₄ or Ph₃SiOH followed by treatment with PhSiH₃. X‐ray diffraction studies show that compounds 2 , 3 , and 4 all have a similar dimeric structure with D_2h symmetry. The reaction of hydride 4 with carbon dioxide and N,N′‐diisopropylcarbodiimide gave formato ( 5 ) and formamidinato ( 7 ) derivatives as a result of the insertion of the heterocumulene into both Zn? H bonds. Reaction with Ph₂CO gave the diphenylmethoxy compound 6 . Hydride 4 shows catalytic activity in the hydrosilylation of 1,1‐diphenylethylene and methanolysis of silanes.     

A method for the calculation of normal-mode vibrational frequencies using symmetry coordinates. Application to the calculation of secondary deuterium isotope effects on carbocations

A method is introduced for the calculation of normal-mode vibrational frequencies of polyatomic molecules based on numerical differencing of analytical gradients in symmetry coordinates. This procedure requires a number of gradient evaluations equal to the largest number of symmetry coordinates belonging to any single irreducible representation of the molecular point group (plus a single gradient evaluation at the equilibrium configuration), which is fewer than the 3N-6 (N atoms) gradient evaluations needed for schemes based on Cartesian or internal coordinates. While the proposed method will not generally be as efficient as procedures which involve the direct calculation of energy second derivatives analytically (as are now available for single-determinant wavefunctions) it appears to be equally accurate, and it should be the method of choice for frequency calculations involving multideterminant wavefunctions for which analytical second-derivative algorithms have yet to be developed. The method is illustrated by the calculation of equilibrium secondary deuterium-isotope effects on a number of reactions involving simple carbocations.     

Positional isomeric effect on the crystallization of chlorine‐substituted N‐phenyl‐2‐phthalimidoethanesulfonamide derivatives

The ortho‐, para‐ and meta‐chloro‐substituted N‐chlorophenyl‐2‐phthalimidoethanesulfonamide derivatives, C₁₆H₁₃ClN₂O₄S, have been structurally characterized by single‐crystal X‐ray crystallography. N‐(2‐Chlorophenyl)‐2‐phthalimidoethanesulfonamide, (I), has orthorhombic (P2₁2₁2₁) symmetry, N‐(4‐chlorophenyl)‐2‐phthalimidoethanesulfonamide, (II), has triclinic (P) symmetry and N‐(3‐chlorophenyl)‐2‐phthalimidoethanesulfonamide, (III), has monoclinic (P2₁/c) symmetry. The molecules of (I)–(III) are regioisomers which have crystallized in different space groups as a result of the differing intra‐ and intermolecular hydrogen‐bond interactions which are present in each structure. Compounds (I) and (II) are stabilized by N—H...O and C—H...O hydrogen bonds, while (III) is stabilized by N—H...O, C—H...O and C—H...Cl hydrogen‐bond interactions. The structure of (II) also displays π–π stacking interactions between the isoindole and benzene rings. All three structures are of interest with respect to their biological activities and have been studied as part of a programme to develop anticonvulsant drugs for the treatment of epilepsy.     

The infinite double‐stranded chain polymer catena‐poly­[[bis­(dicyan­amido)­zinc(II)]‐di‐μ‐1,2‐bis(1,2,4‐triazol‐1‐yl)­ethane‐κ4N4:N4′]

The coordination geometry of the Zn^II atom in the title complex, [Zn(C₂N₃)₂(C₆H₈N₆)₂]_n or [Zn(dca)₂(bte)₂]_n, where bte is μ‐1,2‐bis(1,2,4‐triazol‐1‐yl)­ethane and dca is dicyan­amide, is distorted compressed octahedral, in which the Zn^II atom lies on an inversion center and coordinates four N atoms from the triazole rings of four symmetry‐related bte ligands and two N atoms from two symmetry‐related monodentate dca ligands. The structure is polymeric, with 18‐membered spiro‐fused rings extending in the b direction and each 18‐membered ring involving two inversion‐related bte mol­ecules.     

Planarity of heteroaryldithiocarbazic acid derivatives showing tuberculostatic activity: structure–activity relationships

The search for new tuberculostatics is an important issue due to the increasing resistance of Mycobacterium tuberculosis to existing agents and the resulting spread of the pathogen. Heteroaryldithiocarbazic acid derivatives have shown potential tuberculostatic activity and investigations of the structural aspects of these compounds are thus of interest. Three new examples have been synthesized. The structure of methyl 2‐[amino(pyridin‐3‐yl)methylidene]hydrazinecarbodithioate, C₈H₁₀N₄S₂, at 293 K has monoclinic (P2₁/n) symmetry. It is of interest with respect to antibacterial properties. The structure displays N—H…N and N—H…S hydrogen bonding. The structure of N′‐(pyrrolidine‐1‐carbonothioyl)picolinohydrazonamide, C₁₁H₁₅N₅S, at 100 K has monoclinic (P2₁/n) symmetry and is also of interest with respect to antibacterial properties. The structure displays N—H…S hydrogen bonding. The structure of (Z)‐methyl 2‐[amino(pyridin‐2‐yl)methylidene]‐1‐methylhydrazinecarbodithioate, C₉H₁₃N₄S₂, has triclinic (P) symmetry. The structure displays N—H…S hydrogen bonding.     

A new group of potential antituberculotics: <Emphasis Type="Italic">N</Emphasis>-(2-pyridylmethyl)salicylamides and <Emphasis Type="Italic">N</Emphasis>-(3-pyridylmethyl)salicylamides

As a part of our systematic study of antimycobacterially active derivatives of salicylamides, a series of nineteen derivatives of N-(2-pyridylmethyl)salicylamides and N-(3-pyridylmethyl)salicylamides was synthesised. The compounds exhibited in vitro activity against Mycobacterium tuberculosis and M. avium. Their lipophilicity, R _M, was measured by thin layer chromatography on silica gel impregnated with trioctadecylsilane and the logarithm of the partition coefficient (octanol-water), logP, was calculated. Both the parameters of lipophilicity correlated. The quantitative relationship between the structure and antimycobacterial activity was calculated. Antimycobacterial activity increased with an increase in lipophilicity. The N-(2-pyridylmethyl)salicylamide derivatives were more active than the derivatives of isomeric N-(3-pyridylmethyl)salicylamides. The geometry of compounds was calculated and the calculation was verified by measuring the length of the hydrogen bond between hydroxyl and carbonyl groups on the salicylic moiety.     

Aromaticity of All Possible C26N2 Isomers

The aromaticity of all possible heterofullerenes C₂₆N₂ and C₂₈ based on T_d symmetry has been studied by means of the topological resonance energy and percentage topological resonance energy methods. The relationship between the aromaticity of the C₂₆N₂ isomers and the sites where nitrogen atoms dope at the C₂₈ cage has been discussed. The calculation results show that the most stable isomer of C₂₆N₂ derivatives is formed by nitrogen atoms doping at the two tetrahedral vertices. C₂₆N₂ isomers are more stable than C₂₈, but the C₂₆N₂^2? isomers are less stable than C₂₈ ^4?4. The effect of nitrogen substitution on C₂₈ stability was investigated by the topological charge stabilization rule.     

Manganese dioxide and N,N′,N″‐trihydroxyisocyanuric acid: a novel and recyclable catalytic system for aerobic oxidation of toluene derivatives in PEG‐1000‐based dicationic acidic ionic liquid

N,N′,N″‐trihydroxyisocyanuric acid (THICA) with MnO₂ promotes the aerobic oxidation of toluene derivatives to corresponding acids in PEG‐1000‐based dicationic acidic ionic liquid (PEG₁₀₀₀–DAIL). It is demonstrated that THICA/MnO₂ is very active and selective and several toluene derivatives are efficiently oxidized to corresponding acids under mild conditions. Both the catalyst and PEG₁₀₀₀–DAIL can be reused after simple separation. A plausible mechanism is also proposed based on the experimental observations. Copyright © 2015 John Wiley & Sons, Ltd.