A theoretical study of the force field for carbon trioxide

Geometries force constants and harmonic frequencies are calculated for the cyclic (dioxirane) structure of CO₃ by ab initio SCF methods using the 3-21G, 3-21G(*). 6-31G and 6-31G* bases calculated frequency shifts for isotopomeric species agree with experiment and lend support to the vibrational assignments of Jacox and Milligan. Earlier arguments for and against the cyclic, cyclic and open structures of CO₃, based upon the “physical reasonableness” of valence force constants are shown to be invalid owing to the dependence of conventional “rigid” force constants upon the choice of valence coordinates. The use of “relaxed” force constants as a basis for meaningful comparison of force fields for molecules described by different sets of redundant valence coordinates is demonstrated.     

Molecular mechanics force-field parameterization procedures

A set of procedures and guidelines are presented for the estimation of bond length, bond angle, and torsional potential constants for molecular mechanics force fields. The force field constants are ultimately derived by “subtracting” nonbonded molecular mechanics energies from corresponding molecular orbital energies using a model compound containing the chemical structure to be parameterized. Case study examples of bond length, bond angle, and torsional rotation force field parameterizations are presented. A general discussion of molecular mechanics force field parameterization strategy is included for reference and completeness. Finally, a curve-fitting program to generate force field parameters from raw data is given in Appendix I.     

In-plane vibrational modes of cytosine from an ab initio MO calculation

Harmonic force constants, in-plane vibrational frequencies, and in-plane vibrational modes of cytosine were calculated by an ab initio Hartree—Fock SCF MO method. The force contants were calculated by the use of an energy gardient method with the STO-3G basis set, and then they were corrected into “4-31G force constants” by the scaling factors given by us previously for the case of uracil. The corrected set of force constants can produce a calculated vibrational spectra of cytosine and cytosine-1,amino-d₃, that can be well corrected with the observed Raman and infrared spectra of these compounds, with little ambiguity. Thus, the assignments of all the in-plane vibrations are now practically established. The calculated vibrational modes, in addition, can account for the recently published resonance Raman effects of cytosine residue.     

The harmonic force field and absolute infrared intensities of butyne-2

The frequencies, harmonic force field and absolute IR intensities for butyne-2-d₀ and butyne-2-d₆ are reported. The final set of “harmonized” fundamental frequencies for butyne-2-d₀ and butyne-2-d₆ obeys the Teller—Redlich product rule very well. Starting values for the force constants were obtained from the harmonic force field of propyne, and diagonal force constants were adjusted in order to reproduce the experimental “harmonized” frequencies for the d₀ and d₆ compounds.The integrated IR intensities were measured according to the Wilson—Wells—Penner—Weber method, using nitrogen as a broadening gas. Thirteen sets of ?μ/?S values were obtained from the experimental intensities, using an iterative least-squares fitting procedure. This number could be reduced to one by use of several selection criteria. The signs of the remaining set appeared to be in complete agreement with the best set for propyne as reported both by Kondo and Koga and by Bode et al. The final ?μ/?S parameters were transformed into atomic polar tensors. Both kinds of intensity parameters are discussed and compared with corresponding parameters for related molecules.     

Pseudo-exact force constants by the high and low frequency separation method

A method based on the “Approximate Separation of High and Low Frequencies” by Wilson et al. is developed and applied to molecules with three vibrations in a single species. It is shown that for a number of ZXY₃ (C_3v), ZXY₂ (C_2v), and ZXY (C_s) type molecules, for which exact force constants and isotopic data are available, this method—when used in conjunction with the isotopic data-reproduces the exact force constants of the reduced secular determinant. The high and low frequency separation seems to be a good method for determining the force constants in many n = 3 cases, where the highest and/or lowest frequency vibrations are rather characteristic and where—as in most cases—isotopic frequency data alone are insufficient for the determination of the exact force field. Extension to higher order secular determinants should also be possible.     

Consistent valence force-field parameterization of bond lengths and angles with quantum chemical ab initio methods applied to some heterocyclic dopamine D3-receptor agonists

To secure a broad utilization of molecular mechanics in medicinal chemistry appropriate parameters (e.g., reference values and force constants) are required to describe correctly all possible atomic interactions. For this purpose parameters for bond lengths and bond angles were derived for some heterocyclic dopamine D₃-receptor agonists. Some new atom types were introduced and consistent valence force-field (CVFF) was supplied with several bond-stretching and angle-bending force constants as well as reference values. Representative fragments containing these missing parameters were minimized at the HF/6-31G* level of theory using Gaussian-92. After frequency calculation, corresponding force constants were extracted from the Hessian matrix. The values were then appropriately converted and scaled. Also, reference values were taken from quantum mechanically minimized structures, applying the same basis set. The transferability of the calculated force constants to CVFF was investigated using fragments with already known parameters. The quality of the extended force field was checked in comparison with “automatic parameters” and ab initio-minimized structures. Finally, the evaluated procedure was applied successfully to related structures. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 935–946, 1998     

Vibrational spectra,force fields and electronic structures of sydnones

Normal vibrational analyses of 3-methylsydnone and 3-methylsydnone-d₄ have been performed. On the basis of the set of force constants obtained, the electronic distribution within the mesoionic ring is evaluated and compared to the results of MO calculations. The π-bond order of the sydnone carbonyl group is shown to be lower than that in alicyclic esters and the unusually high “carbonyl stretching” frequency is due to the contributions from other coordinates to this mode. The splitting of the “carbonyl stretching” band observed in the spectra of 3-methylsydnone and of related derivatives is explained by the strong kinematic coupling between mesoionic bonds.     

Finite vibrational displacements in the Eckart—Sayvetz basis

Curvilinear internal coordinates are considered in terms of cartesian displacements in a molecule-fixed basis determined by the Eckart-Sayvetz conditions. The latter are interpreted as a set of restrictions on the metrics of the space and define cartesian displacements of “pure” vibrational character expanded to any order in terms of internal coordinates. Explicit expressions for expansion coefficients are given as a function of contravariant components of the metric tensor taken from existing table. A compact notation is proposed for anharmonic force constants, expansion coefficients of redundancies and coupling terms of the rotation—vibration hamiltonian.     

No‐Barrier Theory: Calculating Rates of Chemical Reactions from Equilibrium Constants and Distortion Energies

No‐barrier theory is a new approach to the calculation of rate constants for reactions in solution, from the corresponding equilibrium constants. It requires relatively small molecular orbital theory calculations, and has been very successful. It is in the spirit of Marcus theory, but does not require an “intrinsic barrier”. The approach is explained, with an examination of the way in which the ideas on which it is based were “in the air”.     

Comment on “Maximum Interaction Model of Force Constant Calculation of the MLx(CO)6-x Type Molecule”

Since the introduction of non-mechanical coupling model proposed by Cotton and Kraihanzel^1-3) for the calculation of nonrigorous carbonyl force constants of metal carbonyls, several criticisms^4-3) and modifications^6-13) on this simplified CO-factored force field has been reported. Recently, a different approach of so-called “maximum interaction model” was proposed by Chen and Hsiang¹⁴⁾. However, we found that basic assumptions of this model are very shaky and questionable since three serious abnormal results could be noted as a result of maximum interaction between carbonyl groups. Here we would like to make some comments on this model.     

Coarse-grained polyethylene: 1. The simplest model for the orthorhombic crystal

The coarse-grained model of polyethylene and alkanes (the united-atom model, in which each CH₂ group is represented by a single bead) was proposed several decades ago. It is widely applied in molecular dynamics simulations. For different tasks, the models with different geometrical and force parameters are used. Until now, it was thought that the coarse-grained model of polyethylene cannot reproduce the orthorhombic crystalline phase, which is typical of this polymer. In the present study, we analyze the simplest coarse-grained model of polyethylene. In this model, the Lennard-Jones potential (6–12) is adopted for van der Waals interactions between the beads of different chains. Of the bonded interactions, only the “valence” bonds between beads and the “bond” and “torsion” angles are taken into account, whereas the cross terms between them are disregarded. We consider the model variation in which the bead (the force center with the mass of a CH₂ group) is displaced from the center of the carbon atom and all the interactions, both bonded and nonbonded, are defined by the positions of these beads. For this model, we find the area of geometrical parameters (the displacement value and the van der Waals radius of the bead) in which all the three known crystalline phases of polyethylene are at equilibrium at low temperatures. We choose the force field constants for the model so that its oscillation spectrum reproduces the low-frequency part of the inelastic neutron scattering spectrum of the orthorhombic polyethylene. It proved to be that this choice can be made unambiguously. We compare the dispersion curves in the terahertz range with experimental data on the Raman scattering and infrared spectroscopy, and discuss the advantages and disadvantages of the analyzed simplest coarse model.     

Formation of Glycinate Complexes of Iron(II) at Different Ionic Strengths of Solution

Complexation of iron(II) in aqueous glycine (α-aminoacetic acid) solutions is studied in the pH range 1.0–8.0 at 298.16 K at various ionic strengths (NaClO₄). The stability constants of the resulting complexes go down as the ionic strength of the solution increases. The stability constants of the complexes are determined using the experimental “electromotive force of the system versus pH” curves by iterative fitting of the theoretical oxidation function to the experimental one with the Excel program. The correlation between the stability constants of complexes and ionic strength of the solution is also calculated using the Debye–Hückel equation and SigmaPlot 10.0 software. Statistical analysis of the calculated data is performed with P value of 0.95.     

Decoupled Hartree-Fock methods. II. Calculation of the potential curves of diatomic molecules

Applying an extended form of the Mulliken approximation and a monopole approximation for the Coulomb integrals the Hartree-Fock nonorthogonal energy expression is decoupled. Thus, the total energy splits into a sum of one-electron increments. The increments are minimized directly with respect to the linear coefficients and orbital exponents. Further, the ZDO approximation is used in the decoupled energy expression to avoid difficulties arising in connection with the evaluation of multicenter integrals. “Rigid core” calculations were carried out for the valence electrons of first-row diatomics. In case of nonpolar molecules good results are obtained for equilibrium distances and force constants. The method fails for molecules with atoms having very different nuclear charges.     

Development of an internal searching algorithm for parameterization of the MM2/MM3 force fields

Application of Allinger's MM2/MM3 force fields to molecules of real interest is frequently hindered by the lack of parameters for various heterocyclic systems and for poly-functionalized molecules. A common approach to this problem is to manually choose missing parameters “by analogy” with those that are part of the force field's internal parameter set. Naturally, this is generally attempted only by those possessing extensive experience with force fields. In order to use the MM2/MM3 force fields to study herbicides, an algorithm has been developed to automate this process for the non MM2 specialist. Using a set of “relative cost” criteria for atom type replacement, the algorithm searches the force field parameter set and selects the most appropriate parameters for a given molecule whose MM2 output file contains “missing parameter” errors. The program selects parameter error messages from a standard MM2 output file, finds analogous parameters, asks the user to verify their appropriateness and creates a standard MM2 parameter deck for the molecule of interest.     

Stability Of 2-Carboxyphenylhydrazoacetoacetanilide,and 2-Carboxyphenylhydrazobenzoylacetone Complexes of Rare-Earth Elements in Mixed Solvents

The overall stability constants of the 1:1 and 2:1 2-Carboxyphenylhydrazoacetoacetanilide (2-CPHAAA) and 2-Carboxyphenylhydrazobenzoylacetone (2-CPHBA) rare-earth chelates, were determined by a potentiometric method. The variation of the overall stability constants, “log β” with atomic number, of the lanthanide was ascribed to different degrees of dehydration of the cations. The 2-CPHBA ligand exhibited less affinity for rare earth cations than 2-CPHAAA. The correlation of “log β” versus the basicity of the ligands showed that 2-CPHAAA and 2-CPHBA form the same type of chelate in polar solvents but differ in non polar solvents.     

Elastic Behaviors of Adsorbed Protein-like Chains

Elastic behaviors of protein-like chains are investigated by Pruned-Enriched-Rosenbluth method and modified orientation-dependent monomer-monomer interactions model. The protein-like chain is pulled away from the attractive surface slowly with elastic force acting on it. Strong adsorption interaction and no adsorption interaction are both considered. We calculate the characteristic ratio and shape factor of protein-like chains in the process of elongation. The conformation change of the protein-like chain is well depicted. The shape of chain changes from “rod” to “sphere” at the beginning of elongation. Then, the shape changes from “sphere” to “rod”. In the end, the shape becomes a “sphere” as the chain leaves away from the surface. In the meantime, we discuss average Helmoholtz free energy per bond, average energy per bond, average adsorbed energy per bond, average α-helical energy per bond, average β-sheet energy per bond and average contact energy per bond.On the other hand, elastic force is also studied. It is found that elastic force has a long plateau during the tensile elongation when there exists adsorption interaction. This result is consistent with SMFS experiment of general polymers. Energy contribution to elastic force and contact energy contribution to elastic force are both discussed. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

A Mechanochemically Triggered “Click” Catalyst

“Click” chemistry represents one of the most powerful approaches for linking molecules in chemistry and materials science. Triggering this reaction by mechanical force would enable site‐ and stress‐specific “click” reactions—a hitherto unreported observation. We introduce the design and realization of a homogeneous Cu catalyst able to activate through mechanical force when attached to suitable polymer chains, acting as a lever to transmit the force to the central catalytic system. Activation of the subsequent copper‐catalyzed “click” reaction (CuAAC) is achieved either by ultrasonication or mechanical pressing of a polymeric material, using a fluorogenic dye to detect the activation of the catalyst. Based on an N‐heterocyclic copper(I) carbene with attached polymeric chains of different flexibility, the force is transmitted to the central catalyst, thereby activating a CuAAC in solution and in the solid state.     

Third-order anharmonic potential constants and equilibrium structures of the formyl and hydroperoxyl radicals

Observed vibration—rotation constants for HCO/DCO and HO₂/DO₂ are combined with vibrational frequencies and ground-state rotational constants in order to derive harmonic as well as third-order anharmonic potential constants, and also equilibrium structure parameters for the formyl and hydroperoxyl radicals. The “diagonal” terms of the third-order anharmonic constants thus obtained for the stretching modes are discussed in terms of the diatomic-molecule model.     

Polymer complexes: XLX. Novel supramolecular coordination modes of structure and bonding in polymeric hydrazone sulphadrugs uranyl complexes

Novel five binuclear polymeric dioxouranium(VI) of azosulphadrugs [(azodrug substances) azobenzene sulphonamides] were prepared for the first time. The infrared spectra of the samples were recorded and their fundamental vibration wave number was obtained. The resulting polymeric uranyl complexes were characterized on the basis of their elemental analyses, conductance and spectral (IR, NMR, and electronic spectra) data. The ligation modes of the azosulphadrugs ligands towards uranyl(II) ions were critically assigned and addressed properly on the basis of their IR and their uranyl(II) complexes. The theoretical aspects are described in terms of the well-known theory of 5d–4f transitions. The coordination geometries and electronic structures are determined from a framework for the modeling of novel polymer complexes. The values of ν₃ of the prepared complexes containing UO₂²⁺ were successfully used to calculate the force constant, F_UO (1n 10^?8 N/Å) and the bond length R_UO of the U–O bond. Wilson's, matrix method, Badger's formula, and Jones and El-Sonbati equations were used to calculate the U–O bond distances from the values of the stretching and interaction force constants. The most probable correlations between U–O force constant to U–O bond distance were satisfactorily discussed in terms of “Badger's rule”, “Jones” and “El-Sonbati equations”.