The impact of approximate VSCF schemes and curvilinear coordinates on the anharmonic vibrational frequencies of formamide and thioformamide

The accuracy of the vibrational self-consistent field (VSCF) method for the computation of anharmonic vibrational frequencies in the infrared (IR) spectrum of formamide and thioformamide is investigated. The importance of triple potentials in the commonly used hierarchical expansion of the potential energy surface (PES) is studied in detail. The PES is expanded in terms of Cartesian as well as internal coordinate normal mode displacements. It is found that triples play an important role when using rectilinear coordinates. A VSCF computation based on rectilinear displacements exhibits serious shortcomings which are only remedied by a large vibrational configuration interaction (VCI) treatment including triple potentials. These limitations are partially removed when using curvilinear coordinates. The merits and disadvantages of either type of displacements for the generation of the PES are discussed.     

The choice of internal coordinates in complex chemical systems

This article presents several considerations for the appropriate choice of internal coordinates in various complex chemical systems. The appropriate and black box recognition of internal coordinates is of fundamental importance for the extension of internal coordinate algorithms to all fields where previously Cartesian coordinates were the preferred means of geometry manipulations. Such fields range from local and global geometry optimizations to molecular dynamics as applied to a wide variety of chemical systems. We present a robust algorithm that is capable to quickly determine the appropriate choice of internal coordinates in a wide range of atomic arrangements. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Canonical force field theory in terms of curvilinear internal coordinates: Application to the methane molecule

This Letter generalizes the Kuczera’s theory of the vibrational canonical force field in order to obtain an unambiguous and uniquely defined expression for the anharmonic force field in terms of curvilinear internal coordinates. By using this generalization it has been shown mathematically that the canonical force constants could be transferred between molecules with the same geometrical structure. As illustration, the theory is used to obtain the expressions for the quadratic and cubic canonical force constants of the methane molecule.     

VSCF in internal coordinates and the calculation of anharmonic torsional mode transitions

The vibrational self-consistent field (VSCF) method assumes separability in normal modes in its usual version. However, the method fails in cases such as soft torsional modes which are better treated by angular variables. We develop VSCF equations based on the assumption of wave function separability in internal coordinates. To test the method, simple illustrative applications to small systems are provided: trans-HONO, cis-HONO, H₂S₂, and H₂O₂. The code directly uses points from ab initio calculations, and the method proves to be accurate for all types of transitions. For typical torsional transitions, the error in the computed frequency is smaller than that of VSCF in normal coordinates. The wave functions for the torsional mode are compared with the corresponding normal mode wave functions. The differences are substantial. The results are encouraging for extension of the model for large polyatomic systems. Work along these lines is in progress.     

The subduction of vibrational states of molecules from the momentum space of simple harmonic motion

A single-particle model of molecular vibrational states is proposed in which the normal modes are projected out of the body vibrations of an infinite simple harmonic sphere. This model assigns the spurious change of mass or centre of mass and leads to removal of mass monopoles and dipoles from the system. These conservation conditions impose strict boundary conditions on the potential and basis functions. On incorporation into the model they result in a set of loop equations in which the potential is proportional to the fundamental vibration. The simplest solutions to these equations strongly resemble the Poschl-Teller generalization of the Morse potential. The solutions have been extended to incorporate the repulsive states and generate the set of net attractive states appropriate to the anharmonic potential.The basis functions of this potential display both angular and radial node structures. The degeneracies between radial and angular mode patterns can be studied by transformation into an angular coordinate space. In this way coupling to other phenomena described in similar angular momentum space can be performed directly before subduction to real displacement space.On leave from the Department of Chemistry, Catholic University of Leuven, Celestijnenlaan 200F, B-3030 Leuven-Belgium     

Theoretical study of dynamical properties on reaction path in molecular internal coordinates

The dynamical properties on reaction path (IRC) in internal coordinates have been obtained, which in. clude ω_K (frequencies orthogonal to IRC), L_K (vibrational modes), B_(KF) (coupling constants between the IRC and vibra tions orthogonal to it), B_(KL) (coupling constants between every two vibrations orthogonal to IRC). A set of theory of teac. tion path in molecular internal coordinates has been also constructed. The dynamical properties, including ω_K, B_(KF) B_(KL) of the reaction H~1O~2H~3 H~4→H~1O~2 H~3H~4 have been calculated, which explicitly explain the interaction, chang ing trend and contribution of each chemical bond (including bond angle) in the reaction.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Perturbed structures generated using coordinates derived from compliance constants in internal vibrations for QTAIM dual functional analysis: Intrinsic dynamic nature of interactions

Perturbed structures for QTAIM dual functional analysis (QTAIM‐DFA) are proposed to generate using the coordinates corresponding to the compliance force constants in internal vibrations (CIV). In QTAIM‐DFA, total electron energy densities H_b( r _c) are plotted versus H_b( r _c) – V_b( r _c)/2 at bond critical points (BCPs) of interactions in question, where V_b( r _c) are potential energy densities at BCPs. Each plot of an interaction based on the data from both perturbed structures and fully optimized one takes the form (θ_p, κ_p), where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ_p values evaluated with CIV are equal to those obtained by partial optimizations with the interaction distance in question being fixed suitably, within the calculation errors. Very high applicability of CIV is demonstrated to generate the perturbed structures for QTAIM‐DFA. Dynamic nature of interactions based on (θ_p, κ_p) with CIV is called “intrinsic dynamic nature of interactions.”     

Insight into the structural and transport properties of methyl and benzyl triphenyl phosphonium based deep eutectic solvents using molecular dynamics simulations

Molecular dynamics simulation of twelve phosphonium based DESs based on methyl triphenyl phosphonium bromide and benzyl triphenyl phosphonium chloride as hydrogen bond acceptors (HBA) with glycerol, ethylene glycol, triethylene glycol and trifluoroacetamide as hydrogen bond donors (HBDs) are carried out with the Generalized Amber Force Field between 25 °C and 95 °C at 1 atm pressure. Isobaric-isothermal ensemble is used for predicting the structural properties, namely, radial distribution function and coordination number. Further, time resolved trajectory data is correlated to predict the transport properties such as, self-diffusivity, binary-diffusivity, ionic conductivity and viscosity. The temperature dependence of predicted density is observed with 4.96 × 10⁻² absolute average deviations from experimental dataset. Further, the self-diffusivities are predicted using Einstein's approach and ionic conductivity is calculated from Nernst-Einstein equation as well as Green-Kubo formulation. Further, the viscosity is also predicted using the Green-Kubo formulation. The predicted ionic conductivities and viscosities are fitted in the Vogel-Fulcher-Tammann (VFT) equation to calculate the VFT parameters for the respective DESs.     

New method for parallel computation of Hessian matrix of conformational energy function in internal coordinates

A new algorithm for parallel calculation of the second derivatives (Hessian) of the conformational energy function of biomolecules in internal coordinates is proposed. The basic scheme of this algorithm is the division of the entire calculation of the Hessian matrix (called "task") into subtasks and the optimization of the assignment of processors to each subtask by considering both the load balancing and reduction of the communication cost. A genetic algorithm is used for this optimization considering the dependencies between subtasks. We applied this method to a glutaminyl transfer RNA (Gln-tRNA) molecule for which the scalability of our previously developed parallel algorithm was significantly decreased when the large number of processors was used. The speedup for the calculation was 32.6 times with 60 processors, which is considerably better than the speedup for our previously reported parallel algorithm. The elapsed time for the calculation of subtasks, data sending, and data receiving was analyzed, and the effect of the optimization using the genetic algorithm is discussed.     

Density functional theory investigations on the conformational stability and vibrational spectra of the model compound of vitamin K

Becke 3-Lee–Yang–Parr density functional theory (DFT/B3LYP) using 6-31G(d) and 6-311G(d) basis sets and the scaled quantum mechanics (SQM) force field method are used to study molecular conformations and vibrational spectra of a model compound of vitamin K (VK). In this molecule, there are six conformers on the torsional potential energy map of the dihedral angles C₈C₁₄C₁₅C₁₆ () and C₇C₈C₁₄C₁₅ (β). It is shown that the VK_1 conformer ( = 237.7° and β = 274.2°) is the most stable form. For this lowest energy conformer, the harmonic force fields calculated by B3LYP/6-311G(d) and B3LYP/6-31G(d) methods are scaled with one scale factor of 0.9623 and a set of different scale factors transferred from the previous studies for the other similar molecules, respectively. The vibrational frequencies, IR intensities, and Raman activities are obtained for the lowest energy conformer. On the basis of B3LYP calculations, the normal mode analysis is performed to assign the vibrational fundamental frequencies according to the potential energy distributions. The computational frequencies are in good agreement with the observed results.     

Parallel algorithm for efficient calculation of second derivatives of conformational energy function in internal coordinates

A parallel algorithm for efficient calculation of the second derivatives (Hessian) of the conformational energy in internal coordinates is proposed. This parallel algorithm is based on the master/slave model. A master processor distributes the calculations of components of the Hessian to one or more slave processors that, after finishing their calculations, send the results to the master processor that assembles all the components of the Hessian. Our previously developed molecular analysis system for conformational energy optimization, normal mode analysis, and Monte Carlo simulation for internal coordinates is extended to use this parallel algorithm for Hessian calculation on a massively parallel computer. The implementation of our algorithm uses the message passing interface and works effectively on both distributed-memory parallel computers and shared-memory parallel computers. We applied this system to the Newton–Raphson energy optimization of the structures of glutaminyl transfer RNA (Gln-tRNA) with 74 nucleotides and glutaminyl-tRNA synthetase (GlnRS) with 540 residues to analyze the performance of our system. The parallel speedups for the Hessian calculation were 6.8 for Gln-tRNA with 24 processors and 11.2 for GlnRS with 54 processors. The parallel speedups for the Newton–Raphson optimization were 6.3 for Gln-tRNA with 30 processors and 12.0 for GlnRS with 62 processors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1716–1723, 1998     

Modelling the vibrational behaviour of the cyclic carboxylic acid dimer. SQM force field of the formic acid dimer

The vibrational behaviour of the cyclic carboxylic acid dimer is modelled through the scaled quantum mechanical (SQM) force field of the cyclic formic acid dimer. The results indicate that the SQM force field technique is very well applicable to hydrogen bonded molecules. The frequency shifts observed on hydrogen bonding can be related to the shifts observed on lowering the temperature. This study also confirms that a clear distinction between cyclic carboxylic acid dimers and catamers can be made through the difference between infrared and Raman frequencies, and it is proved here that these conditions are also valid for weaker hydrogen bonded cyclic carboxylic acid dimers.     

Study of peptide conformation in terms of the ABEEM/MM method

The ABEEM/MM model (atom-bond electronegativity equalization method fused into molecular mechanics) is applied to study of the polypeptide conformations. The Lennard-Jones and torsional parameters were optimized to be consistent with the ABEEM/MM fluctuating charge electrostatic potential. The hydrogen bond was specially treated with an electrostatic fitting function. Molecular dipole moments, dimerization energies, and hydrogen bond lengths of complexes are reasonably achieved by our model, compared to ab initio results. The ABEEM/MM fluctuating charge model reproduces both the peptide conformational energies and structures with satisfactory accuracy with low computer cost. The transferability is tested by applying the parameters of our model to the tetrapeptide of alanine and another four dipeptides. The overall RMS deviations in conformational energies and key dihedral angles for four di- or tetrapeptide, is 0.39 kcal/mol and 7.7 degrees . The current results agree well with those by the accurate ab initio method, and are comparable to those from the best existing force fields. The results make us believe that our fluctuating charge model can obtain more promising results in protein and macromolecular modeling with good accuracy but less computer cost.     

Ab initio spectrograms of the molecular vibrational spectrum

Theoretical spectrograms of the vibrational spectrum of 3,3-dimethylcyclopropene were constructed and juxtaposed with the experimental Raman and IR spectrograms. The theoretical spectrograms are represented as sets of vertical lines starting from the points corresponding to the values of the vibrational frequencies calculated from the scaled quantum-mechanical (QM) force field obtained at the HF/6-31G*//HF/6-31G* level. Two theoretical Raman spectrograms were constructed. In the first case, the heights of the vertical lines correspond to the QM values of the Raman scattering activities. In the second case they represent the relative differential Raman cross-sections calculated using the QM values of Raman scattering activities. The initial vibrational mode matrix remains virtually unchanged upon scaling of the QM force constant matrix because the dispersion of the scale factor values is low. Therefore, the heights of the theoretical lines for the IR spectrogram represent the QM intensities directly. The theoretical spectrogram based on the relative differential Raman cross-sections was shown to depict the experimental Raman spectrum more adequately. This makes it possible to use the results of the corresponding QM calculations more completely and obtain well-substantiated assignments of the vibrational frequencies.     

Chemical forces in terms of the electron density

A previous study of the small deformations produced by the molecular environment in the atomic densities has concluded that these deformations reflect and support all the concepts of the empirical structural chemistry. In the present work the study is extended to the chemical forces. Four types are distinguished: Van der Waals, Pauli, bonding and nuclear unscreening forces. For each type, the origin, the associated density deformations, the force generated by these deformations and the main role played by this force are investigated. It is stressed that Van der Waals complexes, usual molecules, conformers and chemical processes can be described in terms of these four forces, and are determined by the balance between them. It is proved that simple models for the density are often sufficient for semiquantitative predictions of forces, and can be very helpful for rationalizing the chemical properties and behavior. Developments are illustrated and supported with specific examples. Contribution to the Serafin Fraga Memorial Issue. Financial support: Dirección General de Investigación Científica y Técnica (CTQ2004-06615/BQU).     

Prediction of adsorption of small molecules in porous materials based on ab initio force field method

Computational prediction of adsorption of small molecules in porous materials has great impact on the basic and applied research in chemical engineering and material sciences. In this work,we report an approach based on grand canonical ensemble Monte Carlo(GCMC) simulations and ab initio force fields. We calculated the adsorption curves of ammonia in ZSM-5 zeolite and hydrogen in MOF-5(a metal-organic-framework material). The predictions agree well with experimental data. Because the predictions are based on the first principle force fields,this approach can be used for the adsorption prediction of new molecules or materials without experimental data as guidance.     

Intramolecular hydrogen bonding. Spectroscopic and theoretical studies of vibrational transitions in dibenzoylmethane enol

The vibrational structure of the title compound (DBM) was investigated by FTIR spectroscopy in liquid solutions, by FTIR linear dichroism (LD) measurements, and by Raman spectroscopy. The results were supported by the application of theoretical model calculations and analyzed with particular attention to the possible origin of the broad, very strong, and irregularly shaped absorbance band observed in the 1700–1400 cm⁻¹ region. The orientation factors derived from the observed LD data indicate that rotational dynamics of the phenyl groups do not contribute significantly to the broadening of the band. The position of the two sharp Evans transmission windows near 1580 and 1500 cm⁻¹ is unaffected by deuteration of the reactive protons in DBM. The transmissions coincide with prominent peaks in the Raman spectrum and can be assigned to combinations of phenylic modes (9a, 18a) with low IR intensity, but large Raman scattering activity.     

Acetamide, a challenge to theory and experiment? On the molecular structure, conformation, potential to internal rotation of the methyl group and force fields of free acetamide as studied by quantum chemical calculations

The molecular geometry has been optimized without any constraints using different basis sets and levels of theory as: Hartree-Fock with basis sets 6–31+G**, 6–311++G**, cc-pVTZ and aug-cc-pVTZ, MP2 with basis sets 6–311++G** and cc-pVTZ, MP3 with basis set 6–311++G**, and density functional theory with basis sets 6–311++G** and cc-pVTZ. Small basis sets up to 6-31G predict the syn conformation of the methyl group to be the most stable conformation. Larger basis sets predict an unsymmetrical conformation with one of the H atoms perpendicular to the amide skeleton or an anti-like conformation. Dunnings correlation consistent polarized valence triple zeta, cc-pVTZ, basis set including MP2 predict two conformations, one perpendicular and one anti to be the most stable. The DFT calculations predict anti-like conformations. The most accurate calculations predict anti-like conformations which have not been predicted previously. The vibrational frequencies have been calculated for several basis sets and compared to the observed frequencies. The wagging frequency of the NH₂ is very dependent on the basis sets and levels of theory. Most calculations predict a planar NH₂ group in agreement with experiment. A scaled molecular force field has been determined by fitting the calculated frequencies to the observed ones for the perpendicular conformation using MP2/cc-pVTZ. The barrier heights for the methyl group have been calculated. The rotational constants, I_A + I_B − I_C values and dipole moments are compared with experimental values.