Modified Valence Force Field Research Articles

Barrier potentials, molecular structure, force filed calculations and quantum chemical studies of some bipyridine di-carboxylic acids using the experimental and theoretical using (DFT, IVP) approach

ABSTRACTFT-IR and FT-Raman spectra of 2,2′-bipyridine-3,3′-dicarboxylic acid (B3DA), 2,2′-bipyridine-4,4′-dicarboxylic acid (B4DA) and 2,2′-bipyridine-5,5′-dicarboxylic acid (B5DA) were recorded and analysed. The quantum chemical calculations of the title compounds begin with barrier potentials at different rotation angles around the C–C′ and C–Cα bonds in order to arrive conformation of lowest energy using DFT employing B3LYP functional with 6-311++G(d,p) basis set. This confirmation was further optimised to get the global minimum geometry. The vibrational frequencies along with IR, Raman intensities were computed, the rms error between observed and calculated frequencies were 11.2 cm−1, 10.2 cm−1 and 12.2 cm−1 for B3DA, B4DA, and B5DA. An 87-element modified valence force field is derived by solving the inverse vibrational problem using Wilson’s GF matrix method. This force field is refined using 163 observed fundamentals employing in overlay least-squares technique. The average error between computed and experimental frequencies was found as 12.85 cm−1 using potential energy distribution (PED) and eigenvectors. By using the gauge-independent atomic orbital (GIAO) method calculate the 1H and 13C NMR chemical shifts of the molecules and compared with experimental results. The first-order hyperpolarisability, HOMO and LUMO energies, molecular electrostatic potential (MESP) and natural orbital analysis (NBO) of titled compounds were evaluated using DFT.

Molecular structure and vibrational analysis of 2,5-pyridine-dicarboxylic acid using experimental and theoretical methods

The FTIR and FT-Raman spectra of 2,5-pyridine-dicarboxylic acid (PDA) has been recorded in the range 4000-450 cm-1 and 4000-50 cm-1, respectively. The optimized geometry and vibrational frequencies were computed using density functional theory (DFT) employing B3LYP functional with 6-311++G(d,p) basis set. The rms error between observed and calculated frequencies is obtained as 10.8 cm-1. A normal coordinate analysis was carried out for all the vibrations of this molecule by solving inverse vibrational problem (IVP) using a 74-parameter modified valence force field employing overlay technique. This reproduced 35 observed frequencies of this molecule with an error of 9.28 cm-1 in the zero-order calculations, demonstrating the transferability of the force field obtained in our earlier work on some related pyridine-dicarboxylic acids. PED and eigen vectors calculated in the process were used to make unambiguous vibrational assignments of all the fundamentals of the molecule.

Spectroscopic investigation on structure (monomer and dimer), molecular characteristics and comparative study on vibrational analysis of picolinic and isonicotinic acids using experimental and theoretical (DFT & IVP) methods

In this investigation, the monomeric structure is determined for picolinic and isonicotinic acids based on geometry optimization for one of the four possible conformers and intramolecular hydrogen bond of OH⋯O using density functional theory (DFT) employing B3LYP functional supplemented with 6–311++G(d,p) basis set. Using this optimized monomeric form, the dimer structure is determined based on minimum energy and length of hydrogen bonds obtained for two possible dimeric forms yielded due to head-to-tail intermolecular OH⋯N hydrogen bond (dimer 1) linkage and tail-to -tail intermolecular OH⋯O hydrogen bond (dimer 2) linkage between pyridine ring and carboxyl group. The structure parameters obtained for monomer and dimer forms are in good agreement with the experimental literature values. The vibrational assignments have been made unambiguously for all the vibrations from FTIR and FT-Raman spectra based on the potential energy distribution (PED) and eigen vectors obtained in DFT and inverse vibrational problem (IVP) computations. The rms error between the observed and scaled frequencies is 7.7 and 9.4 cm−1 for PIA and INA, respectively. A 74-element modified valence force field is derived by Wilson's GF matrix method using 58 experimental frequencies of the two molecules in overlay least-squares technique. The average error between observed and computed frequencies by this method is calculated to be 10.39 cm−1. The results of both DFT and IVP computations yielded good agreement between observed and calculated frequencies. The NLO behaviour using hyperpolarizability values; and HOMO and LUMO energies; of the two molecules are investigated by DFT. Charge density distribution and site of chemical reactivity of the molecules are studied by molecular electrostatic surface potential (MESP). Stability of the molecules arising from hyper conjugative interactions and charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The 13C and 1H NMR chemical shifts of the molecules are calculated by the gauge independent atomic orbital (GIAO) method and compared with experimental results. UV–visible (UV–Vis) spectra of the compounds are also recorded in the region 200–400 nm. Thermodynamic parameters and rotational constants are also determined and found that they are comparable with experimental literature values for these molecules.

Experimental and theoretical study of 3-methyl-4- nitrobenzoic acid using DFT and IVP methods

The Fourier Transform Infrared (FTIR) and FT-Raman spectra of 3-methyl-4- nitrobenzoic acid have been recorded in the range 4000-400 cm-1 and 3500-50 cm-1, respectively. The optimized geometry of the molecule, its vibrational frequencies have been computed using the Density Functional Theory (DFT) employing B3LYP/6-311++G basis set. The scaled values of harmonic vibrational frequencies so obtained have been compared with their experimental counter parts. The scaling factors have been refined to reproduce the frequencies with an RMS error of 9.26 cm-1 between the experimental and computed frequencies. The theoretically predicted FTIR and FT-Raman spectra agree satisfactorily with those of experimental spectra. A 89-parameter modified valence force field was evaluated by solving inverse vibrational problem (IVP) using Wilson's GF matrix method. The force constants were refined using 44 experimental frequencies of this molecule in overlay least- squares technique. The average error between observed and computed frequencies was found 11.61cm-1. PED and eigen vectors computed in the process were used to make unambiguous vibrational assignments of all the fundamental vibrations of this molecule. The values of dipole moment and hyperpolarizability were determined to study the NLO behaviour of this molecule. The HOMO and LUMO energies were also evaluated for this molecule.

Investigation of torsional potentials, molecular structure, vibrational properties, molecular characteristics and NBO analysis of some bipyridines using experimental and theoretical tools

The Fourier Transform Infrared (FTIR) and Fourier Transform Raman (FT-Raman) spectra of 2,2′-bipyridine (2BPE); 4,4′-bipyridine (4BPE); and 2,4′-bipyridine (24BPE) were measured in the range 4000–450 cm−1 and 4000–50 cm−1, respectively. Torsional potentials were evaluated at various angles of rotation around the C–C inter-ring bond for the three molecules in order to arrive at the molecular conformation of lowest energy. This conformation was further optimized to get ground state geometry. Vibrational frequencies along with infrared and Raman intensities were computed. In the above calculations, DFT employing B3LYP functional with 6311++G(d,p) basis set was used. The rms error between observed and calculated frequencies was 10.0, 10.9 and 10.2 cm−1 for 2BPE, 4BPE and 24BPE, respectively. A 54-parameter modified valence force field was derived by solving inverse vibrational problem using Wilson's GF matrix method. The force constants were refined using 117 experimental frequencies of the three molecules in overlay least-squares technique. The average error between observed and computed frequencies was 12.44 cm−1. PED and eigen vectors calculated in the process were used to make unambiguous vibrational assignments of all the fundamental vibrations. The values of dipole moment, polarizability and hyperpolarizability were computed to determine the NLO behaviour of these molecules. The HOMO and LUMO energies, thermodynamic parameters and molecular electrostatic surface potentials (MESP) were also evaluated. Stability of the molecules arising from hyper conjugative interactions, charge delocalization have been analyzed using natural bond orbital (NBO) analysis.

Experimental (FTIR and FT-Raman) and theoretical investigation of some pyridine-dicarboxylic acids

The FTIR and FT-Raman spectra of 2,3-pyridine-dicarboxylic acid (23PDA); 2,4-pyridine-dicarboxylic acid (24PDA); and 3,4-pyridine-dicarboxylic acid (34PDA) were recorded in the range 4000–450 cm−1 and 4000–50 cm−1, respectively. The optimized geometries and vibrational frequencies along with intensities were computed using DFT employing B3LYP functional with 6-311++G(d,p) basis set. The rms error between observed and calculated frequencies was 11.76, 12.79 and 9.8 cm−1 for 23PDA, 24PDA and 34PDA, respectively. A 74-parameter modified valence force field was evaluated by solving inverse vibrational problem using Wilson's GF matrix method and 99 experimental frequencies of the three molecules were used to refine the force constants in overlay least-squares technique. The average error between observed and computed frequencies was found to be 9.21 cm−1. PED and eigen vectors calculated in the process were used to make unambiguous vibrational assignments. The values of dipole moment, polarizability and hyperpolarizability were computed to determine the NLO behaviour of these molecules. The HOMO and LUMO energies and thermodynamic parameters were also evaluated.

Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation

We investigate the effect of confinement and orientation on the phonon transport properties of ultra-thin silicon layers of thicknesses between 1 nm and 16 nm. We employ the modified valence force field method to model the lattice dynamics and the ballistic Landauer transport formalism to calculate the thermal conductance. We consider the major thin layer surface orientations {100}, {110}, {111}, and {112}. For every surface orientation, we study thermal conductance as a function of the transport direction within the corresponding surface plane. We find that the ballistic thermal conductance in the thin layers is anisotropic, with the {110}/⟨110⟩ channels exhibiting the highest and the {112}/⟨111⟩ channels the lowest thermal conductance with a ratio of about two. We find that in the case of the {110} and {112} surfaces, different transport orientations can result in ∼50% anisotropy in thermal conductance. The thermal conductance of different transport orientations in the {100} and {111} layers, on the other hand, is mostly isotropic. These observations are invariant under different temperatures and layer thicknesses. We show that this behavior originates from the differences in the phonon group velocities, whereas the phonon density of states is very similar for all the thin layers examined. We finally show how the phonon velocities can be understood from the phonon spectrum of each channel. Our findings could be useful in the design of the thermal properties of ultra-thin Si layers for thermoelectric and thermal management applications.

Calculation of Confined Phonon Spectrum in Narrow Silicon Nanowires Using the Valence Force Field Method

We study the effect of confinement on the phonon properties of ultra-narrow silicon nanowires of side sizes of 1-10nm . We use the modified valence force field method to compute the phononic dispersion, and extract the density of states, the transmission function, the sound velocity, the ballistic thermal conductance and boundary scattering-limited diffusive thermal conductivity. We find that the phononic dispersion and the ballistic thermal conductance are functions of the geometrical features of the structures, i.e. the transport orientation and confinement dimension. The phonon group velocity and thermal conductance can vary by a factor of two depending on the geometrical features of the channel. The <110> nanowire has the highest group velocity and thermal conductance, whereas the <111> the lowest. The <111> channel is thus the most suitable orientation for thermoelectric devices based on Si nanowires since it also has a large power factor. Our findings could be useful in the thermal transport design of silicon-based devices for thermoelectric and thermal management applications.

Vibrational analysis and valence force field for nitrotoluenes, dimethylanilines and some substituted methylbenzenes

The Fourier transform infrared (FTIR) and Raman spectra of 2-amino-4-nitrotoluene; 2-amino-5-nitrotoluene; 2,4-dimethylaniline; 2,5-dimethylaniline; 2,6-dimethylaniline; 1,2,4-trimethylbenzene; 1,3,5-trimethylbenzene and pentamethylbenzene have been recorded in the range 4000–400cm−1 and 4000–30cm−1, respectively. A normal coordinate analysis was carried out for both in-plane and out-of-plane vibrations of these molecules using an 81-parameter modified valence force field. The force constants were refined using 369 frequencies of eight molecules in the overlay least-squares technique. The reliability of the force constants was tested by making a zero-order calculation for both in-plane and out-of-plane vibrations for five related molecules. The potential energy distributions and eigen vectors calculated in the process were used to make unambiguous vibrational assignments of all the fundamentals.

Shape and orientation effects on the ballistic phonon thermal properties of ultra-scaled Si nanowires

The effect of geometrical confinement, atomic position, and orientation of silicon nanowires (SiNWs) on their thermal properties are investigated using the phonon dispersion obtained using a Modified Valence Force Field (MVFF) model. The specific heat (Cν) and the ballistic thermal conductance (κlbal) shows anisotropic variation with changing cross-section shape and size of the SiNWs. The Cν increases with decreasing cross-section size for all the wires. The triangular wires show the largest Cν due to their highest surface-to-volume ratio. The square wires with [110] orientation show the maximum κlbal because they have the highest number of conducting phonon modes. At the nano-scale a universal scaling law for both Cν and κlbal are obtained with respect to the number of atoms in the unit cell. This scaling is independent of the shape, size, and orientation of the SiNWs, revealing a direct correlation of the lattice thermal properties to the atomistic properties of the nanowires. Thus, engineering the SiNW cross-section shape, size, and orientation open up new ways of tuning the thermal properties in the nanometer regime.

Influence of cross-section geometry and wire orientation on the phonon shifts in ultra-scaled Si nanowires

Engineering of the cross-section shape and size of ultra-scaled Si nanowires (SiNWs) provides an attractive way for tuning their structural properties. The acoustic and optical phonon shifts of the free-standing circular, hexagonal, square, and triangular SiNWs are calculated using a modified valence force field (MVFF) model. The acoustic phonon blue shift (acoustic hardening) and the optical phonon red shift (optical softening) show a strong dependence on the cross-section shape and size of the SiNWs. The triangular SiNWs have the least structural symmetry as revealed by the splitting of the degenerate flexural phonon modes and these show the minimum acoustic hardening and the maximum optical hardening. The acoustic hardening, in all SiNWs, is attributed to the decreasing difference in the vibrational energy distribution between the inner and the surface atoms with decreasing cross-section size. The optical softening is attributed to the reduced phonon group velocity and the localization of the vibrational energy density on the inner atoms. While the acoustic phonon shift shows a strong wire orientation dependence, the optical phonon softening is independent of wire orientation.

Strain effects on the phonon thermal properties of ultra-scaled Si nanowires

The impact of uniaxial and hydrostatic stress on the ballistic thermal conductance (κl) and the specific heat (Cν) of [100] and [110] Si nanowires are explored using a Modified Valence Force Field phonon model. An anisotropic behavior of κl and isotropic nature of Cν under strain are predicted for the two wire orientations. Compressive (tensile) strain decreases (increases) Cν. The Cv trend with strain is controlled by the high energy phonon sub-bands. Dominant contribution of the low/mid (low/high) energy bands in [100] ([110]) wire and their variation under strain governs the behavior of κl.

Ab initioparameterized valence force field for the structure and energetics of amorphous SiOx(0 ⩽x ⩽2) materials

We present a modified valence force field model for the structure and energetics of amorphous silicon suboxides (a-SiO${}_{x}$, 0 \ensuremath{\leqslant} $x$ \ensuremath{\leqslant} 2). The parameters are optimized to fit the results from cluster and periodic density-functional theory (DFT) calculations of various model structures. The potential model well reproduces the DFT energetics of various $a$-SiO${}_{x}$ systems for all O:Si composition ratios. We also examine how the choice of force fields affects the atomic-level description of phase separation in a-SiO${}_{x}$ and $a$-Si/$a$-SiO${}_{2}$ interfaces using a continuous random network model-based Monte Carlo approach. The results highlight the critical role of the relative rigidity between Si and SiO${}_{2}$ matrices in determination of the structural properties of the Si/SiO${}_{2}$ composite system, such as interface bond topology, degree of phase separation, and abruptness of the interface.

Tuning lattice thermal conductance by porosity control in ultrascaled Si and Ge nanowires

Porous nanowires (NWs) with tunable thermal conductance are examined as a candidate for thermoelectric devices with high efficiency. Thermal conductance (σl) of porous NWs is calculated using the phonon dispersion obtained from a modified valence force field model. Porosity in the NWs break the crystal symmetry leading to the reduction in ballistic σl. [100] Si and Ge NWs show similar percentage reductions in σl for the same amount of porosity. The model predicts an anisotropic reduction in σl in SiNWs, with [111] showing the maximum reduction followed by [100] and [110] for a similar hole radius. The reduction in σl is attributed to phonon localization and anisotropic mode reduction.

Tuning lattice thermal conductance in ultra-scaled hollow SiNW: Role of porosity size, density and distribution

ABSTRACTPorous crystalline Si nanowires (PC-SiNW) represent an attractive solution for enhancing the thermoelectric efficiency (ZT) of SiNWs by reducing the lattice thermal conductance (κl). A modified valence force field (MVFF) phonon model along with Landauer’s approach is used to analyze the ballistic κl in PC-SiNWs. A systematic study focusing on the influence of pore size, density, and distribution on the ballistic κl of PC-SiNWs is presented. The model predicts a maximum reduction of ∼19%, ∼23% and ∼30% for 1, 2 and 3 pores, respectively with a constant removal of ∼12% of the atoms in all the cases. The model also predicts a higher reduction of the ballistic κl as the pore separation increases, in the case of 2, 3 and 4 pores, for the same percentage of atoms removed (∼12%) in all the cases. Thus, the presence of a high number of small, well-separated pores suppress κl strongly. This reduction in ballistic κl, in the coherent limit, is attributed to the reduction of the total number of phonon modes and smaller participation of phonon modes (in κl) with increasing number of pores.

Modified valence force field approach for phonon dispersion: from zinc-blende bulk to nanowires

The correct estimation of the thermal properties of ultra-scaled CMOS and thermoelectric semiconductor devices demands for accurate phonon modeling in such structures. This work provides a detailed description of the modified valence force field (MVFF) method to obtain the phonon dispersion in zinc-blende semiconductors. The model is extended from bulk to nanowires after incorporating proper boundary conditions. The computational demands by the phonon calculation increase rapidly as the wire cross-section size increases. It is shown that nanowire phonon spectra differ considerably from the bulk dispersions. This manifests itself in the form of different physical and thermal properties in these wires. We believe that this model and approach will prove beneficial in the understanding of the lattice dynamics in the next generation ultra-scaled semiconductor devices.

Electron-intramolecular vibration coupling in TTF-TCNQ systems

We report calculations of the linear electron molecular vibration coupling constants in TCNQ, TCNQ−, and TTF. A complete neglect of differential overlap (cndo) type parameterization is used for the electronic structure and a modified valence force field (mvff) approach for the determination of the vibrational normal modes. Direct experimental information on the magnitude of the coupling constants can be obtained in the gaseous phase from photoemission experiments and in the solid state from polarized optical reflectance measurements on organic linear chain conductors. Agreement between theory and experiment is good. The relevance of electron-intramolecular vibrational coupling constants for the stabilization of the charge density wave (cdw) state in TCNQ anion radical salts and in the determination of polaron binding energies is stressed.

Vibrational analysis of mononitro substituted benzamides, benzaldehydes and toluenes: Part I. Vibrational spectra, normal coordinate analysis and transferability of force constants of nitrobenzamides, nitrobenzaldehydes and nitrotoluenes

The Raman and Fourier transform infrared (FTIR) spectra of p-, m- and o-nitrobenzamides, p-, m- and o-nitrobenzaldehydes and p-, m- and o-nitrotoluenes were recorded. Raman polarisation measurements were made for the liquid samples. A normal coordinate analysis was carried out for both in-plane and out-of-plane vibrations of these molecules using 111-parameter modified valence force field. The force constants were refined using 316 frequencies of nine molecules in an overlay least-square technique. The reliability of the force constants was tested by making a zero-order calculation for nine related molecules. Unambiguous vibrational assignments of all the fundamentals were made by using the potential energy distributions and eigen vectors.

Unit cell group analysis of rare earth elpasolites

Vibrational frequencies of rare earth elpasolites, with general formula M 2ALnX 6 (M=Cs, Rb; A=K, Na, Li; Ln=lanthanide element or yttrium; X=I, Br, Cl, F) have been determined from Raman spectroscopy and electronic absorption and emission spectra, at temperatures down to 10 K. A compilation has been made together with available literature data. The 10 unit cell group vibrational frequencies have been satisfactorily fitted by using a modified valence force field. The trends in the derived force constants are reasonable from a physical viewpoint.

Theoretical predictions of unstable two-phase regions in wurtzite group-III-nitride-based ternary and quaternary material systems using modified valence force field model

Group-III (B, Al, Ga, and In)-nitride quaternary alloys and group-III (Al, Ga, and In)-nitride-based mixed anion (As, P, and Sb) quaternary alloys are useful for blue and green light emitting devices and high-temperature, high-power, and high-frequency electronic devices. It is known that these alloys are very difficult to grow in certain compositional regions. The thermodynamical stability of these alloys is studied with respect to an unstable two-phase region in the phase field. The unstable two-phase region is predicted based on a strictly regular solution model. The interaction parameter used in our model is obtained analytically using the valence force field (VFF) model modified for wurtzite structures. The calculated interaction parameters, which are required to predict the unstable two-phase region, agree well with experimental results for related alloy systems. The modified VFF model can also be used to predict the microscopic crystal structure, such as first neighbor anion–cation bond lengths. In order to verify our calculations, we compare the calculated and experimental results for the first neighbor anion–cation bond lengths in the InGaN system. The calculated results agree well with the experimental results. From our calculation results, the unstable two-phase regions for four A1−x−yBxCyD type group-III-nitride quaternary alloys and nine A1−xBxC1−yDy type group-III-nitride mixed anion quaternary alloys are calculated. The predicted unstable two-phase regions agree well with experimentally observed regions of phase separation in ternary alloys, which suggests our model calculations can provide useful guidance in ternary and quaternary systems where there is no experimental data.