Ground state properties of titaniumdiboride

Abstract

The electronics structure, the charge distribution and the total energy of hexagonal titaniumdiboride are calculated using non-local pseudopotentials in both the local density approximation (LDA) and the generalized gradient expansion approximation (GGA). In the LDA we obtain a = 3.023 Å, c = 3.166 Å and B_o = 271. GPa. For these quantities the GGA values are slightly lower and both compare well with experiment. We also determined selected elastic constants by fitting the total energies to a quadratic surface in the lattice parameters. Using strains that do not break the hexagonal symmetry we obtain C₁₁ + C₁₂ = 777.GPa, C₁₃ = 83. GPa and C₃₃ = 568. GPa. Again slightly lower values are obtained using the GGA. These values agree well with a recent experiment.     

Application of self-consistent-field ab initio calculations to organic molecules

The local symmetry force constants of propene have been calculated from extended (4–31 G) self-consistent-field ab initio energies. The previously developed scaling method was used to adjust seven scale factors on 84 observed frequencies of propene and deuterated analogues. The latter were taken from the literature. The average difference between observed and calculated frequencies amounted to 8·3 cm^-1 or 0·63 per cent. The stretching force constant of the carbon-carbon single bond was found to be 0·3–0·4 mdyn Å^-1 larger than those of ethane and propane. Force constants of the CH₃ groups in the series: ethane, propane, propene, methanol and dimethyl ether, written in local symmetry coordinates, seem to be transferable within about 2 per cent. Individual CH bond stretching force constants, written in internal coordinates, show significant chemical variations.     

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

The force constants and equilibrium geometry of water were calculated ab initio from Hartree-Fock self-consistent field wavefunctions using the force method, and a 53/31, a 73/3 + 1 and a 95/41 + 2 gaussian lobe basis set. The force method proved to be very economic and numerically accurate.

The calculated values agree well with the experimental ones. Especially good is the agreement for the interaction constant F_rα . Calculated force constants for the 95/41 + 2 basis are: F_r = 9·158 mdyn/å, F_α = 0·8513 mdyn/å, F_rα = +0·3007, F_rr = -0·1724; the experimental values from isotope frequencies are: F_r = 8·456, F_α = 0·762, F_rα = +0·246, F_rr = -0·100 mdyn/å. The agreement in the geometry is also good for the 95/41 + 2 basis r _e = 0·9518 å, α = 107·49°, and the experimental r _e = 0·9572 å, α = 104·52°.

Force constants were found to be quite insensitive to variation in the basis functions, all three sets giving almost the same result. On the other hand, the dipole moment derivative is very sensitive.     

Amorphous germanium II. Structural properties

The coherent X-ray scattering for momentum transfer, k, between 0·025 and 15·0 Å^?1 has been measured for a series of sputtered amorphous Ge films prepared at various substrate temperatures, T _s, between 0 and 350°C. Differences in the radial distribution function (RDF) of films of different T _s have been determined by an accurate differential scattering technique. The small angle scattering (SAS) of the films is less than 100 electron units for k < 1 Å^?1. From a combination of SAS, RDF and scanning electron microscope studies, it is concluded that an observed increase in film density with increasing T _s occurs through a reduction in the number of voids about 7 Å or less in diameter. No variation of bond length with T _s is found. With increasing T _s, there is an increase in first and second-neighbour coordination and a reduction in bond angle distortion.

The rate of change of coordination, C, with density, ρ₀, is found to be d ln C/d ln ρ₀ = 0·6±0·2. Using a new, general theory of the dependence of the RDF on the dihedral angle distribution, P(θ), it is shown that with increasing T _s there is an increased probability of dihedral angles corresponding to the staggered configuration. For all films, the experimental RDF between r = 4·5 and 6·2 Å agrees with a nearly random P(θ) distribution. Comparison of experimental RDF's of crystalline and amorphous Ge indicates the static distortion of the first-neighbour bond length has a standard deviation of only about 0·04 Å.     

The anharmonic force field and equilibrium structure of methane

The anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species ¹²CH₄, ¹³CH₄, ¹²CH₄, ¹²CH₃D, ¹²CHD₃ and ¹²CH₂D₂. Six of the thirteen cubic force constants have been determined experimentally, the remaining cubic constants being fixed at values derived from ab initio calculations. The quartic force field is very crude, in that only f_rrrr has been refined. It is concluded however that the cubic and quartic force fields, even though they are subject to limitations, provide a considerable improvement in the experimental determination of the r _e structure and the quadratic force field. The equilibrium bond length is found to be r _e(CH) = 1·085₈ ± 0·001 Å.     

Ab initio calculation of force constants and equilibrium geometries

Force constants of the molecules HF, NH₃, CH₄ and BH₄ ^- have been calculated ab initio by the force method with a 73/3 + 1 gaussian lobe basis set. The results, including a former calculation on H₂O, agree well with experiment: the average relative error is 12 per cent for the diagonal force constants and the average absolute error is 0·06 mdyn/Å for the off-diagonal ones. The trends are also correctly reproduced. It is concluded that ab initio calculations of this accuracy can help to solve a number of spectroscopic problems. Force constants of BH₄ ^- have been determined from a combination of spectroscopic and ab initio information. Geometries have been obtained with little computing work and show good agreement with experiment.     

An anharmonic force field for carbonyl sulphide

A 16-parameter force field for OCS based on curvilinear coordinates is presented in table 2 and the agreement between observed and calculated transitions and rotational constants is indicated in tables 4, 5 and 6. The computational approach differs from that of Morino and Nakagawa [2] and similar work on other molecules by other authors, in that perturbation theory is eschewed and the calculated vibrational transitions and rotational constants are derived via the numerical solution of a large matrix. The usual parameters x_ij , y_ijk , α _i ^B and γ _ij ^B are thereby rendered inappropriate intermediates. The approach also leads to estimates of B _e - B ₀ for each isotopic species and thence suggests equilibrium distances r _CO = 1·155386(21) Å and r _CS = 1·562021(17) Å.     

Geometry,strength of binding and Br2 charge redistribution in the complex OC ··· Br2 determined by rotational spectroscopy

The ground-state rotational spectra of the six isotopomers ¹⁶O¹²C ··· ⁷⁹Br⁷⁹Br, ¹⁶O¹²C ··· ⁸¹Br⁷⁹Br, ¹⁶O¹²C ··· ⁸¹Br⁸¹Br, ¹⁶O¹²C ··· ⁷⁹Br⁸¹Br, ¹⁶O¹³C ··· ⁷⁹Br⁷⁹Br, ¹⁶O¹³C ··· ⁸¹Br⁷⁹Br, were observed by pulsed-nozzle, Fourier-transform microwave spectroscopy. The spectroscopic constants B _O, D _J, χ _aa (Br_i), χ _aa (Br_o), M_bb (Br_i) and M _bb (Br_o), where i = inner and o = outer, were determined for each isotopomer. The complex is linear, with the weak bond between the C atom of CO and Br_i. The rotational constants were used to determine the distance r(C ··· Br_i) = 3.1058Å and to show that the Br—Br bond lengthens by ～0.005–0.01Å on complex formation. The intermolecular stretching force constant kσ = 5.0 Nm^?1 was obtained from D_J and the Br nuclear quadrupole coupling constants were interpreted to reveal that a fraction δ = 0.02 of an electronic charge is transferred from Br_i to Br_o when Br₂ is subsumed into the complex. Properties of the two series OC ··· XY and H₃N ··· XY, where XY = C1₂, Br₂ and BrC1, are compared.     

Resonance absorption and fluorescence in argon

Absorption cross sections of argon for argon resonance radiation have been measured by several techniques. The apparent cross sections are small (0·1 to 1·6 × 10^-18 cm²) for resonance absorption and the values depend on the technique used for measurement. These observations are interpreted in terms of extensive reversal and broadening in the source. The excitation and quenching of resonance fluorescence was studied to provide information about the rates of the processes

The rate constants were estimated relative to k _r, the rate constant for radiation. Radiation imprisonment leads to a reduction of k _r from its natural value and observations of the decay of resonance fluorescence suggest that k _r ～ 1·5 × 10⁵ s^-1 in our system at [Ar] = 2 × 10¹⁷ atom cm^-3. Combining this value with the relative values for the quenching rate constants gives k ₁ < 1·5 × 10^-13, k ₁′(M = N₂) ～ 6 × 10^-12, k ₁′(M = NO) ～ 4 × 10^-10, in units of cm³ s^-1 molecule^-1.     

Ab initio calculation of force constants for the linear molecules HCN,FCN, (CN)2 and the ion N2F+

Force constants have been calculated from ab initio Hartree-Fock wave-functions by the force method, using 7s3p/1 and 5s2p/1 gaussian basis sets for HCN, FCN, C₂N₂ and FN₂ ⁺. Agreement of the quadratic and some cubic force constants with experiment is good for HCN and FCN. The influence of anharmonicity upon the l-type doubling constant of FCN is estimated. Both the experimental l-type doubling constant and the ab initio calculations indicate that the quadratic stretch, stretch coupling constant is positive in FCN, contrary to recent results of Wang and Overend, obtained from the Anderson potential function. There is good agreement for the CN, C′N′ coupling in C₂N₂ but the calculated CN, CC coupling, although positive, is much lower than in two recent experimental force fields. The calculated FN, NN coupling in FN₂ ⁺ is small and positive. The predicted geometry of FN₂ ⁺ is r _NF = 1·28 Å, r _NN = 1·10₅ Å. The validity of the Anderson potential function is discussed.     

Coupled cluster calculations for the interstellar molecule HC3NH+

An accurate equilibrium structure has been established for the linear interstellar molecular cation HC₃NH⁺: r _1e(CH) = 1.0703Å, R _1e(C₍₁₎C₍₂₎) = 1.2097 Å, R _2e(C₍₂₎C₍₃₎) = 1.3509Å, R _3e(C₍₃₎N) = 1.1448 Å and r _2e(NH) = 1.0079Å. Ground-state rotational constants for less abundant isotopomers are predicted with an uncertainty of about 0.02 MHz. The equilibrium dipole moment of HC₃NH⁺ is calculated to be 1.61 D.     

Molecular force field and structure of water: Recent microwave results

Recently, microwave studies of the rotational spectra of water and its various isotopic species have been reported. These studies provide rotational constants and among others the quartic distortion constants, which depend on the quadratic part of the vibrational potential function. These data are collected and discussed, and the molecular force field and structure of water is considered in light of this recent microwave data. The quartic distortion data gives force constants which are very reasonable considering the difficulties in the distortion analysis of these light molecules, where as many as 22 parameters are being evaluated to fit the observed spectrum. The infrared and microwave data are combined within the theoretical framework of the small oscillations model and the results compare favorably with the true harmonic force field. The infrared and microwave valence bond force constants of H₂O are (mdyn/Å):

$\text{?}{}_{\mathrm{r}}\text{=7.746, ?}{}_{\mathrm{\theta }}\text{=0.700, ?}{}_{\mathrm{rr}}\text{=?0.093, ?}{}_{\mathrm{r\theta }}\text{=0.379}$

The results further confirm the usefulness of rotation-vibration data in the determination of force constans, and show that even for water with extremely large anharmonicity effects, a very representative force field can be obtained by combining ground state infrared and microwave data.Various molecular structures have been evaluated, and the average structures in the ground vibrational state for H₂O, D₂O and T₂O are found to be:

$\text{〈r〉}\text{〈θ}\text{O-H=0.9724}\text{A}\text{?}\text{HOH=104.50°}\text{O-D=0.9687}\text{A}\text{?}\text{DOD=104.35°}\text{O-T=0.9671}\text{A}\text{?}\text{TOT=104.26°}$

A one-dimensional approximation to the anharmonicity effects is applied to determine the equilibrium molecular structure of H₂O from the average structure data. The result is as follows:

$\text{r}{}_{\mathrm{e}}\text{=0.9587}\text{A}\text{?}\text{and θ}{}_{\mathrm{e}}\text{=103.9°}$

     

Structure and quadrupole coupling measurements on the NO dimer

Rotational transition frequencies for ¹⁴NO-¹⁴NO, ¹⁴NO-¹⁵NO, and ¹⁵NO-¹⁵NO were measured using a pulsed-nozzle Fourier transform microwave spectrometer. Rotational constants for the different isotopic combinations allowed an unambiguous structure determination. The molecule is in a cis planar structure with a bond between the nitrogen atoms and an NNO angle θ = 99.6(2)°. The NN bond length is 2.236(1) Å and the NO bond length is 1.161(4) Å. Hyperfine structure due to nitrogen quadrupole coupling and spin-rotation interactions was observed and analyzed. Rotation constants, quadrupole coupling tensor, and spin-rotation tensor elements are given.     

The structure of carbodiimide,HNCNH

An experimentally determined r _s -type structure of HNCNH is reported: r _NH = 1.0074 Å, r _CN = 1.2242 Å, ∠HNC = 118.63°, ∠NCN = 170.63°, ∠HN ··· NH = 88.99°. The number of digits quoted allow for errors with two significant figures. In order to obtain these values we recorded rotational—torsional spectra of HN¹³CNH, H¹⁵NC¹⁵NH and DNCND, by using isotopically enriched cyanamide. A chemical equilibrium exists between carbodiimide, HNCNH, and the more stable isomer cyanamide, H₂NCN, which strongly favours cyanamide (approximately 1:115 at 110 °C). The expensive C- and N-substituted isotopomers could only be investigated in the millimetre wave region, while for DNCND the far infrared spectrum between 10–350 cm^?1 was also recorded. Rotational constants of the three isotopomers, as well as of the parent species, were determined by fitting the assigned spectral transitions to the Watson Hamiltonian in S reduction. Using fitting programs written by Schwendeman and Rudolph, r _o, r_s and r^ρ _m structures of HNCNH were derived. The experimentally determined structural parameters are compared with an ab initio r_e structure.     

An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2

We have calculated ab initio the three-dimensional potential-energy surface of the NH₂ molecule at 145 nuclear geometries spanning energy ranges of about 18 000 cm^-1 for the NH stretch and 12 000 cm^-1 for the bend. The ab initio configuration-interaction calculations were done using the multireference MRD-CI method. The calculated equilibrium configuration has NH bond length r _e = 1·0207 Å and bond angle α = 103·1°. The rotational-vibrational energies for ¹⁴NH₂, ¹⁴NHD and ¹⁴ND₂ were calculated variationally using the Morse-oscillator rigid-bender internal-dynamics Hamiltonian. For ¹⁴NH₂ we calculate that υ₁ = 3267 (3219) cm^-1, υ₂ = 1462 (1497) cm^-1 and υ₃ = 3283 (3301) cm^-1, where experimental values are given in parentheses.     

The bond force constants and elastic properties of boron nitride nanosheets and nanoribbons using a hierarchical modeling approach

A hierarchical approach bridging the atomistic and nanometric scales is used to compute the elastic properties of boron nitride nanosheets and nanoribbons, examining the effect of sheet size, aspect ratio and anisotropy. The approach consists in obtaining the bond force (force field) constants by dedicated computations based on density functional theory (DFT) and using such constants as input for larger scale structural models solved by finite element analysis (FEA). The bond force constants calculated by DFT are 616.9 N/m for stretching, 6.27×10⁻¹⁹ Nm/rad² for in-plane rotation and 1.32×10⁻¹⁹ Nm/rad² for dihedral rotation. Using these constants, the elastic properties of boron nitride nanosheets and nanoribbons predicted by FEA are almost independent of the sheet size, but strongly dependent on their aspect ratio. The sheet anisotropy increases with increased aspect ratio, with nanoribbons of aspect ratios of 10 exhibiting a ratio of elastic moduli along both in-plane directions of 1.7.     

Infrared spectrum and vibrational potential function of the chlorite anion in the matrix-isolated M+ClO2− species

The chlorite anion, ClO₂^?, was prepared for spectral investigation by depositing alkali metal atoms and chlorine dioxide at high dilution in argon onto a 15°K optical surface. Intense infrared absorptions near 820, 790, and 420 cm^?1, which exhibited small alkali metal effects, are due to the three intraionic modes of the chlorite anion in the M⁺ClO₂^? species. The ClO force constant for ClO₂^? (4.11 mdyn/Å) is less than the value for ClO₂ (6.61 mdyn/Å), which is consistent with the antibonding character of the additional electron on ClO₂^?.     

Theoretical investigations of the structural,electronic and optical properties of Hg1−xCdxTe alloys

The structural, electronic and optical properties of mercury cadmium telluride (Hg_1?xCd_xTe; x = 0.0, 0.25, 0.5, 0.75) alloys are studied using density functional theory within full-potential linearized augmented plane wave method. We used the local density approximation (LDA), generalized gradient approximation (GGA), hybrid potentials, the modified Becke–Johnson (LDA/GGA)-mjb and Hubbard-corrected functionals (GGA/LDA + U), for the exchange-correlation potential (E_ex). We found that LDA functional predicts better lattice constants than GGA functional, whereas, both functionals fail to predict the correct electronic structure. However, the hybrid functionals were more successful. For the case of HgTe binary alloy, the GGA + U functional predicted a semi-metallic behaviour with an inverted band gap of ?0.539 eV, which is closest to the experimental value (?0.30 eV). Ternary alloys, however, are found to be semiconductors with direct band gaps. For the x = 0.25 and 0.50, the best band gaps are found to be 0.39 and 0.81 eV using LDA-mbj functional, whereas, the GGA-mbj functional predicted the best band gap of 1.09 eV for Hg_0.25Cd_0.75Te alloy, which is in a very good agreement with the experimental value (1.061 eV). The optical properties of the alloys are obtained by calculating the dielectric function ?(ω). The peaks of the optical dielectric functions are consistent with the electronic gap energies of the alloys.     

Photoelectron spectra of halides

High resolution photoelectron spectra, obtained with He I (584 Å) resonance radiation, are reported for ClF, ClF₃, BrF₃ and BrF (partial spectrum). In some cases Ne I (736–744 Å) radiation has also been used. Spinorbit and vibrational fine structure is resolved for the ground ²II states of ClF⁺ and BrF⁺; values obtained for ClF⁺ and ζ = 630 cm^-1, v′ = 870 cm^-1, and for BrF⁺ ζ = 2600 cm^-1, v′ = 750 cm^-1. From the vibrational envelope of the X ²∏ states, a bond length change of δr _e (-)0·10 Å for ClF⁺ and BrF⁺ is estimated. Ab initio SCF-MO calculations for ClF and ClF₃ are used to aid in the interpretation of the spectra via Koopmans' theorem. A considerable amount of charge delocalization in the trifluorides is inferred from the photoelectron spectra, and this is borne out by the calculations.