A truncation/recoupling method for eigenvalues and eigenvectors ideal for parallel computation

Summary We review a new truncation/recoupling method to obtain eigenvalues and eigenvectors of anF-mode vibrational Hamiltonian. In particular we focus on the block diagonalization aspects of the method which are ideal for massive parallelization, and we demonstrate this using H₂O₂ as an example. We then present vibrational energies for non-rotating HO₂ and HCN, which illustrate several key advantages of this method.     

Vibrational spectra and H-bondings in anhydrous and monohydrate α-Zr phosphates

A new FTIR and FT-Raman investigation on α-zirconium phosphate (Zr(HPO₄)₂·H₂O) and its anhydrous form has been performed in order to obtain an affordable assignment of their vibrational spectra as well as to highlight the hydrogen bonding structure formed by the P-OH groups and the intercalated water molecules. To this end the spectral changes induced by both temperature and isotopic exchange were observed on several high-purity grade samples of different morphology especially prepared and well characterized by SEM, RX, DSC and TGA. In particular, it is also presented as a detailed discussion of the results obtained by FTIR-PAS for different sample morphology. The observed spectra have been analyzed and interpreted according to the α-Zr(HPO₄)₂·H₂O crystal structure and H-bond geometry. The obtained results allowed to clarify the mechanism of the α-Zr(HPO₄)₂·H₂O→α-Zr(HPO₄)₂ dehydration process as well as the H-bonding changes involved in the high temperature phase transition of anhydrous α-Zr(HPO₄)₂.     

Gegenbauer polynomials in a theoretical study of the vibrational structure of the Ca+–H2 system

This work presents an application of Gegenbauer polynomials in vibrational calculations. We illustrated that by example calculations of vibrational structure of the Ca⁺–H₂ exciplex, in the state correlated with 3D calcium ion state. For this case Gegenbauer polynomials are used for formation of a basis set for a bending mode. We showed that this basis set leads to a faster convergence of results than a basis set formed from Legendre polynomials. Additionally we compared vibrational structure obtained in this manner with results of discrete variable representation-distributed Gaussian basis (DVR–DGB) method.     

Zur formelmäßigen Berechnung der Zuordnung von schwingungsspektroskopischen Frequenzen

For Analytical Calculation of Assignments of Vibrational Spectroscopic Frequencies Using the normal coordinate treatment we calculate assignments of vibrational spectroscopic frequencies of the systems X₃ ( D _3h) and X₄ ( T d) and partially of the systems XY₄ ( D _4h) and XY₆ ( O _h).     

Molecular analysis of water clusters: Calculation of the cluster structures and vibrational spectrum using density functional theory

Density functional theory (DFT) is applied to obtain absorption spectra at THz frequencies for molecular clusters of H₂O. The vibrational modes of the clusters are calculated. Coupling among molecular vibrational modes explains their spectral features associated with THz excitation. THz excitation is associated with vibrational frequencies which are here calculated within the DFT approximation of electronic states. This is done for both isolated molecules and collections of molecules in a cluster. The principal result of the paper is that a crystal-like cluster of 38 water molecules together with a continuum solvent background is sufficient to replicate well the experimental vibrational frequencies.     

Scaled Quantum Mechanical Force Fields for the Peroxynitrates. II. Fluorocarbonyl Peroxynitrate and Chlorocarbonyl Peroxynitrate.

The vibrational properties of fluorocarbonyl peroxynitrate, FC(O)OONO₂ and chlorocarbonyl peroxynitrate, ClC(O)OONO₂ were studied by means of density functional theory (DFT) methods. The obtained results served to revise the reported experimental spectra and their corresponding assignments. Subsequently, the revised data were used in the definition of scaled quantum mechanics (SQM) force fields for these peroxynitrates. A set of internal force constants was also calculated from such force fields.     

Bis(trifluoromethyl)dicarbonate, CF3OC(O)OC(O)OCF3

The synthesis of the new compound, bis(trifluoromethyl)dicarbonate, CF₃OC(O)OC(O)OCF₃, is carried out by reduction of bis(trifluoromethyl)trioxidicarbonate with excess of CO at 0 °C. The product is characterized by IR, Raman, ¹³C and ¹⁹F NMR spectroscopy and its properties are compared with those of the other members of the series CF₃OC(O)O_xC(O)OCF₃, x = 0-3. Single crystals are grown at −25 °C and the X-ray diffraction analysis shows the packing of syn-syn rotamers exhibiting C₂ symmetry. DFT calculations predict this rotamer as the most stable one and also structural and vibrational data are predicted reasonably well.     

Vibrational spectra and reinvestigation of the crystal structure of a polymeric copper(II)-orotate complex, [Cu(μ-HOr)(H2O)2]n: The performance of new DFT methods, M06 and M05-2X, in theoretical studies

The crystal and molecular structure of a polymeric Cu(II)-orotate complex, [Cu(μ-HOr)(H₂O)₂]_n, has been reinvestigated by single crystal X-ray diffraction. It is shown that several synergistic interactions: two axial Cu-O interactions; intramolecular and intermolecular hydrogen bonds; and π-π stacking between the uracil rings contribute to the stability of the crystal structure. The Raman and FT-IR spectra of the title complex are reported for the first time. Comprehensive theoretical studies have been performed by using three unrestricted DFT methods: B3LYP; and the recently developed M06, and M05-2X density functionals. Clear-cut assignments of all the bands in the vibrational spectra have been made on the basis of the calculated potential energy distribution, PED. The very strong Raman band at 1219 cm⁻¹ is diagnostic for the N1-deprotonation of the uracil ring and formation of the copper-nitrogen bond, in this complex. The Cu-O (carboxylate) stretching vibration is observed at 287 cm⁻¹ in the IR spectrum, while the Cu-N (U ring) stretching vibration is assigned to the strong Raman band at 263 cm⁻¹. The molecular structure and vibrational spectra (frequencies and intensities) calculated by the M06 functional method are very similar to the results obtained by the B3LYP method, but M06 performs better than B3LYP in calculations of the geometrical parameters and vibrational frequencies of the interligand O-H?O hydrogen bonding. Unfortunately, the M05-2X method seriously overestimates the strength of interligand hydrogen bond.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X²∑⁺_g of the fluorine molecule have been ac-curately reconstructed employing the Ryderg-Klein-Rees (RKR) method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the cor-responding radial one-dimensional Schr?dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimen-tal data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm?1 and the relative de-viation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F₂ ground state.     

Vibrational spectroscopy,electrical characterization,nonlinear optical properties and DFT calculation of (NEt4)(H2AsO4)(H3AsO4)2

An organic-inorganic compound of tetraethylammonium dihydrogenarsenate bis(arsenic acid) salts of formula (NEt₄)(H₂AsO₄)(H₃AsO₄)₂, a potential new nonlinear optical material, was prepared by a slow evaporation technique and characterized by IR and Raman spectroscopy accomplished with DFT calculation and electrical-dielectrical measurements. The structure has been solved using direct method and refined by least-squares analysis. In this case, the structure consists of infinite parallel two-dimensional planes built of mutually H₂AsO₄^?, H₃AsO₄ tetrahedra connected by strong O–H?O hydrogen bonding giving birth to trimers. The geometry, first hyperpolarizability and harmonic vibrational wavenumbers were calculated by means of density functional theory (DFT) with the B3LYP/6-31G(d) level of theory. Good consistency was found between the calculated and the experimental structure, IR, and Raman results. The first hyperpolarizability β_tot of the title compound is about 1.75 times more than that of the reference crystal KDP. The complex impedance has been investigated in relation to the temperature and frequency ranges 297 and 373 K and 1 to 100 KHz, respectively. The conductivity temperature variation shows a typical Arrhenius-type behavior with a linear dependence on logarithm of conductivity. Transport properties in this material appear to be due to proton hopping mechanism.     

Eine neue Synthese für Nitrosyl‐Salze mit schwach koordinierenden Anionen am Beispiel von NO[B(CF3)4]

A New Synthesis for Nitrosyl Salts with Weakly Coordinating Anions Exemplified by NO[B(CF₃)₄] A new synthesis for nitrosyl salts of weakly coordinating anions is described, using the corresponding guanidinium salts as starting materials. The guanidinium salt [C(NH₂)₃][B(CF₃)₄] was obtained by a metathesis reaction of K[B(CF₃)₄] with [C(NH₂)₃]Cl. Treatment of the guanidinium salt with liquid NO₂ resulted in analytical pure NO[B(CF₃)₄] in quantitative yield. The guanidinium and nitrosyl tetrakis(trifluormethyl)borates were characterized by vibrational and NMR spectroscopy as well as by DSC measurements.     

Optical Study of Radicals (OH, O, H, N) in a Needle-plate Negative Pulsed Streamer Corona Discharge

Optical emission spectroscopy has been applied to study the OH radicals and O, H, and N active atoms produced by a high-voltage negative pulsed streamer corona discharge of N₂ and H₂O mixture gas in a needle-plate reactor at one atmosphere. The relative vibrational populations and the vibrational temperature of N₂(C, v′) were determined. The effects of pulsed peak voltage, pulsed repetition rate, and the addition of O₂ on the relative populations of OH(A²Σ) radicals, O(3p⁵P), H_α (3P), and N(3p⁴P) active atoms were investigated. It was found that the relative populations of those radicals increase with increasing pulsed peak voltage and pulsed repetition rate. The relative population of OH(A²Σ) radicals decreases with increasing O₂ flow rate, while the relative populations of O (3p⁵P), H_α (3P), and N (3p⁴P) active atoms exhibit a maximum over the studied range of the O₂ flow rate. The involved physicochemical processes have also been discussed.     

Darstellung und spektroskopische Charakterisierung von Perfluor(isopropyl)trifluoracetylperoxid (CF3)2C(F)OOC(O)CF3

Preparation and Spectroscopic Characterization of Perfluoro(isopropyl)-trifluoroacetylperoxide (CF₃)₂C(F)OOC(O)CF₃ The reaction of perfluoroacetone (CF₃)₂CO with OF₂ in a ratio 2 : 1 yields Perfluoro(isopropyl)-trifluoroacetylperoxide (CF₃)₂C(F)OOC(O)CF₃. The reaction only occurs under CsF-catalysis. (CF₃)₂C(F)OOC(O)CF₃ is characterized by vibrational, nmr and mass spectra. Using an excess of OF₂ does not give any stable product.     

Anab initio study of the molecules P2O and P2O+

Summary This paper presents a detailedab initio study of the molecules P₂O and P₂O⁺ at the Hartree-Fock, and Multi-Reference Single and Double Excitation Configuration Interaction levels. An analysis of the geometries and relative stabilities of both molecules is presented, together with a discussion of the dissociation channels and of the electronic spectrum of linear P₂O. The results for the ionic species P₂O⁺ suggest a cyclic geometry for this molecule, as indicated by the calculated vibrational frequencies. The calculations also indicate a surface crossing at a relatively low energy which might lead to P₂O dissociation and may hence be one of the factors contributing to the failure to detect it at room temperatures.     

Interpretation der Schwingungsspektren von (CH3)2SO2, (CH3)2SO(NH) und (CH3)2S(NH)2 unter Verwendung eines Kopplungsstufenverfahrens

Normal Coordinate Analysis of (CH₃)₂SO₂, (CH₃)₂SO(NH), and (CH₃)₂S(NH)₂ using the Method of Stepwise Coupling The qualitative assignment of the vibrational spectra of (CH₃)₂SO₂ ( 1 ), (CH₃)₂SO(NH) ( 2 a ), and (CH₃)₂S(NH)₂ ( 3 a ) and of the C and N deuterated derivatives of 2 a and 3 a is used in a normal coordinate analysis by the method of stepwise coupling. The force constants and the energy distributions are calculated in symmetry coordinates using a generalized valence force field.     

UV Spectrum of the Simplest Deuterated Criegee Intermediate CD2OO

The ultraviolet (UV ) absorption spectrum of the simplest deuterated Criegee intermediate CD₂OO has been measured and compared with that of CH₂OO . While the UV spectra of CH₂OO and CD₂OO are similar in the overall shape, distinctive oscillatory structures at the long wavelength side of the absorption band show clear effect of isotopic substitution. The average spacing between the vibrational peaks decreases from 606 cm⁻¹ for CH₂OO to 528 cm⁻¹ for CD₂OO . This large isotope effect cannot be explained by one‐dimensional model along the dissociative O−O bond. Instead, vibrational modes involving motions of the H‐atoms are expected to be responsible for the observed oscillatory structure. This isotope effect offers a stringent test for theoretical investigations on the absorption spectrum and excited‐state dynamics of the simplest Criegee intermediate.     

Molecular structure, IR spectra of 2-mercaptobenzothiazole and 2-mercaptobenzoxazole by density functional theory and ab initio Hartree–Fock calculations

Quantum chemistry calculations have been performed using Gaussian03 program to compute optimized geometry, harmonic vibrational frequency along with intensities in IR and Raman spectra and atomic charges at RHF/6-31+G*, B3LYP/6-31+G* and B3LYP/6-31++G* levels for 2-mercaptobenzothiazole (MBT, C₇H₅NS₂) and 2-mercaptobenzoxazole (MBO, C₇H₅NOS) in the ground state. The scaled harmonic vibrational frequencies have been compared with experimental FT-IR and FT-Raman spectra. The results show that the scaled theoretical vibrational frequencies is very good agreement with the experimental values. A detailed interpretation of the infrared and Raman spectra of 2-mercaptobenzothiazole and 2-mercaptobenzoxazole was reported. Comparison of calculated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes.     

Synthesis,Crystal Structure and Vibrational Spectra of Barium Cyclotetraphosphate Hydrate Ba2(P4O12)∙3.5H2O

Barium tetrametaphosphate hydrate Ba₂(P₄O₁₂)∙3.5H₂O was synthesized as a single‐phase crystalline powder starting from an aqueous solution of barium hydroxide and phosphorus pentoxide at 300 K. Ba₂(P₄O₁₂)∙3.5H₂O crystallizes in a new structure type in which the Ba²⁺ ions form a distorted hexagonal diamond‐like arrangement with the (P₄O₁₂)^4– anions in the trigonal prismatic voids (Ba₂(P₄O₁₂)∙3.5H₂O, C2/c, Z = 4, a = 777.3(2), b = 1297.6(2), c = 1346.1(3) pm, b = 95.38(2)°, wR₂ = 0.071, R₁ = 0.018, 1180 reflections, 118 parameters). The vibrational spectra of Ba₂(P₄O₁₂)∙3.5H₂O and its thermal behavior up to 720 K are also reported.     

Vibrational Properties of [FeH(N2)(depe)2]+ and [FeCl(N2)(depe)2]+]: Dinitrogen Bonding in the Low Activation Limit

The vibrational properties of the two octahedral Fe^II dinitrogen complexes [FeH(N₂)(depe)₂]⁺ ( 1 ) and [FeCl(N₂)(depe)₂]⁺ ( 2 , depe = 1, 2‐bis(diethylphosphino)ethane) are investigated with the help of infrared and Raman spectroscopies. Vibrational data are evaluated with a Quantum Chemistry Assisted Normal Coordinate Analysis (QCA‐NCA; N. Lehnert, F. Tuczek, Inorg. Chem. 1999 , 38, 1659). In agreement with high values found for ν(NN) and the corresponding force constants f(NN), the N₂ ligands in compounds 1 and 2 are non‐activated which corresponds to the observation that N₂ is not protonable in Fe^II systems. Taking into account the short Fe‐N bond lengths, the values of the Fe‐N stretching force constants (2.55mdyn/Å for 1 and 2.58mdyn/Å for 2 ) are found to be compatible with those of other Fe^II low‐spin compounds coordinated to backbonding N‐coordinating ligands. The force fields obtained for the Fe‐N₂ units of 1 and 2 are almost identical although the thermal stability of 1 and 2 with respect to loss of N₂ is different. This indicates that the zero‐point vibrational levels are unaffected by possible ground‐state level crossing processes occuring at larger Fe‐N bond lengths, as observed for 2 (O. Franke, B. E. Wiesler, N. Lehnert, C. Näther, V. Ksenofontov, J. Neuhausen, F. Tuczek, Inorg. Chem. 2002 , 41, 3491).