XY4 Molecules Research Articles

Analytical presentation of symmetrized vibrational functions of high symmetry molecules for applications in molecular spectroscopy and chemical physics: Accurate prediction of the vibrational spectrum of GeH[formula omitted] up to 8000 cm−1 as a relevant application example

We report here the analytical description of vibrational wave functions being most important for applications in quantum mechanics, molecular and chemical physics as applied to the high symmetry XY4 (Td) molecules. A general method is discussed and, for the first time, all vibrational functions of such molecule type are presented in an analytical and symmetrized form for all polyads up to the polyad number N=4. To illustrate the relevant application of the derived results, an accurate prediction of all vibrational band centers up to 8000 cm−1 is made for five stable isotopologues MGeH4(M=76,74,73,72,70) of the germane molecule.

Host isotope effects on the oxygen local vibrations in CdTe

Strong absorption peak observed near 350 cm−1 in the infrared spectrum of CdTe is assigned to a localized vibrational mode of 16O impurity atoms at tellurium sites. In this work, we studied the nature of these vibrations in terms of the effect of isotopic mass variations in the nearest neighbor Cd atoms. We showed that Cd atoms with 8 stable natural isotopes of varying abundances cause the observed line shape in the observed localized vibrational absorption peak. To calculate the effect of isotopic mass variations, we used the XY4 molecular model, X being the impurity atom at a host Te atom site and Y’s are various isotopes of the host Cd atoms. Corresponding frequencies of local modes were calculated for each possible combinations of neighboring Cd atoms. For an XY4 molecule with Td symmetry, only the triply degenerate mode is infrared active. The energies of this mode are higher than those of the others. This mode is possible only when all neigboring Cd atoms are the same isotope. To simulate the absorption data, we used a dynamical matrix approach where a force constant is given for each of the bending and stretching potential energy terms. By diagonalization of the dynamical matrix we were able to fit the calculated spectrum to the data with a proper choice of the bending and stretching force constants. A good agreement with the experiment as well as reported force constants for other impurities in CdTe is obtained.

Improved Theory of the Effective Dipole Moments and Absolute Line Strengths of the XY2 Asymmetric Top Molecules in the X2B1 Doublet Electronic States.

A new effective dipole moment model for the XY2 (C2v-symmetry) molecule in a doublet electronic state is derived that includes (as special cases) all currently known models of effective dipole moments for such types of molecules, and allows us to take into account the influence of spin-rotation interactions on the effective dipole moment operator that were not considered in the preceding studies. Necessary for the analysis of absolute line strengths, the matrix elements of this dipole moment operator are derived. A comparison with the previous analog models is made and discussed. The efficiency of the obtained results is illustrated, which have been applied to a set of the "forbidden" ΔKa=2 transitions of the ν3 band of the OClO free radical molecule.

σ‐Hole intermolecular interactions between carbon oxides and dihalogens: Ab‐initio investigations

Recently, halogen bonding (XB) has received increased attention as a new type of non-covalent interaction widely present in nature. In this work, quantum chemical calculations at DFT level have been carried out to investigate halogen bonding interactions between COn (n= 1 or 2) and dihalogen molecules XY (X=F, Cl, Br, I and Y=Cl, Br, I). Highly accurate all-electron data, estimated by CCSD(T) calculations, were used to benchmark the different levels of computational methods with the objective of finding the best accuracy/computational cost. Molecular electrostatic potential, interaction energy values, charge transfer, UV spectra, and natural bond orbital (NBO) analysis were determined to better understand the nature of the XB interaction. Density of states (DOS) and projected DOS were also computed. Hence, according to these results, the magnitude of the halogen bonding is affected by the halogen polarizability and electronegativity, where for the more polarizable and less electronegative halogen atoms, the σ-hole is bigger. Furthermore, for the halogen-bonded complexes involving CO and XY, the OC∙∙∙XY interaction is stronger than the CO∙∙∙XY interaction. Thus, the results presented here can establish fundamental characteristics of halogen bonding in media, which would be very helpful for applying this noncovalent interaction for the sustainable capture of carbon oxides.

On the method and results of calculation of vibrational tetrahedral sub-level energies and resonance interactions in vibrational spectra of high symmetry molecules: CH[formula omitted] and GeH[formula omitted] as an application of the XY[formula omitted] (T[formula omitted]) molecule

We report here the analytical description of one of the important problems in the study of XY4 (Td) molecules, namely, description of vibrational tetrahedral sub-level structures and resonance interactions caused by the high symmetry of a molecule. The results obtained are applied to description of the vibrational energy spectrum of the CH4 and GeH4 molecules.

Квантово-химическое исследование потенциалов взаимодействия молекул CF-=SUB=-4-=/SUB=-, CH-=SUB=-4-=/SUB=-, SiF-=SUB=-4-=/SUB=- и SiH-=SUB=-4-=/SUB=- с атомом Rb в основном и электронно-возбужденных состояниях

The potentials of the electronic states of RbXY4 molecules, XY4 = CF4, CH4, SiF4 and SiH4, correlating with the ground 5s 2S1/2 and excited 5p 2P1/2, 3/2 states of the Rb atom are studied using the methods of ab initio quantum chemistry. The calculations are performed by the SCF method of the full active space of orbitals, taking into account dynamic electronic correlations and spin-orbital interaction. It is established that the character of the interaction in the A and A' states, correlating respectively with the lower and upper states of the Rb 5p 2P1/2, 3/2 doublet and corresponding to the perpendicular orientation of the Rb p-orbital relative to the Rb–X axis, differ significantly (attraction or repulsion) for different XY4 molecules, which is explained by the difference in the charge distribution in the XY4 molecules. In order to evaluate the accuracy of the calculation results for RbXY4 molecules, similar calculations are performed for the diatomic RbAr molecule using different basis sets. It is found that, as compared with the A and A' states, the potential of the repulsive B state, which correlates with the upper state of the doublet and corresponds to the orientation of the Rb p-orbital along the Rb–X axis, is significantly more sensitive to the size of the basis set which is due to the accuracy of accounting for the configuration interaction with states that correlate with the Rb(6s 2S1/2) and Rb(4d 2D3/2, 5/2) states and other states of the Rb atom lying above Rb(5p 2P1/2, 3/2).

Ab Initio Study of the Interaction Potentials of CF-=SUB=-4-=/SUB=-, CH-=SUB=-4-=/SUB=-, SiF-=SUB=-4-=/SUB=- and SiH-=SUB=-4-=/SUB=- Molecules with the Rb Atom in the Ground and Electronically Excited States

The potentials of the electronic states of RbXY4 molecules, XY4 = CF4, CH4, SiF4 and SiH4, correlating with the ground 5s 2S1/2 and excited 5p ^2P1/2,3/2 states of the Rb atom are studied using the methods of ab initio quantum chemistry. The calculations are performed by the SCF method of the full active space of orbitals, taking into account dynamic electronic correlations and spin-orbital interaction. It is established that the character of the interaction in the A and A' states, correlating respectively with the lower and upper states of the Rb (5p ^2P1/2,3/2) doublet and corresponding to the perpendicular orientation of the Rb p-orbital relative to the Rb-X axis, differ significantly (attraction or repulsion) for different XY4 molecules, which is explained by the difference in the charge distribution in the XY4 molecules. In order to evaluate the accuracy of the calculation results for RbXY4 molecules, similar calculations are performed for the diatomic RbAr molecule using different basis sets. It is found that, as compared with the A and A' states, the potential of the repulsive B state, which correlates with the upper state of the doublet and corresponds to the orientation of the Rb p-orbital along the Rb-X axis, is significantly more sensitive to the size of the basis set which is due to the accuracy of accounting for the configuration interaction with states that correlate with the Rb (6s ^2S1/2) and Rb (4d ^2D3/2,5/2) states and other states of the Rb atom lying above Rb (5p ^2P1/2,3/2). Keywords: alkali metals, excited states, carbon tetrafluoride, quantum chemistry, ab initio calculations.

Isotopic relations for tetrahedral and octahedral molecules

The study and analysis of heavy spherical-top molecules is often not straightforward. The presence of hot bands and of many isotopologues can lead to a high line congestion very difficult for assignment. In this work, using a low-order model we have derived very simple isotopic relations in order to determine initial parameters of the analysis. We also show that an identical approach can be used for XY4 and XY6 molecules and all these results are illustrated by the comparison of numerical computations and experiments.

Regular/abnormal variation in the strength and nature of the halogen bond between H2Te and the dihalogens: Prominent effect of methyl substituents

The halogen‐bonded complexes between H2Te/Me2Te and the dihalogen molecules XY (XY = F2, Cl2, Br2, I2, ClF, ClBr, BrF, BrCl, BrI, IF, ICl, IBr) have been studied to investigate the dependence of its strength and nature on the halogen donor X and its adjoining atom Y, as well as the methyl groups in the electron donor. The interaction energy varies between −1.7 and − 43.5 kcal/mol, indicating that the Te atom in H2Te/Me2Te has a strong affinity for the dihalogen molecules. For the H2Te‐XY complex, the halogen bond is stronger for the heavier halogen donor X atom and the strong electron‐withdrawing group Y. However, for Me2Te‐XY, the halogen bond is stronger for the lighter halogen donor X atom. The H2Te/Me2Te‐F2 complex has the largest interaction energy, although the σ‐hole on F2 is the smallest in magnitude. In most of the complexes, the electrostatic and polarization contributions to the binding strength are similar in magnitude. However, for H2Te/Me2Te‐F2, the polarization contribution is much larger than the electrostatic contribution, with a significant contribution from charge transfer.

The σ-Hole Coulombic Interpretation of Trihalide Anion Formation.

It is shown that the interactions of dihalogen molecules XY with halide anions Z- to form trihalide anions (XYZ)- can be satisfactorily described as Coulombic, involving the σ-holes on the atoms Y, but only if polarization is taken into account. We have approximated the polarizing effect of the halide anion Z- by means of a unit negative point charge. The CCSD/aug-cc-pVTZ computed interaction energies ΔE correlate well with the most positive electrostatic potentials associated with the induced σ-holes over a ΔE range of -12 to -63 kcal mol-1 . The (XYZ)- anions are more stable when the central atom is the largest, as has been observed, because the central atom is then the most polarizable, making the electrostatic potential associated with its σ-hole more positive.

First high–resolution analysis of the dyad of 28SiD4: Appearance of the isotopic substitution properties in the XY4 (Td-symmetry) molecules

The high resolution infrared spectra of SiD4 were recorded with a Bruker IFS125 HR Fourier transform interferometer and analysed in the region of 550–800 cm−1 where the bands ν4 and ν2 are located. The 7279 transitions with Jmax. = 37 were assigned to the ν4/ν2 dyad (the ν2 band is forbidden in absorption for symmetry reasons, and its transitions can appear in the spectrum only because of Coriolis interaction with the allowed ν4 band). The subsequent weighted fit of experimentally assigned transitions was made with the Hamiltonian model which takes the resonance interactions between the (0001) and (0100) vibrational states into account. The initial values of the Hamiltonian parameters have been predicted on the basis of the isotopic substitution theory. As the result, a set of 33 fitted parameters was obtained which reproduces the initial 7279 ro–vibrational transitions with the drms=1.85×10−4 cm−1 which corresponds to the experimental uncertainties.

Linear σ-hole⋯C[tbnd]O⋯σ-hole intermolecular interactions between carbon monoxide and dihalogen molecules XY (X, Y = Cl, Br)

Carbon monoxide can interact with two dihalogen molecules XY (X, Y=Cl, Br) in the form of X(Y)⋯COX(Y)⋯CO⋯X(Y)X(Y) trimeric complex, and their nature and characteristics were investigated at MP2/aug-cc-pVDZ level without and with counterpoise method, together with single point calculations at CCSD(T)/aug-cc-pVDZ level. The optimized geometries, stretching modes and interaction energies of a series of X(Y)⋯COX(Y)⋯CO⋯X(Y)X(Y) trimeric complexes were obtained and discussed. The cooperativity in these complexes was evaluated. EDA analyses reveal that the electrostatic interaction is the dominant net driving force in each trimer, but the contributions of other interactions like exchange, dispersion and polarization interactions are also important. QTAIM and NCI analyses confirm the existence of attractive halogen-bonding interactions. Additionally, EDDMF analysis was employed for the component dimers of these trimers, which indicates that the formation of halogen-bonding interactions is closely related to the charge shift and the rearrangement of electronic density in the formation of these complexes. The results would provide valuable insight into for these linear halogen bonds.

Linear σ‐Hole Bonding Dimers and Trimers Between Dihalogen Molecules XY (X, Y=Cl, Br) and Carbon Monoxide

AbstractIntermolecular interactions between CO and dihalogen molecules XY (X, Y=Cl, Br) were investigated at MP2/aug‐cc‐pVDZ level without and with counterpoise method, and single point calculations at CCSD(T)/aug‐cc‐pVDZ level were performed. XY can interact with one or two CO to form linear σ‐hole bonding dimer or trimer. Their optimized geometries, stretching modes and interaction energies were investigated. The X⋅⋅⋅C (or Y⋅⋅⋅C) interaction is stronger and more competitive than X⋅⋅⋅O (or Y⋅⋅⋅O) interaction, so the OC⋅⋅⋅X−Y⋅⋅⋅CO complex is stronger and more competitive than the CO⋅⋅⋅X−Y⋅⋅⋅OC complex. The interaction strengths of trimeric complexes are dependent upon the property of XY, andthe anticooperative or diminutive effects were observed for them. Electrostatic interaction is the dominant net driving force for the formation of these dimers based on EDA analysis. The formation of two linear halogen bonds in each trimer was identified by bond paths and green circle isosurfaces appearing between the halogen and C (or O) atoms. The results would provide valuable insight into the competition and cooperativity of linear halogen bonds.

Simultaneous interactions of amphoteric halogen in XY (X = Cl, Br and Y = F, Cl, Br) with C and O atoms of CO2 in ring-shaped CO2·X(Y)·CO2 complexes

Dihalogen molecule XY (X=Cl and Br and Y=F, Cl and Br) can interact with two CO2 and form ring-shaped CO2·X(Y)·CO2 trimers, in which the X atom simultaneously interacts with C atom of one CO2 and O atom of the other CO2. Theoretical calculations show that their optimized geometries and stretching vibrational frequencies are different from the individual (CO2)2, CO2⋯XY and YX⋯CO2 dimers. Their interaction energies are stronger than the sum of the interaction energies of the individual dimers, revealing the cooperativity between the dimers. Their binding distances and interaction strengths are closely associated with the electronegativity of X and Y atoms. Energy decomposition analysis suggests that electrostatic force is the main net contribution to total interaction energy. Quantum theory of atoms in molecules analysis confirms the formation of ring-shaped structures and the cooperativity between the dimers. Molecular electrostatic potential was employed to elucidate the formation mechanisms of ring-shaped trimers.

Prediction and characterization of halogen bonds involving formamidine and its derivatives

Ab initio calculations have been carried out for the complexes of formamidine (FA) and some representative halogenated molecules XY (X=Cl, Br, and I; Y=F, CCH, CF3, CN, and NC). The FA-(Z) complex combines with the halogenated molecule through a halogen bond, while the FA-(E) complex is stabilized jointly by both a halogen bond and a X⋯H interaction. The FA-(E) complex is more stable than the FA-(Z) counterpart, with the interaction energy of −3.4 to −23.4kcal/mol, indicating that FA is a good electron donor in halogen bonding. The methyl substituent particularly one at the imino nitrogen atom of FA has an enhancing effect on the strength of halogen bond. The similar effect is found for the phenyl and pyridyl substituents, depending on the FA conformation and substitution position of pyridyl. The stability of stronger halogen bonding is mainly attributed to electrostatic and polarization energies, which is different from the weak one with an electrostatic nature.

Quartic canonical force field in curvilinear internal coordinates for XY3 (D3h) molecules. The case of the BH3 molecule.

Using the canonical force field theory, expressions of quadratic, cubic, and quartic canonical force constants are obtained for XY3 (D3h) molecules in curvilinear redundant coordinates, i.e., simple valence internal coordinates (VICs), in terms of force constants in normal coordinates and in independent symmetry coordinates. To carry out this task, it was previously necessary to obtain for the first time the non-linear redundancy relation and the corresponding orthogonal projection onto the pure vibrational manifold for XY3 (D3h) molecules corresponding to a set of seven VICs. As an application, the quartic canonical force field in curvilinear redundant internal coordinates of BH3 is determined from ab initio force fields in normal coordinates calculated at the coupled-cluster singles and doubles level with perturbative treatment of the triples in conjunction with a triple- and quadruple-ζ size basis set. This anharmonic force field so obtained for the borane molecule, and in general for XY3 (D3h) molecules, is uniquely defined (therefore in an unambiguous form) and depending on the same number of parameters, i.e., force constants, when independent coordinates (natural or symmetry) are used in its description.

Ab initio study of NMR shielding constants and spin-rotation constants in N, P and As diatomic molecules

Ab initio calculations of NMR shielding constants and spin-rotation constants of six diatomic molecules XY where X, Y = N, P or As are described. We analyse the dependence of the results on the description of the correlation effects and their convergence with the extension of the basis set. Our best results, obtained at the CCSD(T)/cc-pV5Zs,p-unc level, appear to be sufficiently accurate for the smaller diatomics—N 2, PN and P 2; for the AsN, AsP and As 2 molecules large relativistic effects should be taken into account. Moreover, relativistic four-component density functional calculations of NMR shielding constants for the latter molecules demonstrate that the relativistic corrections cannot be determined at the Hartree–Fock level. The computed spin-rotation constants for PN and AsP can be compared with experimental data, the differences between theory and experiment are below 2% for PN and ≈10% for AsP.

Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY3 molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH3 where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].

Novel Halogen-Bonded Complexes H3NBH3···XY (XY = ClF, ClCl, BrF, BrCl, and BrBr): Partially Covalent Character

Quantum chemical calculations have been performed to study the interaction of H(3)NBH(3) with dihalogen molecules XY (XY = ClF, ClCl, BrF, BrCl, and BrBr) at the MP2/aug-cc-pVTZ level. It is shown that a halogen-hydride halogen bond is formed between the two molecules, in which the sigma electron of the B-H bond in H(3)NBH(3) acts as the electron donor. The strength of the halogen bond ranges from 14.82 kJ/mol in H(3)NBH(3)-ClCl complex to 40.13 kJ/mol in H(3)NBH(3)-BrF complex at the CCSD(T)/aug-cc-pVTZ level, which is comparable to medium strong hydrogen bonds. The B-H and X-Y bonds are elongated with a concomitance of a red shift. The analyses of natural bond orbital and atoms in molecules have been carried out to understand the nature of properties of this novel interaction. The results show that this interaction has partially covalent character.

Comparison in the complexes of oxygen-containing σ-electron donor with hydrogen halide and dihalogen molecules

Ab initio and “Atoms in Molecules” studies have been carried on the intermolecular interactions between oxygen-containing σ-electron donors B (B = H 2O, H 2CO, (CH 2) 2O) and hydrogen halide HY and dihalogen molecules XY (X, Y = F, Cl, Br). The geometries, energies and topological characteristics of hydrogen-bonded systems have been compared with those of halogen-bonded systems. In general, many properties of the halogen bond are analogous to those of the hydrogen bond. For the same electron acceptor H or X atom, the properties such as bond distance, binding energy, electron density and charge transfer decrease in the sequence of B···HF > B···HCl > B···HBr, B···ClF > B···Cl 2, B···BrF > B···BrCl > B···Br 2. The bond distance, frequency shift and electron density may be applied as the measure of strength of hydrogen and halogen bond. The decrease in the atomic dipolar polarization and the atomic volume are dependent of the strength of halogen-bonded interaction, while they are independent of the strength of hydrogen-bonded interaction.