Anharmonic Vibrational Frequencies Research Articles

Ab Initio Structures and Stabilities of Doubly Charged Diatomic Metal Helides for the First Row Transition Metals

The electronic structure and molecular properties of doubly charge transition metal helides, HeX2+ (where X = Sc−Cu), have been investigated using the all-electron ROHF−UCCSD(T) method. Basis sets have been developed for the first row transition metals to elucidate trends in bonding, dissociation energies, and vibrational frequencies. The ground state for all the doubly charged helides exhibited a 3dn configuration. In addition, states with configurations that have holes in the metal 3dσ orbital exhibited greater binding energies. Relativistic effects have also been investigated using the Cowan-Griffin ansatz. Anharmonic vibrational frequencies have been determined variationally.

Theoretical study of infrared and Raman spectra of hydrated magnesium sulfate salts

Harmonic and anharmonic vibrational frequencies, as well as infrared and Raman intensities, are calculated for MgSO4⋅nH2O (n=1–3). Electronic structure theory at the second order Møller–Plesset perturbation theory level with a triple-ζ+polarization basis set is used to determine the geometry, energetics, charge distributions, and vibrational spectra of pure and hydrated MgSO4 salts. The direct vibrational self-consistent field method and its correlation corrected extension are used to determine anharmonic corrections to vibrational frequencies and infrared intensities for the pure MgSO4 and its complex with one water molecule. Very significant differences are found between vibrational spectra of water molecules in complexes with MgSO4 and pure water. Some of the O–H stretching frequencies are shifted to the red very significantly (by up to 2000 cm−1) upon complexation with magnesium sulfate. They should be observed between 1700 and 3000 cm−1, in a region very different from the corresponding O–H stretch frequency region of pure water (3700–3800 cm−1). In addition, the SO2 stretching vibrations are found at lower frequency regions than the water vibrations. They can serve as unique identifiers for the presence of sulfate salts. The predicted infrared and Raman spectra should be of valuable help in the design of future missions and analysis of observed data from the ice surface of Jupiter’s moon Europa that possibly contains hydrated MgSO4 salts.

Four-component relativistic Kohn-Sham theory.

A four-component relativistic implementation of Kohn-Sham theory for molecular systems is presented. The implementation is based on a nonredundant exponential parametrization of the Kohn-Sham energy, well suited to studies of molecular static and dynamic properties as well as of total electronic energies. Calculations are presented of the bond lengths and the harmonic and anharmonic vibrational frequencies of Au(2), Hg(2+)(2), HgAu(+), HgPt, and AuH. All calculations are based on the full four-component Dirac-Coulomb Hamiltonian, employing nonrelativistic local, gradient-corrected, and hybrid density functionals. The relevance of the Coulomb and Breit operators for the construction of relativistic functionals is discussed; it is argued that, at the relativistic level of density-functional theory and in the absence of a vector potential, the neglect of current functionals follows from the neglect of the Breit operator.

MD+QM calculations of the OH vibrational stretching band in an aqueous aluminium(III) chloride solution

The OH stretching vibrational band has been calculated by an ‘MD+QM’ approach for the water molecules in the first hydration shell of the Al 3+ ion in a dilute AlCl 3 aqueous solution. Molecular Dynamics-generated geometrical snapshots provided the molecular positions, which were subsequently used in ab initio calculations of charge-embedded ion-water clusters at the HF and B3LYP levels. The ion-water clusters which were treated quantum-mechanically were Al 3+(H 2O) 6(H 2O) x ( x=2 or 3), where a few water molecules from the second hydration shell were included. 60 oscillators were selected from the MD dumps, and anharmonic vibrational frequencies were computed from the ab initio-weighted energy curves. Density-of-states bands as well as infrared-intensity-weighted bands are presented. Our average frequency downshift is only 60% of the experimental downshift. Further refinement of the method will concentrate on the description of the remaining part of the second, and the third, hydration shells.

Explicitly correlated SCF study of anharmonic vibrations in (H2O)2

AbstractModeling solvation in high‐pressure liquid chromatography (HPLC) requires calculation of anharmonic vibrational frequencies of solvent clusters for a statistical partition function. An efficient computational method that includes electron correlation is highly desirable for large clusters. A modified version of the “soft Coulomb hole” method of Chakravorty and Clementi has recently been implemented in a Gaussian‐lobe‐orbital (GLO) program (PCLOBE) to include explicit electron–electron correlation in molecules. The soft Coulomb hole is based on a modified form of Coulomb's law: An algorithm has been developed to obtain the parameter “w” from a polynomial in the effective scaling of each primitive Gaussian orbital relative to the best single Gaussian of the H1s orbital. This method yields over 90% of the correlation energy for molecules of low symmetry for which the original formula of Chakravorty and Clementi does not apply. In this work, all the vibrations of the water dimer are treated anharmonically. A quartic perturbation of the harmonic vibrational modes is constrained to be equal to the exact Morse potential eigenvalue based on a three‐point fit. This work evaluates the usefulness of fitting a Morse potential to a hydrogen bond vibrational mode and finds it to be slightly better than using MP2 vibrational analysis for this important dimer. A three‐point estimate of the depth, De, of a Morse potential leads to a correction formula for anharmonicity in terms of the perturbed harmonic frequency: When scaled by 0.9141, the harmonic Morse method leads to essentially the same results as scaling the BPW91 local density method by 0.9827. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Ab initio calculations of anharmonic vibrational spectroscopy for hydrogen fluoride (HF) n ( n=3, 4) and mixed hydrogen fluoride/water (HF) n(H 2O) n ( n=1, 2, 4) clusters

Anharmonic vibrational frequencies and intensities are computed for hydrogen fluoride clusters (HF) n with n=3, 4 and mixed clusters of hydrogen fluoride with water (HF) n (H 2O) n where n=1, 2. For the (HF) 4(H 2O) 4 complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Potential energy surfaces for these systems are obtained at the MP2/TZP level of electronic structure theory. Vibrational states are calculated from the potential surface points using the correlation-corrected vibrational self-consistent field method. The method accounts for the anharmonicities and couplings between all vibrational modes and provides fairly accurate anharmonic vibrational spectra that can be directly compared with experimental results without a need for empirical scaling. For (HF) n , good agreement is found with experimental data. This agreement shows that the Møller–Plesset (MP2) potential surfaces for these systems are reasonably reliable. The accuracy is best for the stiff intramolecular modes, which indicates the validity of MP2 in describing coupling between intramolecular and intermolecular degrees of freedom. For (HF) n (H 2O) n experimental results are unavailable. The computed intramolecular frequencies show a strong dependence on cluster size. Intensity features are predicted for future experiments.

Quantum chemical calculations on FXeSiF

Quantum chemical calculations on FXeSiF are reported. The equilibrium structure, energetics, harmonic and anharmonic vibrational frequencies, and an analysis of the nature of bonding, is presented. All calculations are made at the MP2 level, while energetics is also considered via single-point CCSD(T) calculations. Energetical considerations of FXeSiF suggest that it should be stable compared to its decomposition pathways either via its bending coordinate to Xe+SiF 2 or via the stretching coordinate to F+Xe+SiF. Analysis of electron localization function (ELF) indicates that both fluorines are bound by interactions of unshared-electron type, i.e. by ionic interactions. The Xe–Si bond, however, is shown to be covalent, and this is the first time a covalent Xe–Si bond is predicted in a neutral molecule.

High-level ab initio study of LiO (X 2Π;A 2Σ+) and [formula omitted]: the ionization energy of LiO

RCCSD(T) calculations are performed using basis sets of quadruple- and quintuple-ζ quality. Potential energy curves are calculated for the lowest two neutral states of LiO (X 2 Π and A 2 Σ +), as well as the lowest two triplet states of LiO + (X 3 Σ − and A 3 Π). From these curves spectroscopic parameters are calculated, including anharmonic vibrational frequencies and rotational constants. For the X 2 Π state, excellent agreement with microwave and infrared values is obtained. The 2Σ +– 2Π separation is calculated to be 2419 cm −1 , and the first adiabatic ionization energy (AIE) corresponding to the process X 3 Σ −←X 2 Π is calculated to be 8.55±0.05 eV .

Anharmonic vibrational frequencies of proton transfer coordinates in the clusters of aromatic molecules with water

The vibrational frequencies of OH and NH groups which form hydrogen bonds to a water molecule are calculated using the complete active space self-consistent field (CASSCF) method and the second order perturbation theory based on the CASSCF reference (CASPT2). As model systems indole(H2O), phenol(H2O), and their corresponding cations are chosen. Furthermore, different isomers of the 3-aminophenol(H2O)+ and 4-aminophenol(H2O)+ clusters are considered. For all these clusters IR spectra are known, but the IR spectra of the ionic clusters in the region of the hydrogen-bonded OH and NH groups have not yet been well interpreted. Due to the strong anharmonicity of the OH and NH vibrations it is not possible to predict their frequencies by a simple scaling of harmonic values. By using different active spaces including both π-orbitals as well as σ-orbitals it is shown that the vibrational frequencies can be derived from potentials obtained from CASSCF single-point calculations along the OH and NH stretching modes. These vibrations can be regarded as proton-transfer coordinates. The calculated vibrational frequencies are in excellent agreement with the experimental values obtained for the investigated clusters. Furthermore, a strong shift of the OH stretching frequency is predicted by going from phenol(H2O)+ to aminophenol(H2O)+ clusters, explaining the completely different IR spectra of the investigated species.

Transition from Hydrogen Bonding to Ionization in (HCl)n(NH3)n and (HCl)n(H2O)n Clusters: Consequences for Anharmonic Vibrational Spectroscopy

Anharmonic vibrational frequencies and intensities are calculated for 1:1 and 2:2 (HCl)n(NH3)n and (HCl)n(H2O)n complexes, employing the correlation-corrected vibrational self-consistent field method with ab initio potential surfaces at the MP2/TZP computational level. In this method, the anharmonic coupling between all vibrational modes is included, which is found to be important for the systems studied. For the 4:4 (HCl)n(H2O)n complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Just as the (HCl)n(NH3)n structure switches from hydrogen-bonded to ionic for n = 2, the (HCl)n(H2O)n switches to ionic structure for n = 4. For (HCl)2(H2O)2, the lowest energy structure corresponds to the hydrogen-bonded form. However, configurations of the ionic form are separated from this minimum by a barrier of less than an O−H stretching quantum. This suggests the possibility of experiments on ionization dynamics using infrared excitation of the hydrogen-bonded form. The strong cooperative effects on the hydrogen bonding, and concomitant transition to ionic bonding, makes an accurate estimate of the large anharmonicity crucial for understanding the infrared spectra of these systems. The anharmonicity is typically of the order of several hundred wavenumbers for the proton stretching motions involved in hydrogen or ionic bonding, and can also be quite large for the intramolecular modes. In addition, the large cooperative effects in the 2:2 and higher order (HCl)n(H2O)n complexes may have interesting implications for solvation of hydrogen halides at ice surfaces.

The O–H(D) stretching potentials of the hydrogen bonded water molecules in MCl2·2H2O (M∈{Mn, Co, Fe}). Ab initio and density functional study

The uncoupled anharmonic O–H(D) stretching vibrations of the hydrogen bonded water molecules with local C2 symmetry in compounds of the type MCl2·2H2O (where M∈{Mn, Co, Fe}) were studied at various levels of theory, within the finite-cluster approach. The studied clusters consisted of one water molecule coordinated to the metal atom and hydrogen bonded to two chloride anions. The vibrational potential energy curves for the uncoupled OH stretching vibrations were obtained from pointwise energy calculations at HF, MP2 and gradient-corrected B3-LYP density functional levels of theory. To solve the HF or the Kohn–Sham equations, the standard 6-311G(d,p) basis set was used on O, H and Cl, while the transition metal atoms were treated within the LANL2DZ basis, employing an effective core potential (ECP) description of the inner shell electrons. From the calculated energies of the vibrational eigenstates, both the fundamental anharmonic and harmonic vibrational frequencies, as well as the anharmonicity constants were computed.

A gradient-corrected density functional study of indole self-association through N–H [formula omitted] hydrogen bonding

A B3LYP/6-31++G(d,p) study of indole dimer was performed. The optimized geometry reveals the existence of N–H⋯π hydrogen bond in which the benzenoid ring of one subunit acts as a proton acceptor, the interplanar angle between the two monomeric units being 89.4° (a T-shaped structure), with the center-of-mass separation of 6.207 Å. The counterpoise-corrected interaction energy is 2.15 kcal mol −1 (9.00 kJ mol −1) . Anharmonic vibrational frequencies of monomeric and dimeric N–H oscillators, their change upon dimerization and the intensity enhancement are excellently reproduced by one-dimensional B3LYP/6-31++G(d,p) vibrational potentials.

Ab initio anharmonic intermolecular potential of the C 2H 2–HCl hydrogen bonded complex

A grid calculation of the intermolecular potential of the hydrogen bonded C 2H 2–HCl complex has been performed at the CCSD(T)/cc-pVTZ level of theory. The effects of anharmonicity, of coupling between intramolecular and intermolecular motions, and of the basis set superposition error (BSSE) are independently considered. This calculation yields the center of mass separation of the complex, vibrationaly averaged and corrected of BSSE. It also provides the binding energy D e and the anharmonic vibrational frequency shift of the ν HCL band of the complex correlated with the HCl stretching mode. These properties are compared with experimental results and found to be in very good agreement.

Long live vinylidene! A new view of the H(2)C=C: --> HC triple bond CH rearrangement from ab initio molecular dynamics.

We present complete active space self-consistent field (CASSCF) ab initio molecular dynamics (AIMD) simulations of the preparation of the metastable species vinylidene, and its subsequent, highly exothermic isomerization to acetylene, via electron removal from vinylidene anion (D(2)C=C(-) --> D(2)C=C: --> DC triple bond CD). After equilibrating vinylidene anion-d(2) at either 600 +/- 300 K (slightly below the isomerization barrier) or 1440 K +/- 720 K (just above the isomerization barrier), we remove an electron to form a vibrationally excited singlet vinylidene-d(2) and follow its dynamical evolution for 1.0 ps. Remarkably, we find that none of the vinylidenes equilibrated at 600 K and only 20% of the vinylidenes equilibrated at 1440 K isomerized, suggesting average lifetimes >1 ps for vibrationally excited vinylidene-d(2). Since the anion and neutral vinylidene are structurally similar, and yet extremely different geometrically from the isomerization transition state (TS), neutral vinylidene is not formed near the TS so that it must live until it has sufficient instantaneous kinetic energy in the correct vibrational mode(s). The origin of the delay is explained via both orbital rearrangement and intramolecular vibrational energy redistribution (IVR) effects. Unique signatures of the isomerization dynamics are revealed in the anharmonic vibrational frequencies extracted from the AIMD, which should be observable by ultrafast vibrational spectroscopy and in fact are consistent with currently available experimental spectra. Most interestingly, of those trajectories that did isomerize, every one of them violated conventional transition-state theory by recrossing back to vinylidene multiple times, against conventional notions that expect highly exothermic reactions to be irreversible. The dynamical motion responsible for the multiple barrier recrossings involves strong mode-coupling between the vinylidene CD(2) rock and a local acetylene DCC bend mode that has been recently observed experimentally. The multiple barrier recrossings can be used, via a generalized definition of lifetime, to reconcile extremely disparate experimental estimates of vinylidene's lifetime (differing by at least 6 orders of magnitude). Last, a caveat: These results are constrained by the approximations inherent in the simulation (classical nuclear motion, neglect of rotation-vibration coupling, and restriction to C(s) symmetry); refinement of these predictions may be necessary when more exact simulations someday become feasible.

Direct calculation of anharmonic vibrational states of polyatomic molecules using density functional theory: spectroscopic tests of recently developed functionals

The anharmonic vibrational frequencies of H 2O, Cl −H 2O and (H 2O) 2 are calculated using potential energy surfaces computed from DFT, specifically the generalized-gradient approximation (GGA) functional HCTH and the hybrid functional B97(2c). HCTH gives reasonable agreement with experiment and can be recommended in situations where the use of a hybrid functional would be difficult. B97(2c) is found to be superior in accuracy to all other functionals tested and should be the functional of choice when the anharmonic potential energy surfaces of polyatomic systems are required for spectroscopic or similar applications. This point is illustrated by the excellent agreement with experiment obtained in calculations on formic and acetic acid using the B97(2c) functional.

Direct calculation of anharmonic vibrational states of polyatomic molecules using potential energy surfaces calculated from density functional theory

Potential energy surface points computed from variants of density functional theory (DFT) are used to calculate directly the anharmonic vibrational frequencies of H2O, Cl−H2O, and (H2O)2. The method is an adaptation to DFT of a recent algorithm for direct calculations of anharmonic vibrational frequencies using ab initio electronic structure codes. The DFT calculations are performed using the BLYP and the B3LYP functionals and the results are compared with experiment, and also with those calculated directly from a potential energy surface obtained using ab initio Möller-Plesset second–order perturbation theory (MP2). The direct calculation of the vibrational states from the potential energy points is performed using the correlation-corrected vibrational self-consistent field (CC-VSCF) method. This method includes anharmonicity and correlations between different vibrational modes. The accuracy of this method is examined and it is shown that for the experimentally measured transitions the errors in the CC-VSCF calculations are much less than the errors due to the potential energy surface. By comparison with the experimentally measured frequencies the CC-VSCF method thus provides a test for the quality of the potential energy surfaces. The results obtained with the B3LYP functional, in contrast to those of the BLYP functional, are of comparable quality to those obtained with MP2. The B3LYP anharmonic frequencies are in good agreement with experiment, showing this DFT method describes well the anharmonic part of the potential energy surface. The BLYP results systematically underestimate both the harmonic and anharmonic frequencies and indicate that using this functional for the description of hydrogen-bonded systems may cause significant errors.

Anharmonic force field and vibrational frequencies of tetrafluoromethane (CF4) and tetrafluorosilane (SiF4)

Accurate quartic anharmonic force fields for CF4 and SiF4 have been calculated using the CCSD(T) method and basis sets of spdf quality. Based on the ab initio force field with a minor empirical adjustment, the vibrational energy levels of these two molecules and their isotopomers are calculated by means of high order Canonical Van Vleck Perturbation Theory (CVPT) based on curvilinear coordinates. The calculated energies agree very well with the experimental data. The full quadratic force field of CF4 is further refined to the experimental data. The symmetrization of the Cartesian basis for arbitrary combination bands of Td group molecules is discussed using the circular promotion operator for the doubly degenerate modes, together with tabulated vector coupling coefficients. The extraction of the spectroscopic constants from our second order transformed Hamiltonian in curvilinear coordinates is discussed, and compared to a similar procedure in rectilinear coordinates.

Reliable theoretical treatment of molecular clusters: Counterpoise-corrected potential energy surface and anharmonic vibrational frequencies of the water dimer

Structure, properties and energetics of the water dimer were determined by counterpoise (CP)-corrected gradient optimization which apriori eliminates the basis set superposition error (BSSE). Calculations were carried out at the MP2 level with various basis sets up to the aug-cc-pVQZ one. Besides harmonic vibrational frequencies twelve-dimensional anharmonic frequencies were also determined using the second-order perturbation treatment. Harmonic and anharmonic frequencies were based on CP-corrected Hessians. The equilibrium geometry of the dimer differs from that determined by a standard optimization and the difference becomes small only for the largest basis set (aug-cc-pVQZ). The best theoretical estimate of the intermolecular oxygen–oxygen distance (2.92 A) is shorter than the experimental result of 2.95 A. An estimate of the complete basis set limit of the stabilization energy was obtained by extrapolating the stabilization energies as a function of the reciprocal size of the basis set; this value (21.05 kJ mol-1) is slightly smaller than other literature estimates. Adding the changes due to zero-point energy and temperature-dependent enthalpy terms (determined using anharmonic frequencies obtained from the CP-corrected Hessian) we obtain an estimate to the theoretical stabilization enthalpy at 375 K (12.76 kJ mol-1) which is by 0.8–1.3 kJ mol-1 smaller than the literature results. Our theoretical value supports the very low limit of the experimental value. Red shift of the O–H stretching frequency accompanying formation of the dimer was determined at various theoretical levels and best agreement with the experimental value was found for anharmonic frequencies calculated with CP-corrected Hessians.

Application of the generalized-gradient approximation to rare-gas dimers

By performing numerically precise calculations on the ${\mathrm{He}}_{2},$ ${\mathrm{Ne}}_{2},$ ${\mathrm{Ar}}_{2},$ ${\mathrm{Kr}}_{2},$ HeNe, HeAr, HeKr, NeAr, NeKr, and ArKr diatomic molecules we have determined the capacity of three popular approximations to density-functional theory to accurately describe bonding in these rare-gas systems. The local-density approximation, the Perdew-Wang 1991 generalized-gradient approximation, and the Perdew-Burke-Ernzerhof generalized-gradient approximation are utilized in the calculation of equilibrium bond lengths, atomization energies, and anharmonic and harmonic vibrational frequencies. We also use the density-functional-based determination of atomic polarizabilities and ionization potentials to obtain the coefficients for the long-range ${(1/r}^{6})$ attraction. Our calculations suggest that the interaction from the overlap of atomic densities is the primary binding mechanism in these systems at short range but that the long-range ${1/r}^{6}$ attraction could also contribute to the total binding energy.

The intermolecular potential energy surface of the Ar⋅NO+ cationic complex

The intermolecular potential energy surface of the Ar⋅NO+ cationic complex has been calculated using ab initio methods: RHF, MP2, MP3, MP4, CCSD, and CCSD(T), using the cc-pVDZ and cc-pVTZ basis sets. An additional surface was calculated at the MP2/cc-pVQZ level. All calculations were performed with a fixed NO+ bond length, but in one set of calculations the effect of variation of the NO+ bond length was studied. Finally, the MP2/cc-pVQZ intermolecular potential energy surface was recalculated by performing a point-by-point correction for basis set superposition error. All of these surfaces were used to extract anharmonic intermolecular vibrational frequencies, in order to compare to previous calculations, and experimental results. Rotational energy levels were also calculated.