Accurate Vibrational Frequencies Research Articles

Engineering application of a safety-state evaluation model for hidden frame-supported glass curtain walls based on remote vibration

Laser doppler vibrometer (LDV), which has measurement advantages such as being remote and non-contact, accurate, and having rapid dynamic response, is a useful assessment tool for the safety-state evaluation of hidden frame-supported glass curtain walls (HFSGCW). The engineering application influence factors of a LDV safety-state evaluation model for HFSGCW were analyzed and the vibration frequency for practical cases was tested in this paper. Results show that the first order peak frequency from a frequency spectrum obtained by LDV can be selected as the safety-state evaluation index for HFSGCW caused by structural sealant failure. A rubber hammer is an effective way to excite glass panels to obtain an accurate vibration frequency spectrum. The middle of glass panels is advisable to be selected as the measurement point to obtain an accurate dynamic frequency. The frequency spectrum of a glass panel edge point can be used to determine structural sealant failure position. Binoculars are suggested to be added in order to improve working efficiency of LDV for measurement distance greater than 10 m. Pasting reflective film is an effective way to increase LDV test signal accuracy. The glass panel safety-state of a commercial center building in Guangdong (China) is accurately evaluated by LDV, and those test results provide guidance for real-time monitoring and repair of HFSGCW.

Excited-State Vibrational Frequencies: Restricted Virtual Space Time-Dependent Density Functional Theory.

Calculating accurate vibrational frequencies for molecules with electronically excited states has an important function in many areas of photochemistry. However, calculations are often limited to smaller molecules due to the rapid growth in the degrees of freedom that must be taken into account to accurately describe larger systems. The applicability of the restricted virtual space (RVS) approximation has been studied within adiabatic linear response time-dependent density functional theory when calculating excited-state nuclear vibrational frequencies. Using the S1 and T1 electronic states of CO, CN-, HOF, H2CS, and C2H4 as representative examples, it is found that vibrational frequency calculations are particularly sensitive to this approximation, with no more than 10-20% of orbitals recommended for safe removal without a priori knowledge when using the 6-311+G(d,p) and aug-cc-pVTZ basis sets. Higher-frequency vibrations such as those with a high degree of CH bond stretching character are found to be less sensitive to the RVS than the lower-frequency vibrations, and several of the triplet states are also found to be less sensitive to this approximation than their equivalent singlet states. Occupied core orbitals and high-energy virtual orbitals with core character can also be removed without introducing significant error.

Use of Density Functional Based Tight Binding Methods in Vibrational Circular Dichroism.

Vibrational circular dichroism (VCD) is a spectroscopic technique used to resolve the absolute configuration of chiral systems. Obtaining a theoretical VCD spectrum requires computing atomic polar and axial tensors on top of the computationally demanding construction of the force constant matrix. In this study we evaluated a VCD model in which all necessary quantities are obtained with density functional based tight binding (DFTB) theory. The analyzed DFTB parametrizations fail at providing accurate vibrational frequencies and electric dipole gradients but yield reasonable normal modes at a fraction of the computational cost of density functional theory (DFT). Thus, by applying DFTB in composite methods along with DFT, we show that it is possible to obtain accurate VCD spectra at a much lower computational demand.

Origin of Many-Body Vibrational Frequency Shifts in Water Clusters.

We have demonstrated the application of many-body expansions to calculations of the anharmonic, local-mode, OH-stretching vibrational frequencies of water clusters. We focused on five low-lying isomers of the water hexamer and the DD*(20,1) isomer of (H2O)21. Our approach provides accurate OH-stretching vibrational frequencies when treating one- and two-body interactions with the CCSD(T)-F12 level of theory and the three- and four-body interactions with the DF-MP2-F12 level. Additionally, we have investigated the physical origin of the large contribution that two- and three-body interactions make to the shifts of vibrational frequencies using symmetry-adapted perturbation theory (SAPT). We conclude that while two-body vibrational frequency shifts can be correlated linearly with electrostatic energies, all strongly shifted three-body interactions can be correlated to the induction energy with a single regression coefficient of approximately 70 cm-1 (kcal·mol-1)-1.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Characterization of isolated 1-aza-adamantan-4-one (C9H13NO) from microwave, millimeter-wave and infrared spectroscopy supported by electronic structure calculations

We have synthesized 1-aza-adamantan-4-one (C9H13NO) starting from commercial 1,4-cyclohexanedionemonoethylene acetal and tosylmethylisocianide, following a procedure already described in the literature. The high degree of sample purity was demonstrated by gas chromatography and mass spectrometric measurements and its structure evidenced by 1H and 13C NMR spectroscopy. Among numerous interests in physical chemistry, this target molecule is of high relevance for mechanistic evaluation and the synthesis of novel pharmaceutical compounds. We present a thorough spectroscopic study of this molecule by gas phase vibrational and rotational spectroscopy. Accurate vibrational frequencies have been determined from infrared and far-infrared spectra. The pure rotational spectrum of the molecule has been recorded both by cavity-based Fourier transform microwave spectroscopy in the 2–20GHz region by supersonically expanding the vapor pressure of the warm sample and by room-temperature absorption spectroscopy in the 140–220GHz range. Accurate sets of rotational and centrifugal distortion parameters of 1-aza-adamantan-4-one in its ground state and in five vibrationally excited states have been derived from these measurements and compared to accurate quantum chemical calculations. The hyperfine parameters have been discussed in terms of molecular structure around the nitrogen quadrupole nucleus.

Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement

Theoretical investigation on the mechanism of temporal depolarization effect in a polarization optical time-domain reflectometry (POTDR) system is conducted. First, the relationship between the dynamic range of the incomplete POTDR system and the degree of polarization (DOP) of the backscattered optical signal is derived. Second, a temporal depolarization suppressed POTDR system is proposed by introducing quasi-distributed Fresnel reflections. Third, the DOP distribution of the proposed system is demonstrated by numerical simulations and experiments. It is shown that the temporal depolarization effect can be significantly suppressed to maintain sufficient dynamic range for fast and accurate polarimetric measurement. The signal-to-noise ratio (SNR) of the received optical signal is also improved with the help of Fresnel reflections. With high DOP and improved SNR, instantaneous intrusion sensing and accurate vibration frequency measurement along the fiber link have been achieved without performing any data averaging.

From small fullerenes to the graphene limit: A harmonic force-field method for fullerenes and a comparison to density functional calculations for Goldberg-Coxeter fullerenes up to C980.

We introduce a simple but computationally very efficient harmonic force field, which works for all fullerene structures and includes bond stretching, bending, and torsional motions as implemented into our open-source code Fullerene. This gives accurate geometries and reasonably accurate vibrational frequencies with root mean square deviations of up to 0.05 Å for bond distances and 45.5 cm(-1) for vibrational frequencies compared with more elaborate density functional calculations. The structures obtained were used for density functional calculations of Goldberg-Coxeter fullerenes up to C980. This gives a rather large range of fullerenes making it possible to extrapolate to the graphene limit. Periodic boundary condition calculations using density functional theory (DFT) within the projector augmented wave method gave an energy difference between -8.6 and -8.8 kcal/mol at various levels of DFT for the reaction C60 →graphene (per carbon atom) in excellent agreement with the linear extrapolation to the graphene limit (-8.6 kcal/mol at the Perdew-Burke-Ernzerhof level of theory).

Density functional theory (DFT) prediction of structural and spectroscopic parameters of cytosine using harmonic and anharmonic approximations

The applicability of popular and efficient B3LYP hybrid density functional and medium-size Pople-type basis set in combination with computationally expensive anharmonic model to obtain more accurate theoretical structure, vibrational frequencies and GIAO NMR parameters of cytosine was tested. We report on prediction of cytosine equilibrium (R e ) and rovibrationally averaged (R v ) structures and vibrational frequencies in the gas phase and DMSO solution using density functional theory combined with 6-311++G** basis set. The harmonic and anharmonic vibrational frequencies (using second-order vibrational perturbation theory, VPT2) were critically discussed. In comparison with initial harmonic data, a significantly better agreement between scaled and anharmonic frequencies and experiment was observed. Proton and carbon nuclear magnetic shieldings were calculated at R e and R v structures of cytosine in the gas phase and DMSO solution using BHandH and B3LYP density functionals combined with 6-311++G**, aug-cc-pVTZ-J and STO-3Gmag basis sets. The obtained NMR results were compared with available experimental data and discussed at length.

High order forces and nonlocal operators in a Kohn-Sham Hamiltonian.

Real space pseudopotentials have a number of advantages in solving for the electronic structure of materials. These advantages include ease of implementation, implementation on highly parallel systems, and great flexibility for describing partially periodic systems. One limitation of this approach, shared by other electronic structure methods, is the slow convergence of interatomic forces when compared to total energies. For real space methods, this requires a fine grid to converge a solution of the Kohn-Sham problem, which is accompanied by concurrent increase in memory and additional matrix-vector multiplications. Here we introduce a method to expedite the computation of interatomic forces by employing a high order integration technique. We demonstrate the usefulness of this technique by calculating accurate bond lengths and vibrational frequencies for molecules and nanocrystals without using fine real space grids.

Effects of density functionals and dispersion interactions on geometries, bond energies and harmonic frequencies of E[tbnd]UX3 (E = N, P, CH; X = H, F, Cl)

Quantum-chemical calculations have been performed to evaluate the geometries, bonding nature and harmonic frequencies of the compounds [EUX3] at DFT, DFT-D3, DFT-D3(BJ) and DFT-dDSc levels using different density functionals BP86, BLYP, PBE, revPBE, PW91, TPSS and M06-L. The stretching frequency of UN bond in [NUF3] calculated with DFT/BLYP closely resembles with the experimental value. The performance of different density functionals for accurate UN vibrational frequencies follows the order BLYP>revPBE>BP86>PW91>TPSS>PBE>M06-L. The BLYP functional gives accurate value of the UE bond distances. The uranium atom in the studied compounds [EUX3] is positively charged. Upon going from [EUF3] to [EUCl3], the partial Hirshfeld charge on uranium atom decreases because of the lower electronegativity of chlorine compared to flourine. The Gopinathan–Jug bond order for UE bonds ranges from 2.90 to 3.29. The UE bond dissociation energies vary with different density functionals as M06-L<TPSS<BLYP<revPBE<BP86<PBE≈PW91. The orbital interactions ΔEorb, in all studied compounds [EUX3] are larger than the electrostatic interaction ΔEelstat, which means the UN bonds in these compound have greater degree of covalent character (in the range 63.8–77.2%). The UE σ-bonding interaction is the dominant bonding interaction in the nitride and methylidyne complexes while it is weaker in [PUX3]. The dispersion energy contributions to the total bond dissociation energies are rather small. Compared to the Grimme’s D3(BJ) corrections, the Corminboeuf’s dispersion corrections are larger with metaGGA functionals (TPSS, M06-L) while smaller with GGA functionals.

Theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes.

A theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis- and trans-1,2-difluoroethylenes is reported. The results obtained using density functional theory (DFT) combined with large basis sets and gauge-independent atomic orbital calculations were critically compared with experiment and conventional, higher level correlated electronic structure methods. Accurate structural, vibrational, and NMR parameters of difluoroethylenes were obtained using several density functionals combined with dedicated basis sets. B3LYP/6-311++G(3df,2pd) optimized structures of difluoroethylenes closely reproduced experimental geometries and earlier reported benchmark coupled cluster results, while BLYP/6-311++G(3df,2pd) produced accurate harmonic vibrational frequencies. The most accurate vibrations were obtained using B3LYP/6-311++G(3df,2pd) with correction for anharmonicity. Becke half and half (BHandH) density functional predicted more accurate (19)F isotropic shieldings and van Voorhis and Scuseria's τ-dependent gradient-corrected correlation functional yielded better carbon shieldings than B3LYP. A surprisingly good performance of Hartree-Fock (HF) method in predicting nuclear shieldings in these molecules was observed. Inclusion of zero-point vibrational correction markedly improved agreement with experiment for nuclear shieldings calculated by HF, MP2, CCSD, and CCSD(T) methods but worsened the DFT results. The threefold improvement in accuracy when predicting (2)J(FF) in 1,1-difluoroethylene for BHandH density functional compared to B3LYP was observed (the deviations from experiment were -46 vs. -115 Hz).

ACCURATE SPECTROSCOPIC CHARACTERIZATION OF OXIRANE: A VALUABLE ROUTE TO ITS IDENTIFICATION IN TITAN'S ATMOSPHERE AND THE ASSIGNMENT OF UNIDENTIFIED INFRARED BANDS.

In an effort to provide an accurate spectroscopic characterization of oxirane, state-of-the-art computational methods and approaches have been employed to determine highly accurate fundamental vibrational frequencies and rotational parameters. Available experimental data were used to assess the reliability of our computations, and an accuracy on average of 10 cm-1 for fundamental transitions as well as overtones and combination bands has been pointed out. Moving to rotational spectroscopy, relative discrepancies of 0.1%, 2%-3%, and 3%-4% were observed for rotational, quartic, and sextic centrifugal-distortion constants, respectively. We are therefore confident that the highly accurate spectroscopic data provided herein can be useful for identification of oxirane in Titan's atmosphere and the assignment of unidentified infrared bands. Since oxirane was already observed in the interstellar medium and some astronomical objects are characterized by very high D/H ratios, we also considered the accurate determination of the spectroscopic parameters for the mono-deuterated species, oxirane-d1. For the latter, an empirical scaling procedure allowed us to improve our computed data and to provide predictions for rotational transitions with a relative accuracy of about 0.02% (i.e., an uncertainty of about 40 MHz for a transition lying at 200 GHz).

Structure of Au40/−1 in the gas phase: A joint geometry relaxed ab initio calculations and vibrationally resolved photoelectron imaging investigation

We have combined photoelectron velocity-map imaging spectroscopy and high-level ab initio calculations to elucidate the geometries of Au4 (0/-1). Well-resolved ground-state electronic transition was observed in the photoelectron spectrum of Au4 (-) at 446 nm, leading to more accurate electron affinity and vibrational frequencies for the ground state of the neutral Au4 (-). The pure and vibrationally resolved spectra provide definitive experimental evidence for the resolution of the ground-state gold tetramer in the gaseous phase, with the aid of the ab initio calculations and Franck-Condon simulations. The comprehensive comparisons between the experiment and theoretical calculations suggest that the Y-shaped structure is the global minimum for both the neutral and anionic Au4.

Modeling of high-order terms in potential energy surface expansions using the reference-geometry Harris–Foulkes method

The reference-geometry Harris-Foulkes (RGHF) approach has been used to model high-order terms within the expansion of multi-dimensional potential energy surfaces (PES) as needed within the calculation of accurate vibrational frequencies beyond the harmonic approximation. The key step of this method is a localization of the electron density to the atoms of the molecule at a given reference structure and a subsequent transfer of these atom-centered partial densities to the atom positions of distorted structures. This concept has been used to evaluate the 3-mode coupling terms of a multi-mode expansion of the PES as arising in the Watson Hamiltonian. Systematic benchmark calculations for vibrational frequencies obtained from vibrational configuration interaction (VCI) theory have been performed in order to study the effects of this approximation on the fundamental modes of a test suite of 28 molecules.

DCMB that combines divide‐and‐conquer and mixed‐basis set methods for accurate geometry optimizations, total energies, and vibrational frequencies of large molecules

We present a method, named DCMB, for the calculations of large molecules. It is a combination of a parallel divide-and-conquer (DC) method and a mixed-basis (MB) set scheme. In this approach, atomic forces, total energy and vibrational frequencies are obtained from a series of MB calculations, which are derived from the target system utilizing the DC concept. Unlike the fragmentation based methods, all DCMB calculations are performed over the whole target system and no artificial caps are introduced so that it is particularly useful for charged and/or delocalized systems. By comparing the DCMB results with those from the conventional method, we demonstrate that DCMB is capable of providing accurate prediction of molecular geometries, total energies, and vibrational frequencies of molecules of general interest. We also demonstrate that the high efficiency of the parallel DCMB code holds the promise for a routine geometry optimization of large complex systems.

Accurate ab initio quartic force fields of cyclic and bent HC2N isomers

Highly correlated ab initio quartic force fields (QFFs) are used to calculate the equilibrium structures and predict the spectroscopic parameters of three HC(2)N isomers. Specifically, the ground state quasilinear triplet and the lowest cyclic and bent singlet isomers are included in the present study. Extensive treatment of correlation effects were included using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted as CCSD(T). Dunning's correlation-consistent basis sets cc-pVXZ, X = 3,4,5, were used, and a three-point formula for extrapolation to the one-particle basis set limit was used. Core-correlation and scalar relativistic corrections were also included to yield highly accurate QFFs. The QFFs were used together with second-order perturbation theory (PT) (with proper treatment of Fermi resonances) and variational methods to solve the nuclear Schrödinger equation. The quasilinear nature of the triplet isomer is problematic, and it is concluded that a QFF is not adequate to describe properly all of the fundamental vibrational frequencies and spectroscopic constants (though some constants not dependent on the bending motion are well reproduced by PT). On the other hand, this procedure (a QFF together with either PT or variational methods) leads to highly accurate fundamental vibrational frequencies and spectroscopic constants for the cyclic and bent singlet isomers of HC(2)N. All three isomers possess significant dipole moments, 3.05 D, 3.06 D, and 1.71 D, for the quasilinear triplet, the cyclic singlet, and the bent singlet isomers, respectively. It is concluded that the spectroscopic constants determined for the cyclic and bent singlet isomers are the most accurate available, and it is hoped that these will be useful in the interpretation of high-resolution astronomical observations or laboratory experiments.

Accurate Anharmonic Vibrational Frequencies for Uracil: The Performance of Composite Schemes and Hybrid CC/DFT Model.

The vibrational spectrum (frequencies as well as intensities) of uracil has been investigated at a high level of theory. The harmonic force field has been evaluated at the coupled-cluster (CC) level in conjunction with a triple-ζ basis set. Extrapolation to the basis set limit as well as inclusion of core-correlation and diffuse-function corrections have been considered by means of the second-order Møller-Plesset perturbation theory. To go beyond the harmonic approximation, a hybrid CC/DFT approach has been employed, which will be proved to provide state-of-the-art results. As the spectroscopic investigation of uracil is hampered by numerous Fermi resonances, models for explicitly taking them into account have been implemented and applied. On general grounds, the computational procedure presented is able to provide the proper accuracy to support experimental investigations of large molecules of biological interest.

Theoretical study on vibrational circular dichroism spectra of tris(acetylacetonato)metal(III) complexes: Anharmonic effects and low-lying excited states

The open-shell density functional theory calculations with M06 exchange-correlation functional and all-electron Douglas-Kroll second order scalar relativistic correction were performed to interpret the vibrational circular dichroism (VCD) spectra of four kinds of tris(acetylacetonato)metal(III), [M(III)(acac)(3)] (acac = acetylacetonato, M = Ru, Cr, Co, and Rh). It was deduced that the experimental spectra were well reproduced by the calculation with harmonic approximation in case of [Co(III)(acac)(3)] (d(6); S = 0), [Rh(III)(acac)(3)] (d(6); S = 0), and [Ru(III)(acac)(3)] (d(5); S = 1/2). In case of [Cr(III)(acac)(3)] (d(3); S = 3/2), anharmonic effects should be taken into account to predict the accurate vibrational frequencies of closely located modes. Time-dependent density functional theory calculations were performed to estimate the contribution of excited states in the VCD spectra. As a consequence, the presence of the low-lying excited states was predicted for [Ru(III)(acac)(3)] alone, which agreed with the experimental observation.

SPECTROSCOPIC CONSTANTS FOR13C AND DEUTERIUM ISOTOPOLOGUES OF CYCLIC AND LINEAR C3H3+

Recently, we reported ab initio quartic force fields (QFFs) for the cyclic and linear forms of the C3H3+ molecular cation, referred to as c-C3H3+ and l-C3H3+. These were computed using high levels of theory. Specifically the singles and doubles coupled-cluster method that includes a perturbational estimate of connected triple excitations, CCSD(T), was used in conjunction with extrapolation to the one-particle basis set limit, and corrections for scalar relativity and core correlation were included. In the present study, we use these QFFs to compute highly accurate fundamental vibrational frequencies and other spectroscopic constants for the c-13CC2H3+, c-C3H2D+, c-13CC2H2D+ isotoplogues of c-C3H3+, and the H2CCCD+, HDCCCH+, H213CCCH+, H2C13CCH+, and H2CC13CH+ isotopologues of l-C3H3+. Improvements in ab intitio methods have now made it possible to identify small molecules in an astronomical observation without the aid of high-resolution experimental data. We also report dipole moment values and show that the above-mentioned cyclic isotopologues have values of 0.094, 0.225, and 0.312 D, respectively, while the l-C3H3+ isotopologues have values that range between 0.325 and 0.811 D. Thus, it is hoped that the highly accurate spectroscopic constants and data provided herein for the 13C and deuterium isotopologues of the cyclic and linear forms of C3H3+ will enable their identification in astronomical observations from the Herschel Space Observatory, the Stratospheric Observatory for Infrared Astronomy, the Atacama Large Millimeter Array, and in the future, the James Webb Space Telescope.