Anharmonic Fundamental Frequencies Research Articles

Efficiently Calculating Anharmonic Frequencies of Molecular Vibration by Molecular Dynamics Trajectory Analysis.

Two efficient methods, the Eckart frame algorithm and the multiorder derivative algorithm, for vibrational frequency calculation directly based on the raw data of atomic trajectory from the state-of-the-art first-principles molecular dynamics simulation are presented. The Eckart frame approach is robust to retrieve the full set of anharmonic fundamental frequencies of any molecule from the atomic trajectory for a sufficiently long molecular dynamics simulation at a temperature close to 0 K. In addition to the fundamental vibrational frequencies, the multiorder derivative approach is universal for the calculations of vibrational frequencies based on the molecular dynamics result in a wide range of temperatures. The accuracy, efficiency, and applicability of these two methods are demonstrated through several successful examples in calculating the anharmonic fundamental vibrational frequencies of methane, ethylene, water, and cyclobutadiene.

Quantum Chemical Analysis of the CO-HNN+ Proton-Bound Complex.

Proton-bound complexes produce exceptionally bright vibrational modes for stretches involving the hydrogen atom. Binding a proton between various arrangements of N2 and carbon monoxide molecules is known to produce such behavior, and there are four distinct structures involving N2, CO, and a proton. The problem arises in that all four have the same mass and are, consequently, extremely difficult, if not impossible, to resolve experimentally. Fortunately, quantum chemical predictions have produced accurate descriptions of this bright mode and other spectral features for OCHCO+, NNHNN+, and NN-HCO+. The last of this family to be analyzed is CO-HNN+, which is done here. Utilizing high-level coupled cluster computations and quartic force fields, the bright vibrational mode of CO-HNN+ is shown to shift to the red, and the C-O bond is destabilized in this arrangement as opposed to the lower-energy NN-HCO+ isomer studied previously. Furthermore, the 1.87 D center-of-mass dipole moment, spectroscopic constants, and other anharmonic fundamental frequencies and intensities are produced for CO-HNN+ to assist in definitive experimental and even astrochemical classification of this and the other three related mass-57 proton-bound complexes.

CCSD(T) Study of CD3–O–CD3 and CH3–O–CD3 Far-Infrared Spectra

From a vibrationally corrected 3D potential energy surface determined with highly correlated ab initio calculations (CCSD(T)), the lowest vibrational energies of two dimethyl-ether isotopologues, (12)CH(3)-(16)O-(12)CD(3) (DME-d(3)) and (12)CD(3)-(16)O-(12)CD(3) (DME-d(6)), are computed variationally. The levels that can be populated at very low temperatures correspond to the COC-bending and the two methyl torsional modes. Molecular symmetry groups are used for the classification of levels and torsional splittings. DME-d(6) belongs to the G(36) group, as the most abundant isotopologue (12)CH(3)-(16)O-(12)CH(3) (DME-h(6)), while DME-d(3) is a G(18) species. Previous assignments of experimental Raman and far-infrared spectra are discussed from an effective Hamiltonian obtained after refining the ab initio parameters. Because a good agreement between calculated and experimental transition frequencies is reached, new assignments are proposed for various combination bands corresponding to the two deuterated isotopologues and for the 020 → 030 transition of DME-d(6). Vibrationally corrected potential energy barriers, structural parameters, and anharmonic spectroscopic parameters are provided. For the 3N - 9 neglected vibrational modes, harmonic and anharmonic fundamental frequencies are obtained using second-order perturbation theory by means of CCSD and MP2 force fields. Fermi resonances between the COC-bending and the torsional modes modify DME-d(3) intensities and the band positions of the torsional overtones.

Potential energy surfaces and properties of ICN− and ICN

AbstractICN and ICN− have been studied at the MR‐SO‐CISD level of theory with triple‐zeta basis sets for all three atoms. The potential surfaces for the ground states of ICN and ICN− as well as for the first five excited states of ICN− have been generated from the electronic energies, and properties of these states are described. The minimum energy geometry of ICN− is linear, with a local minimum in the INC− geometry. The zero‐point corrected energy difference between these two isomers is 0.38 eV, and they are separated by a 0.5 eV barrier. The I···CN(COM) equilibrium distances are 3.27 and 3.14 Å in the ICN− and INC− geometries, respectively. These values are 0.6 Å larger than the I···CN distances in the corresponding minima in the ICN potential. Likewise, the zero‐point amplitude of both the I···CN stretch and bend are much larger in ICN− than in ICN. This is captured by the calculated anharmonic fundamental frequencies for ICN− of 70 and 235 cm−1 for the bend and stretch, compared to anharmonic frequencies of 302 and 488 cm−1 for the bend and stretch fundamentals in ICN. The frequencies are lowered further in INC− where the bend and stretch fundamentals have frequencies of 59 and 220 cm−1. © 2012 Wiley Periodicals, Inc.

Fundamental vibrational frequencies and dominant resonances in methylamine isotopologues byab initio and density functional theory methods

Ab initio and density functional theory (DFT) calculations were performed for obtaining fundamental vibrational frequencies of methylamine, CH3NH2, and its deuterated variants CH3ND2, CD3NH2, and CD3ND2. The calculations were carried out using the CCSD(T) coupled cluster approximation with cc-pVTZ and cc-pVQZ basis sets, and by the DFT method with the semiempirical hybrid functional B97-1 with polarization consistent pc-2 and pc-3 basis sets. Reasonable performance of the DFT harmonic and ab initio harmonic calculations was found, which improved considerably upon combination of the harmonic fundamental frequencies with anharmonic corrections from the smaller, pc-2, basis. The computed anharmonic fundamental frequencies of methylamine isotopologues agree very well with the experimental values and represent a useful tool for assignment and analysis of the dominant resonances.

Accurate calculation of anharmonic vibrational frequencies of medium sized molecules using local coupled cluster methods

Local coupled cluster methods were applied for the automated generation of accurate multidimensional potential energy surfaces for a set of test molecules ranging from six to nine atoms. Based on these surfaces anharmonic fundamental frequencies were computed using vibrational self-consistent field and configuration interaction methods. The computed vibrational frequencies are compared to those obtained from similar calculations using conventional coupled cluster methods and to experimental values. The results from local and conventional methods are found to be of similar accuracy and in close agreement with experimental values. In addition, an efficient parallelization of the fully automated surface generation code is presented.

Ab initio study of the far infrared spectrum of glycine

AbstractIn glycine, four large amplitude vibrations, the three internal rotations of the CC, COH, and CN bonds, and the amine group inversion are responsible for the nonrigidity of the molecule. They present 12 potential energy surface minima corresponding to eight different conformers. The energy levels for the four motions mentioned above and the HNH bending were determined using ab initio calculations and three different flexible models in one, two, and three dimensions. For this purpose, eight different MP4/cc‐pVTZ potential energy surfaces, five one‐dimensional for each internal coordinate, one two‐dimensional potential depending on the amine wagging and bending coordinates, and one three‐dimensional potential depending on the three internal rotation coordinates, were calculated. For the most stable conformer, the harmonic frequencies corresponding to the HNH bending, NH2 inversion, and the CC, COH, and CN torsions were calculated at 1677, 955, 65, 657, and 218 cm−1, and the anharmonic fundamental frequencies to be 1454, 803, 78, 522, and 175 cm−1 with the one‐dimensional model. The NHN bending and amine wagging fundamentals are determined to be 1688, and 799 with the two‐dimensional model. The fundamentals of the CC, COH and CN torsions were calculated to be 86, 546, and 189 cm−1 with the three‐dimensional model. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Rovibrational states and vibrational intensities of the χ 2A1 state of He2C3+

The all-electron CCSD(T)/cc-pCVTZ level of theory was used to generate a 63 point discrete potential energy hypersurface for the χ 2A1 electronic state of He2C3+. The optimized geometry was of C2v symmetry with a RC–He bond length of 1.218 Aand an included bond angle of 107.9°. Dissociation products were also examined. A Pade′ (4,5) potential function, employing a Simons–Parr–Finlan expansion variable, was used in subsequent calculations. The fit to the discrete abinitio surface yielded a (χ2)1/2 value of 1.35×10-5Eh. The potential function was embedded in an Eckart–Watson rovibrational Hamiltonian, which was solved variationally. The '‘full’' anharmonic fundamental frequencies for the breathe, bend and asymmetric stretch vibrations were 1199.2, 673.4 and 1411.9 cm-1 respectively. Vibrational intensities were calculated using the variational wavefunctions and a dipole moment function generated from an all-electron QCISD/aug-cc-pVTZ 43 point dipole moment surface.

Four-dimensional model calculation of torsional levels of cyclic water tetramer

Quantum four-dimensional model calculations of the coupled intermolecular torsional vibrations of the cyclic homodromic water tetramers (H2O)4 and (D2O)4 are presented, based on the analytical modEPEN4B potential energy surface [S. Graf and S. Leutwyler, J. Chem. Phys. 109, 5393 (1998), preceding paper] and a four-dimensional discrete variable representation approach. The lowest 50 torsional levels were calculated up to 420 and 500 cm−1 for (D2O)4 and (H2O)4, respectively. For both clusters, the torsional ground state is split by a synchronous O–H torsional inversion process, similar to inversion tunneling in ammonia, with calculated tunnel splittings of 21.8 and 0.000 12 MHz for (H2O)4 and (D2O)4, respectively. As for the cyclic water trimer and pentamer, the four torsional fundamentals of the tetramer lie above the torsional interconversion barriers, between 185–200 cm−1 for (D2O)4 and 229–242 cm−1 for (H2O)4, but also lie below the one-dimensional torsionally adiabatic barriers. The anharmonic fundamental frequencies lie both above and below the normal-mode frequencies, by up to 33%. Slightly above the fundamental torsional excitations, at 257–260 and 280–281 cm−1 for (H2O)4 and (D2O)4, respectively, lie four states corresponding to four versions of the {uudd} isomer, which form a pseudorotational manifold; the torsional interconversion occurs by a sequence of double O–H flips. Higher excited pseudorotational states are calculated up to a vibrational angular momentum of k=3. At ≈295 and ≈300 cm−1, a further group of eight states is found, corresponding to the eight permutationally equivalent versions of yet another isomer, the {uuud} structure. The four {uudd} and eight {uuud} states of (H2O)4 exhibit inverse isotope effects, and lie at lower energy than their (D2O)4 counterparts.

Ab initio calculations of the rovibrational states of He 2C 2 + 1

The low-lying rovibrational states of the dihelium carbene dication, He 2C 2+, have been calculated using ab initio techniques. A 75-point potential energy surface was constructed using an all-electron coupled cluster single, double and triple excitation (CCSD (T)) method together with a correlation-consistent polarised core valence triple-zeta basis set. The CCSD(T) optimised geometry was of C 2v symmetry with an R C- He bondlength of 1.570 Å and a bond angle of 84.1 °. The discrete potential energy surface was fitted using a Padé (4, 5) power series expansion yielding a ( x 2) 1 2 of 8.2 × 1 −6 a.u. The potential function was embedded in the Eckart-Watson Hamiltonian, which was solved variationally. The anharmonic fundamental frequencies for the breathe, bend and asymmetric stretch vibrations were calculated to be 683.1, 329.5, 623.8 cm −1 respectively. The low-lying rovibrational states were calculated variationally using a 560-configuration basis involving products of the vibrational eigenfunctions and plus and minus combinations of regular symmetric-top rotor functions.

Variational calculations of the rovibrational energy levels of K 2Na +

Ab initio variational calculations of the low-lying rovibrational states of K 2Na + were performed. A sixth order power series expansion using an exponential Dunham variable was embedded in the Eckart-Watson Hamiltonian, which was solved variationally. The anharmonic fundamental frequencies for the breathe, bend and asymmetric stretch vibrations were calculated to be 188.2 (A 1), 78.2 (A 1) and 94.9 (B 2) cm −1 respectively. The low-lying rovibrational states were calculated using a 560 configuration basis involving products of the vibrational eigenfunctions and plus and minus combinations of regular symmetric-top rotor functions.

Vibrational spectra of 1,3-dideuterioallene and normal mode calculations for allene

Infrared and Raman spectra of 1,3- d 2-allene were measured and fundamental frequencies were assigned. The frequencies were used with previously published data for the d 0, d 4, d 1 and 1,1,- d 2 isotopomers of allene in force field calculations. A new ab initio quantum mechanical force field calculated at the 6-31G** level was scaled to fit the anharmonic fundamental frequencies and used to provide some of the interaction constants for a second, conventionally refined force field.