Fast coupled-cluster singles and doubles for extended systems: Application to the anharmonic vibrational frequencies of polyethylene in theΓapproximation (original) (raw)
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International Journal of Quantum Chemistry, 2019
Anharmonic vibrational frequencies for closed-shell molecules computed with CCSD(T)-F12b/augcc-pVTZ differ from significantly more costly composite energy methods by a mean absolute error (MAE) of 7.5 cm −1 per fundamental frequency. Comparison to a few available gas phase experimental modes, however, actually lowers the MAE to 6.0 cm −1. Open-shell molecules have an MAE of nearly a factor of six greater. Hence, open-shell molecular anharmonic frequencies cannot be as well-described with only explicitly correlated coupled cluster theory as their closed-shell brethren. As a result, the use of quartic force fields and vibrational perturbation theory can be opened to molecules with six or more atoms, whereas previously such computations were limited to molecules of five or fewer atoms. This will certainly assist in studies of more chemically interesting species, especially for atmospheric and interstellar infrared spectroscopic characterization.
The Journal of Chemical Physics, 2010
The frequencies of the infrared-and/or Raman-active ͑k =0͒ vibrations of polyethylene and polyacetylene are computed by taking account of the anharmonicity in the potential energy surfaces ͑PESs͒ and the resulting phonon-phonon couplings explicitly. The electronic part of the calculations is based on Gaussian-basis-set crystalline orbital theory at the Hartree-Fock and second-order Møller-Plesset ͑MP2͒ perturbation levels, providing one-, two-, and/or three-dimensional slices of the PES ͑namely, using the so-called n-mode coupling approximation with n =3͒, which are in turn expanded in the fourth-order Taylor series with respect to the normal coordinates. The vibrational part uses the vibrational self-consistent field, vibrational MP2, and vibrational truncated configuration-interaction ͑VCI͒ methods within the ⌫ approximation, which amounts to including only k = 0 phonons. It is shown that accounting for both electron correlation and anharmonicity is essential in achieving good agreement ͑the mean and maximum absolute deviations less than 50 and 90 cm −1 , respectively, for polyethylene and polyacetylene͒ between computed and observed frequencies. The corresponding values for the calculations including only one of such effects are in excess of 120 and 300 cm −1 , respectively. The VCI calculations also reproduce semiquantitatively the frequency separation and intensity ratio of the Fermi doublet involving the 2 ͑0͒ fundamental and 8 ͑͒ first overtone in polyethylene.
We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive analytical gradients. For systems dominated by a single reference configuration, even MP2.5 is a viable alternative, at MP3 cost. MP2.5 performance for vibrational frequencies is comparable to double hybrids such as DSD-PBEP86-D3BJ, but without resorting to empirical parameters. DCSD is also quite suitable for computing zero-point vibrational energies in computational thermochemistry.
Toward anharmonic computations of vibrational spectra for large molecular systems
The subtle interplay of several different effects makes the interpretation and analysis of experimental spectra in terms of structural and dynamic characteristics a very challenging task. In this context, theoretical studies can be very helpful, and this is the reason behind the rapid evolution of computational spectroscopy from a highly specialized research field toward a versatile and widespread tool. However, in the case of vibrational spectra of large molecular systems, the most popular approach still relies on a harmonic treatment, because of the difficulty to explore the multidimensional anharmonic potential energy surface. These can be overcome considering that, in many cases, the vibrational transitions are well localized and only some of them are observed experimentally. To this aim, the procedure for the simulation of vibrational spectra of large molecular systems beyond the harmonic approximation is discussed. The quality of system-specific reduced dimensional anharmonic approaches is first validated by comparison with computations taking into account all modes simultaneously for anisole and glycine. Next, the approach is applied to two larger systems, namely glycine adsorbed on a silicon surface and chlorophyll-a in solution, and the results are compared with experimental data showing significant improvement over the standard harmonic approximation. Our results show that properly tailored reduced dimension anharmonic approaches stand as feasible routes for state-of-the-art computational spectroscopy studies and allow to take into account both anharmonic and environmental effects on the spectra even for relatively large molecular systems.
The Journal of Chemical Physics, 2008
A new general and effective procedure to compute Franck-Condon spectra from first principles is exploited to elucidate the subtle features of the vibrationally resolved optical spectra of anisole. Methods based on the density functional theory and its time-dependent extension for electronic excited states ͓B3LYP/ 6-311+ G͑d,p͒ and TD-B3LYP/ 6-311+ G͑d,p͔͒ have been applied to geometry optimizations and harmonic frequency calculations. Perturbative anharmonic frequencies ͓J. Chem. Phys. 122, 014108 ͑2005͔͒ have been calculated for the ground state, and the Duschinsky matrix elements have been used to evaluate the corresponding anharmonic corrections for the first excited electronic state. The relative energetics of both electronic states has been refined by single point calculations at the coupled clusters ͑CC͒ level with the aug-cc-pVDZ basis set. Theoretical spectra have been evaluated using a new optimized implementation for the effective computation of Franck-Condon factors. The remarkable agreement between theoretical and experimental spectra allowed for revision of some assignments of fundamental vibrations in the S 1 state of anisole.
The Journal of Chemical Physics, 2019
Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schrödinger equation applicable to floppy, polyatomic systems with multiple large-amplitude motions. This progress is achieved through the combination of (i) the numerical kinetic-energy operator (KEO) approach of [E. Mátyus, G. Czakó, and A. G. Császár, J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak non-product grid method of [G. Avila and T. Carrington, Jr., J. Chem. Phys. 131, 174103 (2009)]. The numerical representation of the KEO makes it possible to choose internal coordinates and a body-fixed frame best suited for the molecular system. The Smolyak scheme reduces the size of the direct-product grid representation by orders of magnitude, while retaining some of the useful features of it. As a result, multi-dimensional (ro)vibrational states are computed with system-adapted coordinates, a compact basis-and gridrepresentation, and an iterative eigensolver. Details of the methodological developments and the first numerical applications are presented for the CH 4 •Ar complex treated in full (12D) vibrational dimensionality.
Journal of Chemical Theory and Computation, 2010
This work aims to provide reliable benchmark data on the accuracy of harmonic and anharmonic vibrational frequencies computed with the B2PLYP double-hybrid density functional method. The exchange-correlation contributions required for the B2PLYP analytical second derivatives are presented here, which allow for the effective calculation of harmonic frequency as well as cubic and semidiagonal quartic force fields. The latter, in turn, are necessary to compute the anharmonic vibrational frequencies with the perturbative approach (VPT2). The quality of harmonic vibrational frequencies computed in conjunction with basis sets of double-to quadruple-quality has been checked against reference data from the F38 benchmark set. Then, for an additional set of small closed-and open-shell systems, both harmonic frequencies and anharmonic contributions computed at the B2PLYP/N07D and the B2PLYP/aug-cc-pVTZ levels have been compared to their CCSD(T) counterparts. Moreover, for selected medium-size molecules (furan, pyrrole, thiophene, uracil, anisole, phenol, and pyridine), anharmonic frequencies have been compared to well established experimental results. Such benchmark studies have shown that the B2PLYP/N07D model provides good quality harmonic frequencies and describes correctly anharmonic contributions, the latter being of similar accuracy to their B3LYP/N07D counterparts, but obtained at significantly larger computational cost. Additionally, increased accuracy can be obtained by adopting hybrid models where the B2PLYP/N07D anharmonic contributions are combined with harmonic frequencies computed with more accurate quantum mechanical (QM) approaches or by B2PLYP with larger basis sets. This work confirmed also that most of the recently developed density functionals are significantly less suited for vibrational computations, while the B2PLYP method can be recommended for spectroscopic studies where a good accuracy of vibrational properties is required.
Semiempirical calculations of molecular vibrational frequencies: The MNDO method
Journal of Molecular Structure, 1978
In recent years the value of calculating molecular force fields from semiempirical molecular orbital theory has become increasingly apparent. Thus in our own laboratories we have studied numerous chemical reactions using both the highly successful MINDO/3 [l] method and more recently the newly developed MNDO [2] procedure based on Pople and Beveridge's NDDO [3] approximation, In such studies (regardless of the particular MO method used) it is essential to demonstrate that the force constant matrix of a putative ~si~on state has a single negative eigenvalue co~~sponding to a vibrational motion coinciding with a small but fiite segment of the reaction path connecting reactant, transition state and product [4]. These statements apply even more forcefully if symmetry constraints have been imposed. Thus work in these [5] and other [4,6] laboratories has revealed numerous cases of apparently bona fide transition states (i.e. species representing energy maxima between reactants and products) which nevertheless failed to satisfy this criterion and are therefore not genuine position states, The force constant matrix is also useful for characterising minima. Stationary points which are not true minima may be obtained if unwarranted symmetry is imposed during the geometry optimisation. This occurred in our recent study of the boron hydrides [ 2b] _ Thus we now routinely calculate the force constant matrices of all calculated species for which there is any chance of error, It is therefore natural to ask with what accuracy the theoretical force fields reproduce the molecular vibrational frequencies when these are known. We have previously presented such a comprehensive analysis for 34 molecules calculated in the MINDO/$ approximation in which we demonstrated that the average error was about 10% [ 7 3. Moreover, many of the errors were systematic, similar deviations occurring for a given type of vibration in different molecules. As a bonus we also found that these fre-
Journal of Physical Chemistry
The performance of some recently proposed DFT functionals by Truhlar's group (mPW1B95, mPWLYP1W, PBELYP1W, and PBE1W [Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B 2005, 109, 317. Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6908.]) was tested primarily with respect to computation of anharmonic vibrational frequency shifts upon hydrogen bond formation in small molecular/ionic dimers. Five hydrogenbonded systems with varying hydrogen bond strengths were considered: methanol-fluorobenzene, phenol-carbon monoxide in ground neutral (S 0 ) and cationic (D 0 ) electronic states, phenol-acetylene, and phenol-benzene(+). Anharmonic OH stretching frequency shifts were calculated from the computed vibrational potentials for free and hydrogen-bonded proton-donor molecules. To test the basis set convergence properties, all calculations were performed with 6-31++G(d,p) and 6-311++G(2df,2pd) basis sets. The mPW1B95 functional was found to perform remarkably better in comparison to more standard functionals (such as B3LYP, mPW1PW91, PBE1PBE) in the case of neutral dimers. In the case of cationic dimers, however, this is not always the case. With respect to prediction of anharmonic OH stretching frequency shifts upon ionization of free phenol, all DFT levels of theory outperform MP2. Some other aspects of the functional performances with respect to computation of interaction and dissociation energies were considered as well.