**Cristina Puzzarini**

Department of Chemistry “Giacomo Ciamician”, University of Bologna

https://site.unibo.it/rotational-computational-spectroscopy

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### Abstract

Implementation of very accurate *ab initio* methods on one hand and improvements in computer facilities on the other hand allow the determination of structural, molecular, and spectroscopic properties of small- to medium-size molecules to a very high accuracy. The predictive capabilities have such an accuracy that theoretical calculations can guide, support and even challenge experimental determinations. To perform accurate quantum-chemical calculations of spectroscopic parameters, post-HF methods, such as the coupled cluster ones, should be employed in conjunction with extrapolative and additive techniques in order to account for basis set and wave function truncation errors as well as to include important corrections, such as those related to core correlation and vibrational effects.

Concerning rotational spectra, the starting point is the computation of an accurate equilibrium geometry for the evaluation of the corresponding rotational constants. Next, quadratic and cubic force constants allow the determination of vibrational corrections to rotational constants together with the quartic and sextic centrifugal-distortion constants. Finally, accurate dipole moment components and, when needed, quadrupole-coupling constants complete the list of the needed quantities. The most effective strategy relies on coupled-cluster (CC) evaluations (at the CC singles and doubles augmented by a perturbative treatment of triple excitations, CCSD(T)) of equilibrium geometries, properties, and, possibly, quadratic force constants in a normal-mode representation (i.e., harmonic frequencies), also considering extrapolation to the complete basis set (CBS) limit and core− valence correlation (CV) contributions. These results can be complemented by density functional theory (DFT) evaluations of the anharmonic contributions (employing hybrid or double hybrid functionals, like B3LYP and B2PLYP, in conjunction with medium-sized basis sets). For larger molecules, benchmark studies suggest that the computationally expensive (and slowly converging) evaluation of harmonic frequencies at the CCSD(T)/CBS level augmented by CV corrections can be replaced by effective B2PLYP computations without any dramatic reduction of the accuracy for both rotational and vibrational spectroscopy investigations.

Concerning vibrational spectroscopy, the simulation of fully anharmonic spectra including fundamental, overtones, and combination bands requires, in addition to the quantities discussed above for the rotational spectra, quartic (at least semi-diagonal) force constants together with second and third derivatives of the electric dipoles (for IR spectra). Once again, hybrid and double hybrid functionals perform very well in the computation of anharmonic contributions, provided that, for the evaluation of the electric dipoles, diff use functions are properly included in the basis set. Subsequently, the vibrational problem can be solved by either variational or perturbative approaches. For semi-rigid molecules, second-order vibrational perturbation theory (VPT2) is particularly effective, provided that nearly resonant contributions are treated by means of a variational approach, thus leading to the so-called generalized VPT2 model (GVPT2).

### References

1) Puzzarini, C.; Heckert, M.; Gauss, J. The Accuracy of Rotational Constants Predicted by High-level Quantum-Chemical Calculations. I. Molecules Containing First-row Atoms. *J. Chem. Phys.* **2008**, 128, 194108.

2) Puzzarini, C.; Biczysko, M.; Barone, V. Accurate Harmonic/Anharmonic Vibrational Frequencies for Open-Shell Systems: Performances of the B3LYP/N07D Model for Semirigid Free Radicals Benchmarked by CCSD(T) Computations. *J. Chem. Theory Comput*. **2010**, 6, 828−838.

3) Puzzarini, C.; Stanton, J. F.; Gauss, J. Quantum-chemical Calculation of Spectroscopic Parameters for Rotational Spectroscopy. *Int. Rev. Phys. Chem*. **2010**, 29, 273−367.

4) Puzzarini, C.; Barone, V. Extending the Molecular Size in Accurate Quantum-Chemical Calculations: the Equilibrium Structure and Spectroscopic Properties of Uracil. *Phys. Chem. Chem. Phys*. **2011**, 13, 7189−7197.

5) Puzzarini, C.; Biczysko, M.; Barone, V. Accurate Anharmonic Vibrational Frequencies for Uracil: The Performance of Composite Schemes and Hybrid CC/DFT Model. *J. Chem. Theory Comput.* **2011**, 7, 3702−3710.

6) Computational Strategies for Spectroscopy: from Small Molecules to Nano Systems; *Barone, V.*, Ed.; John Wiley & Sons, Inc.: **2011**

7) Puzzarini, C. Rotational spectroscopy meets theory. Phys. Chem. Chem. Phys. **2013**, 15, 6595−6607.

8) Barone, V.; Biczysko, M.; Bloino, J.; Puzzarini, C. The Performance of Composite Schemes and Hybrid CC/DFT Model in Predicting Structure, Thermodynamic and Spectroscopic Parameters: the Challenge of the Conformational Equilibrium in Glycine. *Phys. Chem. Chem. Phys.* **2013**, 15, 10094−10111.

9) Barone, V.; Biczysko, M.; Bloino, J. Fully Anharmonic IR and Raman Spectra of Medium-size Molecular Systems: Accuracy and Interpretation. *Phys. Chem. Chem. Phys.* **2014**, 16, 1759−1787.

10) Barone, V.; Biczysko, M.; Bloino, J.; Puzzarini, C. Accurate Molecular Structures and Infrared Spectra of trans-2,3-dideuterooxirane, Methyloxirane, and trans-2,3 dimethyloxirane. *J. Chem. Phys.* **2014**, 141, 034107/1−17.

11) Barone, V.; Biczysko, M.; Bloino, J.; Cimino, P.; Penocchio, E.; Puzzarini, C. CC/DFT Route toward Accurate Structures and Spectroscopic Features for Observed and Elusive Conformers of Flexible Molecules: Pyruvic Acid as a Case Study. *J. Chem. Theory Comput.* **2015**, 11, 4342−4363.