Substitution Structures of Large Molecules and Medium Range Correlations in Quantum Chemistry Calculations Luca Evangelisti Dipartmento di Chimica “Giacomo Ciamician” Universita Di Bologna Brooks H. Pate Department of Chemistry University of Virginia ISMS 2017 MI05

Rotational Spectroscopy and Molecular Structure Traditional application of molecular rotational spectroscopy Potential for quantitative structures from isotopologue analysis (Kraitchman) Tests of quantum chemistry methods Library free analysis of mixtures of volatile gases Structures of complexes to determine absolute configuration of chiral molecules

Testing Quantum Chemistry Methods The most common analysis is comparing percent errors of molecular rotational constants Does the comparison between experimental and theoretical rotational spectroscopy provide any information about the quality of the molecular structure? Can this information be used to obtain improved structures from lower levels of theory (much like scaled vibrational spectra)?

Quantum Chemistry and Accurate Predictions of Rotational Constants Rotational Constants too Large Moments-of-inertia too Small (Structure too Compact) Rotational Constants too Small Moments-of-inertia too Large (Structure too Open) B2PLYP D3 has best performance MP2 rotational constants are too large B3LYP rotational constants are too small B3LYP D3 offers significant improvement

Quantum Chemistry and Accurate Molecular Structures Different quantum chemistry methods capture the medium and long range correlation effects with different accuracy Is there a quantitative way to characterize the “shrinking” of the molecular structure to understand the differences in theoretical and experimental structures?

Rotational Spectroscopy Data Set and Analysis Approach Structure Parameter: RCOM No imaginary coordinates from inertial defect issues. 92 atom positions from natural abundance isotopologues Can the center-of-mass distance be used to quantify the “shrinking” effects in the molecular structure? Nathan Seifert and Lorenzo Spada

Assessment of Best Theoretical Reference Structure and Comparison between Quantum Chemistry Structures Basis Set: 6-311++G** (Standard) Using the usual comparison of percent error, B2PLYP D3 gives best agreement Differences in COM Atom Distances using the B2PLYP D3 structure as the reference Heavy atoms only (Lower scatter for B3LYP D3BJ) Rmethod = Rref + CmethodRref = Rref (1+Cmethod) B3LYP B2PLYP D3 B3LYP D3BJ MP2

Implications: Single Scale Factor for Structure Improvement Structure scale factor can be obtained from the ratio of the rotational constants

Comparison to Experiment: Inertial Defect Rotational constant (moment-of-inertia) ratios are related to R0 coordinates In comparing the substitution distance coordinates to theory, the effect of the inertial defect is clear (Rtheory/R0)2 Asymptotic: (Re/Rtheory)2 The variation is fit using the Costain assumption of a single, constant contribution to the inertial defect. Fit value is 7 times larger than the Costain value used for error estimates in substitution structures Inertia dominated by atoms at large center-of-mass distance B3LYP B2PLYP D3 B3LYP D3BJ MP2

Inertia Defect Analysis

Structure Correction Scale Factors Comments: Dispersion corrected results give structures closer to experiment The scale factors for the two analysis methods (rotational constant and substitution structure) are nearly identical B3LYP D3BJ offers best combination of computation speed and accuracy Correction factor fixes average “shrinking” effect, fluctuations around this correction also play a role in structure quality

Acknowledgements This work supported by the National Science Foundation (CHE 1531913) and BrightSpec Special thanks to Nathan Seifert and Lorenzo Spada

Conclusions A single scale factor can be used to improve molecular structures from different levels of theory by accounting for “shrinkage” from medium and long-range correlation The correction factor relative to the experimental structure is obtained from the ratio of the rotational constants (moments-of-inertia) This result explains the remarkable accuracy of predicting 13C rotational constants using ratios of experimental and theoretical rotational constants of the normal species as a scale factor B3LYP D3BJ (not B3LYP D3 in Gaussian) offers a good balance of computation speed and accuracy (6-311++G**) The inertial defect is found to be much larger for molecules in this size range than the value used by Costain (evidence it scales with molecular size)