1. 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

2. 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

3. 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)?

4. 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

5. 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?

6. 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

7. Assessment of Best Theoretical Reference Structure and Comparison between Quantum Chemistry Structures
Basis Set: 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

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

9. 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

10. Inertia Defect Analysis

11. 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

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

13. 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 ( 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)