Semi-Experimental Equilibrium (r_e^SE) and Theoretical Structures of Pyridazine (o-C₄H₄N₂)

Abstract

A semi-experimental equilibrium structure (r e SE ) of pyridazine (o-C 4 H 4 N 2 ) has been determined using the rotational spectra of 18 isotopologues. Spectroscopic constants of four isotopologues are reported for the first time (measured from 235 to 360 GHz), while spectroscopic constants for previously reported isotopologues are improved by extending the frequency coverage (measured from 130 to 375 GHz). The experimental values of the ground-state rotational constants (A 0 , B 0 , and C 0 ) from each isotopologue were converted to determinable constants (A 0 ″, B 0 ″, and C 0 ″), which were then corrected for the effects of vibration−rotation interactions and electron-mass distributions using CCSD(T)/cc-pCVTZ calculations. The resultant r e SE for pyridazine determines bond distances to within 0.001 Å and bond angles within 0.04°, a reduction in the statistical uncertainties by at least a factor of two relative to the previously reported r e SE . The improvement in precision appears to be largely due to the use of higher-level theoretical calculations of the vibration− rotation and electron-mass effects, though the incorporation of the newly measured isotopologues ([4-2 H, 4-13 C]-, [4-2 H, 5-13 C]-, [4-2 H, 6-13 C]-, and [4,5-2 H, 4-13 C]-pyridazine) is partially responsible for the improved determination of the hydrogen-containing bond angles. The computed equilibrium structure (r e ) (CCSD(T)/cc-pCV5Z) and a "best theoretical estimate" of the equilibrium structure (r e ) both agree with the updated r e SE structure within the statistical experimental uncertainty (2σ) of each structural parameter.

Precise Equilibrium Structure of Benzene

“…Further correction for the electron-mass distribution reduces the inertial defects ( i e ) to an average value of 0.0018 uÅ 2 , which is a factor of 17 smaller than the uncorrected ( i 0 ) values. The magnitudes of the fully corrected inertial defects ( i e ) are similar in absolute value to those of other aromatic species treated in a similar fashion, 30,32,39,40 giving further confidence in the experimentally determined rotational constants and theoretical corrections. The rotational constants for all isotopologues appear to be quite adequately determined, despite the very limited transition data sets available for some isotopologues.…”

“…For all species, all of the determinable constants from the A and S reductions agreed to within 0.008 MHz, with most agreeing to 0.001 MHz, indicating that both reduced Hamiltonians were adequately modeling the data set. In a fashion consistent with previous works, ,,, B ″ constants were converted to their corresponding moments of inertia and used in the structure determination. The newly determined S reduction, III r representation spectroscopic constants are presented in Table for each asymmetric-top isotopologue .…”

“…The xrefit module of CFOUR was utilized to obtain the semi-experimental r e SE structure by least-squares fitting all of the isotopologue equilibrium moments of inertia determined from the input rotational constants and the vibration-rotation interaction and electron-mass corrections. A recently described script, xrefiteration , was used to investigate the impact of incorporating each isotopologue beyond those in the original isotopologue set used by Plı́va et al The script selects the next isotopologue to incorporate into the data set based upon its ability to most lower the statistical uncertainties of the parameters. Xrefiteration continues adding isotopologues with the greatest lowering of the uncertainties until all isotopologues are incorporated into the r e SE structure.…”

“…As has been demonstrated for other aromatic compounds, r e SE structures determined using the more expedient DFT methods display reasonable agreement with r e SE structures determined using higher-level CCSD(T) methods. 30,32,39,40 The aforementioned r e SE structures only take advantage of the four symmetric-top benzene isotopologues. Kunishige et al 37 determined a new r e SE structure using a combined data set of rotational constants from nine isotopologues by including data from previous works.…”

Toward Spectroscopic Accuracy for the Structures of Large Molecules at DFT Cost: Refinement and Extension of the Nano-LEGO Approach

“…The SE equilibrium structures of the 12 organobromine and 6 organoiodine molecules discussed in the two preceding sections have been added to our structural database together with those of 9 other molecules (1,3,4-oxadiazole, H 2 O 2 , benzonitrile and phenylacetilene, H 2 CO–O, glycolic acid, 1-chloro-2-fluoroethene, 1-chloro-2,2-difluoroethene, aminoacetonitrile). Furthermore, the SE equilibrium structures of 3 molecules already present in the SE100 database (pyrimidine, pyridazine, and thiophene) have been revised employing improved experimental data. − The updated database, now containing 127 different molecules, will be referred to as SE127.…”