^{1,2}and David A. Mazziotti

^{1,a)}

### Abstract

The isomerization of nitrosomethane to *trans*-formaldoxime is treated with the parametric variational two-electron reduced-density-matrix (2-RDM) method. In the parametric 2-RDM method, the ground-stateenergy is minimized with respect to a 2-RDM that is parameterized to be both size extensive and nearly -representable. The calculations were performed with an efficient version of the 2-RDM method that we developed as an extension of the PSI3*ab initio* package. Details of the implementation, which scales like configuration interaction with single and double excitations, are provided as well as a comparison of two optimization algorithms for minimizing the energy functional. The conversion of nitrosomethane to *trans*-formaldoxime can occur by one of two pathways: (i) a 1,3-sigmatropic hydrogen shift or (ii) two successive 1,2-sigmatropic hydrogen shifts. The parametric 2-RDM method predicts that the reaction channel involving two sequential 1,2-shifts is about 10 kcal/mol more favorable than the channel with a single 1,3-shift, which is consistent with calculations from other *ab initio* methods. We computed geometric parameters and harmonic frequencies for each stationary point on the reaction surfaces. Transition-state energies, geometries, and frequencies from the 2-RDM method are often more accurate than those from traditional wave function methods of a similar computational cost. Although electronic-structure methods generally agree that the 1,2-shift is more efficient, the energy ordering of the reactant nitrosomethane and the 1,2-shift intermediate formaldonitrone is unresolved in the literature. With an extrapolation to the complete-basis-set limit the parametric 2-RDM method predicts formaldonitrone to be very slightly more stable than nitrosomethane.

D.A.M. gratefully acknowledges the NSF Career Grant No. 0644888, the Henry-Camille Dreyfus Foundation, the David-Lucile Packard Foundation, and the Microsoft Corporation for their support. A.E.D. acknowledges funding provided by the Computational Postdoctoral Fellowship through the Computing, Engineering, and Life Sciences Division of Argonne National Laboratory.

I. INTRODUCTION

II. THEORY

A. Parametric 2-RDM methods

B. PSI3 implementation

C. Minimization algorithms

III. APPLICATIONS

A. Computational details

B. Results and discussion

IV. CONCLUSIONS

### Key Topics

- Electronic structure
- 9.0
- Excitation energies
- 7.0
- Configuration interaction
- 6.0
- Isomerization
- 6.0
- Wave functions
- 6.0

## Figures

Critical points on the potential energy surface for the isomerization of nitrosomethane to *trans*-formaldoxime as computed by the 2-RDM method in the aug-cc-pVTZ basis set. The dashed line represents a 1,3-hydrogen shift; the solid line represents successive 1,2-shifts. The figure shows that 1,2-shift is energetically more favorable than the 1,3-shift by about 10 kcal/mol.

Critical points on the potential energy surface for the isomerization of nitrosomethane to *trans*-formaldoxime as computed by the 2-RDM method in the aug-cc-pVTZ basis set. The dashed line represents a 1,3-hydrogen shift; the solid line represents successive 1,2-shifts. The figure shows that 1,2-shift is energetically more favorable than the 1,3-shift by about 10 kcal/mol.

## Tables

Absolute energies of the stationary points on the potential energy surfaces corresponding to the rearrangement of nitrosomethane to formaldoxime via 1,3- or successive 1,2-hydrogen shifts. Results are given for the CCSD, CCSD(T), and 2-RDM methods in the aug-cc-pVTZ basis set. Zero-point vibrational energies as computed in the cc-pVDZ basis set are given in parentheses. All energies are reported in hartrees.

Absolute energies of the stationary points on the potential energy surfaces corresponding to the rearrangement of nitrosomethane to formaldoxime via 1,3- or successive 1,2-hydrogen shifts. Results are given for the CCSD, CCSD(T), and 2-RDM methods in the aug-cc-pVTZ basis set. Zero-point vibrational energies as computed in the cc-pVDZ basis set are given in parentheses. All energies are reported in hartrees.

Relative energies of the stationary points on the potential energy surfaces corresponding to the rearrangement of nitrosomethane to formaldoxime via 1,3- or successive 1,2-hydrogen shifts. Results are given for the CCSD, CCSD(T), 2-RDM, and G2 methods in the aug-cc-pVTZ basis set and the MP2 method in the basis set. MP2 and G2 results are from Ref. 40. All energies are reported relative to the energy of nitrosomethane 1 in units of kcal/mol. The numbers that represent each stationary point correspond to those given in Fig. 1.

Relative energies of the stationary points on the potential energy surfaces corresponding to the rearrangement of nitrosomethane to formaldoxime via 1,3- or successive 1,2-hydrogen shifts. Results are given for the CCSD, CCSD(T), 2-RDM, and G2 methods in the aug-cc-pVTZ basis set and the MP2 method in the basis set. MP2 and G2 results are from Ref. 40. All energies are reported relative to the energy of nitrosomethane 1 in units of kcal/mol. The numbers that represent each stationary point correspond to those given in Fig. 1.

The energy of formaldonitrone relative to nitrosomethane in the cc-pVXZ basis sets, with , T, and Q and the CBS limit. In the CBS limit, both the 2-RDM and CCSD(T) methods predict that formaldonitrone is more stable than nitrosomethane, while CCSD predicts the opposite ordering. Energies are given in units of kcal/mol.

The energy of formaldonitrone relative to nitrosomethane in the cc-pVXZ basis sets, with , T, and Q and the CBS limit. In the CBS limit, both the 2-RDM and CCSD(T) methods predict that formaldonitrone is more stable than nitrosomethane, while CCSD predicts the opposite ordering. Energies are given in units of kcal/mol.

Structural parameters for nitrosomethane, *trans*-formaldoxime, and formaldonitrone as computed by the CCSD, CCSD(T), and 2-RDM methods in the cc-pVDZ basis set. The subscripts i, o, c, and t denote in-plane, out-of-plane, *cis*-to-the-oxygen, and *trans*-to-the oxygen hydrogen atoms. Experimental values for nitrosomethane were obtained from Ref. 51. Experimental values for formaldoxime were taken from Refs. 52 and 53.

Structural parameters for nitrosomethane, *trans*-formaldoxime, and formaldonitrone as computed by the CCSD, CCSD(T), and 2-RDM methods in the cc-pVDZ basis set. The subscripts i, o, c, and t denote in-plane, out-of-plane, *cis*-to-the-oxygen, and *trans*-to-the oxygen hydrogen atoms. Experimental values for nitrosomethane were obtained from Ref. 51. Experimental values for formaldoxime were taken from Refs. 52 and 53.

Harmonic frequencies for nitrosomethane, formaldonitrone, and the transition state for the *cis-trans* isomerization of formaldoxime 6 as computed by the CCSD, CCSD(T), and 2-RDM methods in the cc-pVDZ basis set. For each method the transition state 6 has only 11 frequencies with the final imaginary frequency omitted. All frequencies are given in .

Harmonic frequencies for nitrosomethane, formaldonitrone, and the transition state for the *cis-trans* isomerization of formaldoxime 6 as computed by the CCSD, CCSD(T), and 2-RDM methods in the cc-pVDZ basis set. For each method the transition state 6 has only 11 frequencies with the final imaginary frequency omitted. All frequencies are given in .

Article metrics loading...

Full text loading...

Commenting has been disabled for this content