^{1,a)}and Agnieszka J. Gordon

^{1}

### Abstract

In this paper, the electronic structures of *cis*- and *trans*-ClONO and BrONO are studied at the CCSD/aug-cc-pVTZ, CASSCF(14,12)/aug-cc-pVTZ, and B3LYP/aug-cc-pVTZ computational levels. For the Cl–O bond, topological analysis of the electron density field, *ρ*(r), shows the prevalence of the shared-electron type bond (∇^{2} *ρ* _{(3,−1)} < 0). The Br–O bond, however, represents the closed-shell interaction (∇^{2} *ρ* _{(3,−1)} > 0). Topological analysis of the electron localization function, *η*(r), and electron localizability indicator (ELI-D), *ϒ* _{D} ^{ σ }(**r**), shows that the electronic structure of the central N–O bond is very sensitive to both electron correlation improvements (coupled-cluster single double (CCSD), CASSCF, density functional theory(DFT)) and bond length alteration. Depending on the method used, the N–O bond can be characterized as a “normal” N–O bond with a disynaptic V(N,O) basin (DFT); a protocovalent N–O bond with two monosynaptic, V(N) and V(O), basins (CCSD, CASSCF); or a new type, first discovered for FONO, characterized by a single monosynaptic, V(N) basin (CCSD, DFT). The total basin population oscillates between 0.46–0.96 e (CCSD) and 0.86–1.02 e (CASSCF). The X–O bond is described by the single disynaptic basin, V(X,O), with a basin population between 0.76 and 0.81 e (CCSD) or 0.77 and 0.85 e (CASSCF). Analysis of the localized electron detector distribution for the *cis*-Cl–O1–N=O2 shows a manifold in the Cl⋅⋅⋅O2 region, associated with decreased electron density.

The authors would like to thank the Wroclaw Centre for Networking and Supercomputing for generous allocation of computer time. Mr. Jaroslaw Kalinowski is thanked for help with the LED function calculations. Dr. Charles M. Gordon is gratefully acknowledged for final editing and proofreading the text.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

A. The geometrical structure of XONO

B. Analysis of the chemical bonds

IV. CONCLUSIONS

### Key Topics

- Chemical bonds
- 90.0
- Attractors
- 19.0
- Light emitting diodes
- 12.0
- Density functional theory
- 10.0
- Electronic structure
- 9.0

## Figures

Optimized geometrical structures of *cis*- and *trans*- XONO (X=Cl, Br).

Optimized geometrical structures of *cis*- and *trans*- XONO (X=Cl, Br).

Comparison of the electron density *ρ*(r) values and the electron density Laplacian values **∇** ^{ 2 } *ρ*(r) for (3,−1) CP, localized for the X–O bond in *cis*- and *trans*-XONO (X=F, Cl, Br, I).

Comparison of the electron density *ρ*(r) values and the electron density Laplacian values **∇** ^{ 2 } *ρ*(r) for (3,−1) CP, localized for the X–O bond in *cis*- and *trans*-XONO (X=F, Cl, Br, I).

2D-plot of the electron localization function (ELF) for cis-ClONO with marked positions of core and valence attractors and schematic Lewis bonds. Calculations have been performed at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. The picture is viewed along a molecular plane.

2D-plot of the electron localization function (ELF) for cis-ClONO with marked positions of core and valence attractors and schematic Lewis bonds. Calculations have been performed at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. The picture is viewed along a molecular plane.

2D and 3D-plots of the electron localization function (ELF) for *trans*-ClONO with marked positions of core and valence attractors and schematic Lewis bonds. Calculations performed at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. The picture is presented for molecular plane. At 3D-plots the basin populations are presented.

2D and 3D-plots of the electron localization function (ELF) for *trans*-ClONO with marked positions of core and valence attractors and schematic Lewis bonds. Calculations performed at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. The picture is presented for molecular plane. At 3D-plots the basin populations are presented.

(a) Superimposition of 2D (molecular plane) and 3D (core regions) representations of the localized electron detector (LED) function for *cis*-ClONO. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. (b) Superimposition of 3D representations of the localized electron detector (LED) function for *cis*-ClONO. The core regions (solid black) are represented for LED=3.7 and the valence regions (black points) for LED=0.7. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

(a) Superimposition of 2D (molecular plane) and 3D (core regions) representations of the localized electron detector (LED) function for *cis*-ClONO. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. (b) Superimposition of 3D representations of the localized electron detector (LED) function for *cis*-ClONO. The core regions (solid black) are represented for LED=3.7 and the valence regions (black points) for LED=0.7. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

(a) Superimposition of 2D (molecular plane) and 3D (core regions) representations of the localized electron detector (LED) function for *trans*-ClONO. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. (b) A superimposition of 3D representations of the localized electron detector (LED) function for *trans*-ClONO. The core regions (solid black) are represented for LED=2.18 and valence regions (black points) for LED being in range between 0.03 and 2.18. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

(a) Superimposition of 2D (molecular plane) and 3D (core regions) representations of the localized electron detector (LED) function for *trans*-ClONO. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level. (b) A superimposition of 3D representations of the localized electron detector (LED) function for *trans*-ClONO. The core regions (solid black) are represented for LED=2.18 and valence regions (black points) for LED being in range between 0.03 and 2.18. Calculations at the CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

Evolution of total energy and mean electron population () for the V(Br,O1) bonding basin in *trans*-BrO1NO2 for the dissociation of the Br–O1 bond. Calculations at B3LYP/aug-cc-pVTZ level.

Evolution of total energy and mean electron population () for the V(Br,O1) bonding basin in *trans*-BrO1NO2 for the dissociation of the Br–O1 bond. Calculations at B3LYP/aug-cc-pVTZ level.

A dissociation of the N–O1 bond in *trans*-Br–O1–N=O2. An evolution of the total energy and mean electron population () for the basin characterizing the N–O1 bond. Calculations at B3LYP/aug-cc-pVTZ level. (b) Dissociation of the N–O1 bond in *cis*-Br–O1–N=O2. Evolution of total energy and mean electron population () for the basin characterizing the N–O1 bond. Calculations at B3LYP/aug-cc-pVTZ level.

A dissociation of the N–O1 bond in *trans*-Br–O1–N=O2. An evolution of the total energy and mean electron population () for the basin characterizing the N–O1 bond. Calculations at B3LYP/aug-cc-pVTZ level. (b) Dissociation of the N–O1 bond in *cis*-Br–O1–N=O2. Evolution of total energy and mean electron population () for the basin characterizing the N–O1 bond. Calculations at B3LYP/aug-cc-pVTZ level.

## Tables

The optimized geometrical parameters of ClONO and BrONO. The C_{s} point group of symmetry.

The optimized geometrical parameters of ClONO and BrONO. The C_{s} point group of symmetry.

The total energy difference (Δ*E*) [kJ/mol] calculated between the trans- and cis-isomers (*E* _{tot} ^{cis} – *E* _{tot} ^{trans}) corrected by the zero-point energy difference (Δ*E* + ΔZPVE).

The total energy difference (Δ*E*) [kJ/mol] calculated between the trans- and cis-isomers (*E* _{tot} ^{cis} – *E* _{tot} ^{trans}) corrected by the zero-point energy difference (Δ*E* + ΔZPVE).

Summary of NPA and NBO analysis for *cis-* and *trans*-XO1NO2 (X=Cl, Br) performed at the B3LYP/aug-cc-pVTZ level. The core and lone pairs of X atom have been omitted.The contribution of *d* orbitals is less than 1% and has been omitted.

Summary of NPA and NBO analysis for *cis-* and *trans*-XO1NO2 (X=Cl, Br) performed at the B3LYP/aug-cc-pVTZ level. The core and lone pairs of X atom have been omitted.The contribution of *d* orbitals is less than 1% and has been omitted.

Results of perturbative analysis of NBO donor-acceptor interactions for *cis*- and *trans*-XONO (X=Cl, Br) performed at the B3LYP/aug-cc-pVTZ level. Only second-order energy lowerings larger than 42 kJ/mol (10 kcal/mol) are presented and mixing with Rydberg orbitals has been omitted.

Results of perturbative analysis of NBO donor-acceptor interactions for *cis*- and *trans*-XONO (X=Cl, Br) performed at the B3LYP/aug-cc-pVTZ level. Only second-order energy lowerings larger than 42 kJ/mol (10 kcal/mol) are presented and mixing with Rydberg orbitals has been omitted.

The topological data calculated from topological analysis of the electron density field (AIM) at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level for Cl–O1–N=O2 and Br–O1–N=O2 molecules.

The topological data calculated from topological analysis of the electron density field (AIM) at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level for Cl–O1–N=O2 and Br–O1–N=O2 molecules.

The basin populations (e) calculated from topological analysis of the ELF field at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level for Cl–O1–N=O2 and Br–O1–N=O2 molecules.

The basin populations (e) calculated from topological analysis of the ELF field at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level for Cl–O1–N=O2 and Br–O1–N=O2 molecules.

The N and O1 atomic contributions [e] to ELF-basins of the N–O1 bond in cis- and trans-isomers of Cl–O1–N=O2 and Br–O1–N=O2 calculated at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

The N and O1 atomic contributions [e] to ELF-basins of the N–O1 bond in cis- and trans-isomers of Cl–O1–N=O2 and Br–O1–N=O2 calculated at the CCSD/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

The basin populations calculated for the X–O1, O1–N, and N=O2 bonds in cis- and trans-isomers of Cl–O1–N=O2 and Br–O1–N=O2 from topological analysis of the ELI-D field at CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

The basin populations calculated for the X–O1, O1–N, and N=O2 bonds in cis- and trans-isomers of Cl–O1–N=O2 and Br–O1–N=O2 from topological analysis of the ELI-D field at CASSCF(14,12)/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ level.

The fragmentation energies (kJ/mol) for *cis*-XONO(^{1}A^{′}) X=Cl, Br.

The fragmentation energies (kJ/mol) for *cis*-XONO(^{1}A^{′}) X=Cl, Br.

The bond length and topological data calculated from topological analysis of the electron density and electron localization function fields at the B3LYP/aug-cc-pVTZ level for Cl–O1–N=O2 and Br–O1–N=O2 molecules.

The bond length and topological data calculated from topological analysis of the electron density and electron localization function fields at the B3LYP/aug-cc-pVTZ level for Cl–O1–N=O2 and Br–O1–N=O2 molecules.

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