*ab initio*full quartic force fields for HOOH, HOOOH, HOOOOH, and their isotopologues

^{1}and Henry F. Schaefer III

^{1,a)}

### Abstract

Explicitly correlated *ab initio* methods have been used to compute full quartic force fields for the three chain minima for HOOOOH, which are found to lie within 1 kcal mol^{−1}. The CCSD(T)-F12 method with the cc-pVTZ-F12 basis set was used to compute equilibrium structures, anharmonic vibrational frequencies, and rotational constants for HOOH, HOOOH, and three chain isomers of HOOOOH, with the two former force fields being used as benchmarks for the latter three. The full quartic force fields were computed in such a way as to yield fundamental frequencies for all isotopologues at once. The present research confirms the recent experimental identification of HOOOH and provides reliable force fields in support of future experimental work on the enigmatic bonding paradigms involved in the HOOOOH chain.

This research was supported by the Department of Energy, Office of Basic Energy Sciences, Chemistry Division, Fundamental Interactions Program, Grant No. DE-FG02-97-ER14748, and used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U. S. Department of Energy under Contract No. DE-AC02-05CH11231.

I. INTRODUCTION

II. COMPUTATIONAL METHODS

III. RESULTS AND DISCUSSION

A. HOOH benchmark

B. HOOOH benchmark

1. Geometric properties

C. HOOOOH

1. Geometric analysis

2. Structural analysis

3. Comparison of geometric properties

4. Spectroscopic properties

5. Barriers and relative energies

IV. CONCLUSIONS

### Key Topics

- Rotation constants
- 9.0
- Hydrogen reactions
- 6.0
- Coupled cluster
- 5.0
- Ozone
- 5.0
- Ab initio calculations
- 4.0

## Figures

The CCSD(T)-F12/cc-pVQZ-F12 optimized equilibrium geometry of HOOH. To the precision given, this is also the CCSD(T)-F12/cc-pVTZ-F12 geometry, with the exception of the OO bond length, which is 1.451 Å at this level of theory.

The CCSD(T)-F12/cc-pVQZ-F12 optimized equilibrium geometry of HOOH. To the precision given, this is also the CCSD(T)-F12/cc-pVTZ-F12 geometry, with the exception of the OO bond length, which is 1.451 Å at this level of theory.

The CCSD(T)-F12/cc-pVTZ-F12 geometry of *trans*-HOOOH, the isomer for which experimental results are available. The structure has *C* _{2} symmetry, and only unique geometric features are labeled.

The CCSD(T)-F12/cc-pVTZ-F12 geometry of *trans*-HOOOH, the isomer for which experimental results are available. The structure has *C* _{2} symmetry, and only unique geometric features are labeled.

CCSD(T)-F12/cc-pVTZ-F12 geometry for chain isomer **1**, predicted to be the lowest energy chain structure of HO_{4}H. This structure has *C* _{1} symmetry, and thus all geometric parameters are shown. The inset shows the view looking down the O2–O3 bond, useful for distinguishing the structures qualitatively.

CCSD(T)-F12/cc-pVTZ-F12 geometry for chain isomer **1**, predicted to be the lowest energy chain structure of HO_{4}H. This structure has *C* _{1} symmetry, and thus all geometric parameters are shown. The inset shows the view looking down the O2–O3 bond, useful for distinguishing the structures qualitatively.

CCSD(T)-F12/cc-pVTZ-F12 geometry for chain isomer **2**, predicted to lie 0.63 kcal mol^{−1} above chain **1**. This structure has *C* _{2} symmetry, and thus only unique geometric parameters are shown. The inset shows the view looking down the O2–O3 bond, useful for distinguishing the structures qualitatively.

CCSD(T)-F12/cc-pVTZ-F12 geometry for chain isomer **2**, predicted to lie 0.63 kcal mol^{−1} above chain **1**. This structure has *C* _{2} symmetry, and thus only unique geometric parameters are shown. The inset shows the view looking down the O2–O3 bond, useful for distinguishing the structures qualitatively.

CCSD(T)-F12/cc-pVTZ-F12 geometry for chain isomer **3**, predicted to lie 0.87 kcal mol^{−1} above chain **1**. This structure has *C* _{2} symmetry, and thus only unique geometric parameters are shown. The inset shows the view looking down the O2–O3 bond, useful for distinguishing the structures qualitatively.

CCSD(T)-F12/cc-pVTZ-F12 geometry for chain isomer **3**, predicted to lie 0.87 kcal mol^{−1} above chain **1**. This structure has *C* _{2} symmetry, and thus only unique geometric parameters are shown. The inset shows the view looking down the O2–O3 bond, useful for distinguishing the structures qualitatively.

The three chain isomers, viewed with the O_{2}–O_{3} bond perpendicular to the plane of the paper. Isomer 3 is portrayed in its stereoisomeric form.

The three chain isomers, viewed with the O_{2}–O_{3} bond perpendicular to the plane of the paper. Isomer 3 is portrayed in its stereoisomeric form.

Newman-like projections of the three HO_{4}H chain isomers.

Newman-like projections of the three HO_{4}H chain isomers.

## Tables

Spectroscopic features at the CCSD(T)-F12 level of theory with various basis sets for HOOH, DOOD, and compared with experiment. All values are in cm^{−1}. Note that V*n*Z refers to the cc-pV*n*Z-F12 basis sets, as discussed in the text. Experimental values are from gas phase spectra unless otherwise indicated. Values for other possible isotopologues with H, D, ^{16}O, ^{17}O, and ^{18}O are included in the supplementary material (Ref. 78).

Spectroscopic features at the CCSD(T)-F12 level of theory with various basis sets for HOOH, DOOD, and compared with experiment. All values are in cm^{−1}. Note that V*n*Z refers to the cc-pV*n*Z-F12 basis sets, as discussed in the text. Experimental values are from gas phase spectra unless otherwise indicated. Values for other possible isotopologues with H, D, ^{16}O, ^{17}O, and ^{18}O are included in the supplementary material (Ref. 78).

Experimental and theoretical rotational constants, in MHz, for HOOH at the CCSD(T)-F12/cc-pV*n*Z-F12 level of theory with zero-point and centrifugal distortion corrections included. The cc-pV*n*Z-F12 basis sets are represented in the table as simply V*n*Z.

Experimental and theoretical rotational constants, in MHz, for HOOH at the CCSD(T)-F12/cc-pV*n*Z-F12 level of theory with zero-point and centrifugal distortion corrections included. The cc-pV*n*Z-F12 basis sets are represented in the table as simply V*n*Z.

Experimental and theoretical rotational constants, in MHz, for HOOOH and DOOOD at the CCSD(T)-F12/cc-pV*n*Z-F12 level of theory with zero-point and centrifugal distortion corrections included. The cc-pV*n*Z-F12 basis sets are represented in the table as simply V*n*Z.

Experimental and theoretical rotational constants, in MHz, for HOOOH and DOOOD at the CCSD(T)-F12/cc-pV*n*Z-F12 level of theory with zero-point and centrifugal distortion corrections included. The cc-pV*n*Z-F12 basis sets are represented in the table as simply V*n*Z.

Spectroscopic features for HOOOH, DOOOD, DOOOH, and predicted at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. All values are in cm^{−1}. Note that the experimental results were obtained in argon matrices. Values for all other possible isotopologues with H, D, ^{16}O, ^{17}O, and ^{18}O are included in the supplementary material (Ref. 78).

Spectroscopic features for HOOOH, DOOOD, DOOOH, and predicted at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. All values are in cm^{−1}. Note that the experimental results were obtained in argon matrices. Values for all other possible isotopologues with H, D, ^{16}O, ^{17}O, and ^{18}O are included in the supplementary material (Ref. 78).

CCSD(T)-F12/cc-pVTZ-F12 fundamental vibrational frequencies for the HO_{4}H and DO_{4}D isotopologues of chain isomers **1**, **2**, and **3**. All values are given in cm^{−1}. (No irreducible representations are given for **1** since it has *C* _{1} symmetry.) The modes are ν_{1}, O_{4} torsion; ν_{2} and ν_{3}, HO_{3} torsions; ν_{4} to ν_{8}, various OOO bends and OO stretches; ν_{9} and ν_{10}, HOO bends; ν_{11} and ν_{12}, OH stretches. Values for all other possible isotopologues with H, D, ^{16}O, ^{17}O, and ^{18}O are included in the supplementary material (Ref. 78).^{a}

CCSD(T)-F12/cc-pVTZ-F12 fundamental vibrational frequencies for the HO_{4}H and DO_{4}D isotopologues of chain isomers **1**, **2**, and **3**. All values are given in cm^{−1}. (No irreducible representations are given for **1** since it has *C* _{1} symmetry.) The modes are ν_{1}, O_{4} torsion; ν_{2} and ν_{3}, HO_{3} torsions; ν_{4} to ν_{8}, various OOO bends and OO stretches; ν_{9} and ν_{10}, HOO bends; ν_{11} and ν_{12}, OH stretches. Values for all other possible isotopologues with H, D, ^{16}O, ^{17}O, and ^{18}O are included in the supplementary material (Ref. 78).^{a}

Computed rotational constants, in MHz, for HO_{4}H and DO_{4}D isotopologues of all three chain isomers at the CCSD(T)-F12/cc-pVTZ-F12 level of theory with zero-point and centrifugal distortion corrections included. More isotopologues, as well as values computed with the cc-pVDZ-F12 basis set, are included in the supplementary information (Ref. 78).

Computed rotational constants, in MHz, for HO_{4}H and DO_{4}D isotopologues of all three chain isomers at the CCSD(T)-F12/cc-pVTZ-F12 level of theory with zero-point and centrifugal distortion corrections included. More isotopologues, as well as values computed with the cc-pVDZ-F12 basis set, are included in the supplementary information (Ref. 78).

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