Journal of Chemistry

Volume 2019, Article ID 4057848, 23 pages

https://doi.org/10.1155/2019/4057848

## Basis Set Effects in the Description of the Cl-O Bond in ClO and XClO/ClOX Isomers (X = H, O, and Cl) Using DFT and CCSD(T) Methods

CCBG, DETEMA, Facultad de Química, Isidoro de María 1616, 11800 Montevideo, Uruguay

Correspondence should be addressed to Oscar N. Ventura; moc.liamg@arutnev.n.racso

Received 1 October 2018; Accepted 16 January 2019; Published 26 February 2019

Academic Editor: Davut Avci

Copyright © 2019 Kenneth Irving et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The performance of a group of density functional methods of progressive complexity for the description of the ClO bond in a series of chlorine oxides was investigated. The simplest ClO radical species and the two isomeric structures XClO/ClOX for each *X* = H, Cl, and O were studied using the PW91, TPSS, B3LYP, PBE0, M06, M06-2X, BMK, and B2PLYP functionals. Geometry optimizations and reaction enthalpies and enthalpies of formation for each species were calculated using Pople basis sets and the (aug)-cc-pVnZ Dunning sets, with = *D*, *T*, *Q*, 5, and 6. For the calculation of enthalpies of formation, atomization and isodesmic reactions were employed. Both the precision of the methods with respect to the increase of the basis sets, as well as their accuracy, were gauged by comparing the results with the more accurate CCSD(T) calculations, performed using the same basis sets as for the DFT methods. The results obtained employing composite chemical methods (G4, CBS-QB3, and W1BD) were also used for the comparisons, as well as the experimental results when they are available. The results obtained show that error compensation is the key for successful description of molecular properties (geometries and energies) by carefully selecting the method and basis sets. In general, expansion of the one-electron basis set to the limit of completeness does not improve results at the DFT level, but just the opposite. The enthalpies of formation calculated at the CCSD(T)/aug-cc-pV6Z for the species considered are generally in agreement with experimental determinations and the most accurate theoretical values. Different sources of error in the calculations are discussed in detail.

#### 1. Introduction

Ozone loss over the Antarctic was reported by Farman et al. in 1985 [1]. Several hypotheses were proposed to explain the Antarctic ozone hole, of which the ones obtaining the largest success were those related to halogen-catalyzed ozone loss [2–4]. Ground-based measurements of ClO, HCl, ClONO_{2}, and OClO obtained in Antarctica during 1986 indicated that ozone depletion is associated with elevated abundances of ClO. A plethora of research on the behavior of chlorine and bromine compounds in the atmosphere was then started.

It is known today that stratospheric ozone is largely destroyed by radical reactions involving XO radicals (*X* = H, Cl, or Br). Self-reaction of these radicals, with the same or different *X*, gives rise to XYO_{2} species (with and also H, Cl, or Br). Two of the most interesting species are HClO_{2} and Cl_{2}O_{2} [5]. These species exhibit a similar behavior, with several possible stable isomers. Many theoretical studies have been performed, but it is not absolutely clear whether the most stable isomer computed is actually the observed one. For instance, it is well known that chlorous acid has the structure HOClO, at least in solution. However, the most stable isomer in the gas phase seems to be the HOOCl peroxide. In the case of Cl_{2}O_{2} instead, the most stable isomer seems to be ClClO_{2} instead of the peroxide structure.

Theoretical studies are aimed fundamentally at determinating thermochemical and kinetic data, which are essential for building models of the catalytic cycles. Calculating accurate data, which rival the experimental determinations when these latter are known, is not a trivial matter. Geometries, spectroscopic properties, and energetic information obtained depend heavily on the theoretical methods employed and the one-electron basis sets used. Recent papers by Somers and Simmie [6] and by Rogers et al. [7] discuss some of the complexities associated with the study of enthalpies of formation, central to the formulation of atmospheric kinetic models.

In the case of composite methods, good accuracy is obtained through the addition of energies calculated at different theoretical levels using different basis sets [7]. In the case of direct calculations, high-level molecular orbital methods (CCSD(T) usually) or density functional methods (DFT) are combined with isogyric or isodesmic reactions [8, 9].

It is well known that molecular orbital methods depend heavily on the basis set chosen. It is less commonly recognized that this is also true in certain cases for DFT methods. In this work, we have performed a careful investigation of the effects of methods and basis sets on the description of the ClO bond in ClO and XClO (*X* = H, O, and Cl) species, using molecular orbital methods (MP2 and CCSD(T)), chemical models (the composite methods CBS-QB3, G4, and W1BD), and DFT methods, representing different rungs of Jacob’s ladder (PW91PW, TPSS, B3LYP, PBE0, M06, M06-2X, BMK, and B2PLYP) [10, 11]. Our purpose is to compare the performance of DFT methods with that of molecular orbital methods, as well as their rate of convergence with increasingly extended basis sets. To this end, we have used Pople´s basis sets and Dunning´s correlation consistent basis sets from cc-pVDZ to aug-cc-pV6Z.

Results are reported for geometries, IR spectra, and energies of ClO, XClO, and XOCl, where *X* = H, O, or Cl. Whenever possible, the theoretical results have been compared with the experimental ones. In cases when these results are not available, a rational guess of the estimated values with their expected error bars is provided.

#### 2. Methods

Geometry optimization and calculation of the energies were performed at the molecular orbital and DFT levels. MP2, CCSD(T) [12, 13], and composite models CBS-QB3 [14], G4 [15], and W1BD [16] were employed on the molecular orbital side. On the DFT side, methods belonging to different rungs in Jacob´s ladder [17] were used. The methods chosen were the GGA PW91 [18] (for both exchange and correlation); the meta-GGA TPSS [19]; the hybrid GGAs PBE0 [20] and B3LYP [21]; the hybrid meta-GGAs M06 [22], M06-2X [22], and BMK [23]; and the double hybrid B2-PLYP [24].

Two Pople basis sets, 6–31 + G(d,p) and 6–311++G(2df,2pd), were chosen as representative of those commonly employed in theoretical chemistry calculations. Convergence of different properties was investigated using Dunning´s cc-pVnZ and aug-cc-pVnZ, with = *D*, *T*, *Q*, 5, and 6 (which includes up to *i* functions on the chlorine atom) (see [25, 26] and references therein).

Geometry optimization of all the species was fully performed for each and all models (method/basis set combination). Forces were reduced until a precision of at least 10^{−4} Å was obtained in the Cartesian coordinates. Thermochemical properties were obtained within the harmonic oscillator/rigid rotor model. Analytical second derivatives were used whenever possible.

Calculations were performed using the Gaussian 09 set of computer programs [27] for the DFT and model chemistry calculations and the Molpro code [28, 29] for the post-Hartree–Fock calculations. A mixed cluster of Xeon and Opteron machines was employed for the calculations, with a maximum of 32 cores per job and 4 GB per core.

#### 3. Results and Discussion

ClO is the simplest chlorine oxide possible. The experimental bond length was determined in 1968 by Amano et al. [30] as 1.5696 Å and more recently by Drouin et al. [31] as 1.569539 Å. The heat of formation at 298.15 K was measured experimentally as 24.29 ± 0.03 kcal/mol [32], while it is listed as 24.192 kcal/mol in the JANAF data tables [33]. Grant et al. [34] calculated this enthalpy of formation as 24.9 kcal/mol using the R/UCCSD(T) method [12, 13] with the augmented correlation consistent basis sets aug-cc-pVnZ ( = *D*, *T*, *Q*, and 5). The best theoretical value was reported by Karton et al. [35], who obtained 24.19 ± 0.19 kcal/mol at 0 K and 24.18 ± 0.03 at 298 K using the W4 method (see [36] and references therein).

In this paper, we calculated the enthalpy of formation employing both the atomization reactionand the reaction of formation from the diatomics

The necessary experimental enthalpies of formation of the atoms in reaction (1) are (Cl,g) = 28.992 ± 0.002 kcal/mol and (O,g) = 59.555 ± 0.024 kcal/mol according to Cox et al. [37]. The standard enthalpies of formation of the diatomics in reaction (2) are zero by definition.

Different degrees of error compensation are expected in the determination of the enthalpy of formation using reactions (1) and (2). Errors associated with the representation of the triplet state oxygen atom or molecule within each method/basis set model will not be compensated neither in reaction (1) nor in (2) since no other triplet species is present. However, reaction (1) does present a doublet species in the right-hand side (*rhs*) and, therefore, would be expected to compensate for the errors associated to the description of the nonpaired single electron in ClO. Neither of these reactions are homodesmic or isogyric so that error compensation is expected to be low. Moreover, to obtain a reasonable estimate of the bonding energy of ClO, which allows accurate calculation of the enthalpy of formation from reaction (1), one should include in the CCSD method full calculation of triples and perturbation estimation of quadruples (CCSDT(Q)), correct for core correlation, introduce relativistic corrections, and account for anharmonicity. This is clearly not the goal of this work, a task already performed by the application of W4 methods, but just the comparison between DFT and CCSD(T) methods to describe the ClO bond.

The calculated optimum bond length of ClO and the enthalpies of reaction for reactions (1) and (2) are deployed in Table 1. Experimental results for the enthalpies of reaction, obtained from the experimental enthalpies of formation of the species involved, are listed in the last entry of the table. The calculated enthalpies of formation at 298.15 K of ClO using the different models were obtained from the calculated enthalpies of reaction and the experimental enthalpies of formation of the species involved. These are also listed in the table, as well as the signed error with respect to the experimental result.