Ab initio calculations and modeling of diabaticpotential energy surfaces for the Van der Waals

complex Clð2PÞ � � �CH4ðX1A1ÞJacek Kłos

Institute of Theoretical Chemistry, NSRIM, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands

Received 10 April 2002; in final form 29 April 2002

Abstract

The three lowest potential energy surfaces, R, Px and Py of the Van der Waals complex Clð2PÞ þ CH4ðX1A1Þ arederived from accurate ab initio calculations for the vertex, edge and face geometries. The restricted coupled cluster

singles, doubles and non-iterative triples excitations [RCCSD(T)] level of theory is applied with a large basis set. The

global Van der Waals minimum, which is 348 cm�1 deep, occurs at R ¼ 3:3 �AA on the R surface and is located in the

vicinity of the face arrangement. � 2002 Elsevier Science B.V. All rights reserved.

1. Introduction

The study of the interaction between atomicchlorine and the methane molecule is of greatimportance in the chemistry of the stratosphere.The reaction

Clð2PÞ þ CH4 ! CH3 þHCl

is the main pathway of chlorine removal in theozone depletion cycle [1–3]. This reaction is thesubject of many experimental investigations (cf.[4–6] and references therein) in which variousquantities have been measured, mainly rate con-stants.

Most of the theoretical investigations of thepotential energy surface of Cl–CH4 system were

focused on the transition state and reactive region[7,8]. Reactive scattering calculations and thermaland vibrationally selected rate constants have beencalculated and compared to experimental resultsby several groups.

Some potentials [9] give an unphysical descrip-tion of the Van der Waals region, as was pointedout in [10]. Therefore our goal in this Letter is todescribe the Van der Waals region of the entrancechannel to the reaction between Cl and methane.This reaction is an example of a heavy-light-heavysystem where a hydrogen atom is abstracted. Re-cently, we published [11] a study of the entrancechannel region to the reaction Clð2PÞ þHCl,which is of similar type. We will use state-of-the-art methods of electronic structure calculations.

Atomic chlorine is an open-shell system with a2P ground state. The threefold spatial degeneracyis removed when a methane molecule starts to

20 June 2002

Chemical Physics Letters 359 (2002) 309–313

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interact with the chlorine atom. There are threeorientations of the singly occupied 3p chlorineorbital with respect to the vector ~RR. One orienta-tion, which defines one of the three diabatic states,has the singly occupied 3p orbital pointing towardthe carbon atom along ~RR. We will refer to thispotential surface as the R diabat. The two orien-tations of the singly occupied chlorine orbitalperpendicular to ~RR define two diabatic surfacesreferred to as Px and Py .

2. Computational methods

2.1. Geometries and basis sets

The position of the chlorine atom is describedby the usual polar coordinates ðR; h;UÞ with re-spect to a frame fixed to methane [12], as is shownin Fig. 1. This frame is such that the xz-plane is amirror plane, i.e., the two protons above the xy-plane are in the xz plane. The CH4 monomer waskept rigid and the CH bond length was fixed at thevalue r ¼ 1:085 �AA close to the experimental equi-librium value. Calculations employed the aug-mented correlation-consistent polarized basis setsof triple zeta quality of Dunning and his cowork-ers [13–15], referred to as AVTZ basis. Calcula-tions included also bond functions of Tao and Pan[16], with the exponents: sp 0.9, 0.3, 0.1; d 0.6, 0.2denoted as (3 3 2). Bond functions that are cen-tered in the middle of the vector ~RR have been

shown to be both effective and economical for aquite a number of Van der Waals complexes [17–20,11].

2.2. Ab initio calculations of interaction energies

All calculations reported in this Letter wereperformed by the aid of the MOLPRO package [21].The supermolecular method was used in calcula-tions of three diabatic potential energy surfaces.This method derives the interaction energy as thedifference between the energies of the dimer ABand the monomers A and B

DEðnÞ ¼ EðnÞAB � EðnÞ

A � EðnÞB : ð1Þ

The superscript (n) denotes the level of ab initiotheory. In CCSD(T) calculations the use of theabove equation is straightforward, and free fromarbitrary choices, as long as the dimer andmonomer energies are calculated with the samedimer centered basis set (DCBS). The basis setsuperposition error was removed according tocounterpoise procedure of Boys and Bernardi [22].For a given diabatic state, the orientation of thesingly occupied orbital for the Cl monomer inthe DCBS was kept the same as in dimer. TheCCSD(T) method is well-known to be very effec-tive in recovering electron correlation effects inVan der Waals complexes calculations [23,24], andis the preferred method of choice as long as asingle-reference approach is valid and efficient.

2.3. One-dimensional fitting

Interaction energies for the vertex, edge andface orientations were fit to the following expres-sion due Degli-Esposti and Werner [25]

V ðRÞ ¼ GðRÞe�aðR�ReÞ

"� T ðRÞ

X7i¼3

C2i

R2i

#ð2Þ

with

GðRÞ ¼X8j¼0

gjRj: ð3Þ

The damping function T is

T ðRÞ ¼ 12ð1þ tanhð1þ tRÞÞ: ð4ÞFig. 1. Molecule fixed frame for the Cl–CH4 complex.

310 J. Kłos / Chemical Physics Letters 359 (2002) 309–313

The parameters a, gj, t and Ci are optimized. Thelargest root mean square error of the fit was0:004 cm�1.

3. Modeling of the anisotropy

To fit the anisotropy we expanded the potentialfor each state in a series of tetrahedral harmonicsTlðh;UÞ transforming according to the A1 repre-sentation of the group Td :

V ðR; h;UÞ ¼Xl

VlðRÞTlðh;UÞ: ð5Þ

The radial Vl coefficients were determined by solv-ing systems of algebraic equations using the factthat we have already radial fits for the vertex, edgeand face geometries. The expansion was truncatedafter the first three tetrahedral harmonics, T0, T3and T4 [26] adapted to the current frame:

T0ðh;UÞ ¼ C0;0ðh;UÞ; ð6Þ

T3ðh;UÞ ¼ C3;2ðh;UÞ; ð7Þ

T4ðh;UÞ ¼ffiffiffiffiffi21

p

6C4;0ðh;UÞ �

ffiffiffiffiffi15

p

6C4;4ðh;UÞ; ð8Þ

where

Cl;mðh;UÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðl� mÞ!ðlþ mÞ!

sPml ðhÞ cosðmUÞ: ð9Þ

The Pml are associated Legendre functions [27].

Harmonics with l ¼ 1; 2 do not appear in the de-scription of tetrahedral anisotropy. Thus, the tet-rahedral symmetry of the potential is assured.Figs. 2–4 show contour plots of the R, Px and Py

diabat for the angle U ¼ 0�. Potentials are avail-able upon request from Kłos [28].

4. Features of the potential energy surfaces

The global Van der Waals minimum occurs forthe R diabat in the proximity of a face of the tet-

Fig. 2. Contour plot of the R diabatic potential energy surface

for U ¼ 0�. Energies in cm�1.

Fig. 3. Contour plot of the Px diabatic potential energy surface

for U ¼ 0�. Energies in cm�1.

Fig. 4. Contour plot of the Py diabatic potential energy surface

for U ¼ 0�. Energies in cm�1.

J. Kłos / Chemical Physics Letters 359 (2002) 309–313 311

rahedron, which means that the complex has C3v

symmetry. The well depth is 348 cm�1 and chlo-rine is located 3.3 �AA away from the carbon atom.There is also a local minimum for h ¼ 0�, whichcorresponds to a geometry with chlorine on theedge of the tetrahedron. This minimum is276 cm�1 deep. The vertex geometry is a saddlepoint on the R surface of 110 cm�1 high. Thissaddle point corresponds to a hydrogen bondedcomplex with radial minimum located at 3.9 �AA.

The diabats of P character are roughly threetimes shallower than the R diabat. In the case ofthe vertex arrangement the Px and Py , diabats arepractically identical in the bonding region. Even inthe repulsive region they are practically the same.To a good approximation the P diabats are de-generate for the vertex geometry. This is not thecase for the edge and face orientations, where thetwo different perpendicular orientations of the 3pchlorine orbital result in different interaction en-ergies. The differences are not large, though, on theorder of 10 cm�1 or less, so that we can concludethat they are the same in very good approxima-tion. The Px diabat reveals one minimum for theface geometry around R ¼ 3:75 �AA and is 120 cm�1

deep. The vertex and edge orientations are con-nected by a valley of 100 cm�1 deep. The Py diabathas two Van der Waals minima, for the face andvertex orientations, respectively. The minimum forthe face arrangement is approximately 10 cm�1

deeper than for the vertex geometry and is110 cm�1 deep.

It is interesting to compare the R diabat shownin Fig. 2 with the Ar–CH4 surface reported in [12]and shown there in Fig. 2. The anisotropy is verysimilar. The face well is approximately 2.5 deeperfor Cl–CH4 than for the Ar–CH4 system.

5. Summary and conclusions

The three lowest diabatic potential energy sur-faces of the Van der Waals complex Clð2PÞ–CH4

have been presented, calculated at the RCCSD(T)level of theory with the AVTZ+332 basis set. Theglobal Van der Waals minimum occurs on the Rdiabat and the well depth is 348 cm�1. Diabats ofP character are three times shallower and less

anisotropic, and are very similar to each other.Diabatic potentials developed in this work modelinteraction of a 2P chlorine atom with the groundstate methane. The model is approximate, as off-diagonal nonadiabatic coupling matrix elementsneeded for transformation to adiabatic surfaceshave been disregarded. Yet, for the first time in theliterature, presented surfaces provide descriptionof weak interactions in the Cl–CH4 complex, basedon highly accurate ab initio calculations.

Acknowledgements

The author thanks Prof. A. van der Avoird, Dr.P.E.S. Wormer and G. Chałasi�nnski for discussionsand their critical reading of the manuscript. Theauthor acknowledges support from the EuropeanResearch Training Network (THEONET II). Thiswork is supported also by the National ScienceFoundation (Grant No. CHE-0078533) and by thePolish Committee for Scientific Research (KBN)(Grant No. 3 T09A 112 18).

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