Ab initio calculations of F-HBr system with linear geometry

Article history: Received July 21, 2015 Received in revised form August 29, 2015 Accepted 16 October 2015 Available online 16 October 2015 Two potential energy surfaces 1 2A1 and 1 2B1 for linear geometry of F-H-Br system have been computed with aug-cc-pVQZ basis set using dynamically weighted state averaged MCSCF followed by MRCI-F12 method. State 1 2A1 has smaller barrier height (3.49 kcal/mol) than 1 2B1. (13.6 kcal/mol). The latter has deep van der Waals well in Br-HF valley (2.12 kcal/mol). © 2016 Growing Science Ltd. All rights reserved.


Introduction
Reactions between a halogen atom and hydrogen halide diatomic molecule present a special interest.Many chain reactions comprise them as propagation step.However, first of all an accurate global potential energy surface (PES) is required to initiate the computation.There has been a number of PESs for systems F-H-F 1-2 , F-H-Cl 3 , Cl-H-Cl [4][5][6][7] , Br-H-Br 8 .Due to open-shell character of such systems multiple electronic states are needed to properly describe the dynamics.To our knowledge systems with bromine and/or iodine atoms were studied using only semiempirical PESs [9][10] .Therefore the goal of this paper is to obtain the accurate ab initio PESs for F-H-Br system.Despite the presence of heavy atom, we neglect here by all relativistic effects.Also in this work only linear arrangement of all atoms is considered.Thus this paper represents a first step toward global ab initio surfaces for F-H-Br system.The chosen arrangement can be used in the description of the following collinear reactions F + HBr → HF + Br (1) Br + HF → HBr + F (2) Within chosen linear geometry the molecular system belongs to the C2v point group symmetry.become the same symmetry states 1 2 A' and 2 2 A', respectively.They cannot cross anymore and form avoided crossing region.

Computational Methods
The geometric configuration of the studied molecular system and notations for internal coordinates is presented in Figure 1.Only two coordinates are needed because as mentioned above it is implied that all three atoms lie along a straight line.These coordinates are interatomic distances R1 and R2 as shown in Fig. 1.

Fig. 1. Geometry of the studied molecular system
All calculations were carried out using Molpro2012 package 11 .Initial states were calculated using state-averaged multi-configurational self-consistent field (SA-MCSCF) with aug-cc-pVTZ and aug-cc-pVQZ basis sets.As was shown for similar system F-H-Cl 3 , in the TS area states with charge transfer also must be included in state averaging in order to fully describe molecular system.Therefore a total of six states are included in the dynamically weighting SA-MCSCF calculation (two lowest of each of the following: 2 A1, 2 B1, 2 B2) with the decay coefficient β -1 =2.78 eV 12 .The active space includes 8 active orbitals (4A1, 2B1, 2B2, 0A2).One valence orbital of A1 symmetry is closed to excitation in order to keep consistent ordering of orbitals in Molpro and avoid discontinuities in the PESs 3 .Figure 2 shows six SA-MCSCF states at fixed value of R2=3.30a0.As seen, states 1 2 A1 and 1 2 B1 cross at some point.However, the same symmetry states 1 2 B1 and 2 2 B1 experience avoided crossing.These conical interaction seams make these surfaces unsmooth.
Since MCSCF does not provide sufficiently accurate results, further computations are required.Usually multi-reference configuration interaction (MRCI) 13 is then employed with initial states obtained within the MCSCF calculation.Our focus is restricted only on three lowest states 1 2 A1, 1 2 B1 and 1 2 B2 (actually two states, because 1 2 B1 and 1 2 B2 are degenerate everywhere).Instead of conventional MRCI method we used explicitly correlated MRCI-F12 14 .This method employs wave functions that explicitly depend on the electron-electron distance.As a result, it has better convergence with basis set.For example, the MRCI-F12 method yields results with near complete basis set limit accuracy already with triple-ζ basis sets.So the obtained dynamically weighted SA-MCSCF orbitals were used as references in MRCI-F12.The Davidson correction (+Q) was accounted as well.

Results and Discussion
The first test for ab initio calculations is comparison of the asymptotic parameters of the PESs with experimental data.Of course, both PESs coincide here.1 summarizes the dissociation energies, equilibrium distances, zero point energies and harmonic frequencies for two diatomic molecules HF and HBr.The experimental dissociation energy for HBr is given without spin-orbit effect because our calculations neglect it.As seen, there are no significant discrepancies between the results for both basis sets and it would be sufficient to run all computations only with aug-cc-pVTZ basis.However, all further computations used aug-cc-pVQZ basis.It is important to note that even with such a large basis set the computed dissociation energies are not in excellent agreement with the experimental ones.This is not a limitation of MRCI-F12 or basis set convergence but rather the size of the active space.In order to achieve the accuracies of 0.1 kcal/mol, 3sF and 3pF orbitals are to be included into the active space.But this means that all 4dBr orbitals also must be included thus significantly increasing the number of occupied orbitals and making the computation prohibitively expensive.Another check is comparison of exothermicity for F+HBr→Br+HF reaction.According to Table 2 the computed ΔH agrees well with the experimental value.Fig. 3a shows the contour plots of 1 2 A1 PES.It is smooth and does not have van der Waals (vdW) wells and conical seams.The TS is located at R1=2.85a0, R2=2.74a0 and is of 3.49 kcal/mol high.The 1 2 B1 PES has qualitative differences (Figure 3b).It has the vdW wells in both reactants and product valleys.Also it has conical intersection seams.The saddle point is shifted towards lower F-H and higher H-Br distances (R1=2.58a0,R2=2.86a0) and the barrier is much higher namely 13.6 kcal/mol.The avoided crossing makes this surface discontinuous.Unfortunately these discontinuities lie close to the TS area.But since the barrier height for 1 2 A1 PES is lower, it would not affect the reaction dynamics for this linear configuration.
The 1 2 A1 PES does not exhibit any vdW wells in both reactant and product valleys.It is due to absence of dipole-and quadrupole-quadrupole interaction for this symmetry.However, the 1 2 B1 state has this sort of interaction leading to two vdW wells.The reactant region exhibits a F-HBr well depth of 0.62 kcal/mol at R1=4.66a0, R2=2.69a0 (Fig. 4).The product valley has much deeper well of 2.12 kcal/mol with respect to the asymptote.It is located at R1=1.75a0, R2=4.66a0 (Fig. 5).Similar results are derived for the F-H-Cl system 3 .The wells are 0.67 and 1.95 kcal/mol deep for reactant and product valleys, respectively.Stronger vdW well for Br-HF complex is due to larger bromine atom size.The presence of such vdW wells significantly influences reaction dynamics 16 .

Conclusions
This paper presents results of ab initio computation for linear geometry of F-H-Br system.Two lower states 1 2 A1 and 1 2 B1 (which are degenerate in asymptotic regions) were computed using dynamical weighted SA-MCSCF method followed by MRCI-F12 calculation.Even though this method provides better convergence with basis set than conventional MRCI, the correlation energy is not fully extracted.Better agreement with experimental data is possible if larger portion of the correlation energy is extracted.This can be accomplished only by employment of larger active space.However, in this case the computations may become prohibitively expensive.State 1 2 A1 has much lower barrier height than state 1 2 B1.As a result, the reaction dynamics in the TS region will be mainly governed by 1 2 A1 state.However, at long distances between the atom and diatom the dynamics is influenced by both states.A special effect comes from 1 2 B1 state due to the vdW well.As shown in work 16 , its presence can quantitatively change the system behavior.Therefore the full reactive dynamics for this system implies non-adiabatic study on two coupled PESs.The number of these PESs grows with deflection from linear configuration.In this case the symmetry reduces and states 2 2 A' and 1 2 A'' (1 2 B1 and 1 2 B2 for linear arrangement, respectively) are not degenerate anymore.Moreover, since now states 1 2 A' and 2 2 A' belong to the same symmetry, they form avoided crossings.Ab initio calculations for global PESs with subsequent study of the reactive dynamics are planned for our future research.

R
A rectangular grid of points R1= [1.35-14.0]a0and R2=[2.0-14.0]a0was constructed with total number of 567 nodes.The density of the grid was larger in the TS and asymptotic regions.It is necessary to properly sample these important areas of the PESs.Then 2D-cubic spline interpolation was performed using MATLAB® suite and two PESs were generated.

Fig. 4 .Fig. 5 .
Fig. 4. The vdW well in the reactant valley of 1 2 B1 PES Three lower electronic states are Σ Since these states belong to different symmetry species they cross at some intermediate distances.Such energy reordering is due to different electrostatic interaction.In the TS region the singly occupied porbital of the F atom pointing directly towards the H atom of HBr ( Σ

Table . 1
. Parameters for the diatomic molecules derived from the PESs at asymptotic regions compared with experimental data (De -dissociation energy, Re -equilibrium bond length, ZPEzero point energy, ωe -harmonic frequency).