New Potential Energy Surface Features for the Li + HF â LiF + H

Article pubs.acs.org/JPCA

New Potential Energy Surface Features for the Li + HF → LiF + H Reaction Qunchao Fan,† Huidong Li,† Hao Feng,*,† Weiguo Sun,† Tongxiang Lu,‡ Andrew C. Simmonett,‡ Yaoming Xie,‡ and Henry F. Schaefer, III*,‡ †

Research Center for Advanced Computation, School of Physics and Chemistry, Xihua University, Chengdu, Sichuan, China 610039 Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States

‡

ABSTRACT: The existing potential energy surfaces for the Li + HF system have been challenged by the experiments of Loesch, Stienkemeier, and coworkers. Here a very accurate potential energy surface has been obtained with rather rigorous theoretical methods. Methods up to full CCSDT have been pursued with basis sets as large as core correlated quintuple ζ. Reported here are the reactants, products, two transition states, and three intermediate complexes for this reaction. These reveal one previously undiscovered equilibrium geometry. The stationary point relative energies are very sensitive to level of theory. The reaction has a classical endothermicity of 2.6 kcal mol−1. The complex Li···HF in the entrance valley lies 6.1 kcal/mol below the reactants. The expected transition state Li···H···F is bent with an angle of 72.2° and lies 4.5 kcal/mol above the reactants. The latter predicted classical barrier should be no more than one kcal/mol above the exact barrier. Not one but two product complexes lie 1.6 and 2.2 kcal/mol above reactants, respectively. Between the two product complexes, a second transition state, very broad, is found. The vibrational frequencies and zero-point vibrational energies (ZPVE) of all stationary points are reported, and significantly affect the relative energies.

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INTRODUCTION The potential energy surfaces of three-atom reactions are important topics for both experimental and theoretical chemists. After the H + H2 and F + H2 systems,1 the Li + HF → LiF + H reaction is naturally an ideal candidate, because it is the simplest known reaction involving three different atoms. A variety of experimental research has been devoted to the title reaction.2−6 As early as 1980, pioneering high resolution crossed molecular beams experiments on the Li + HF reaction were performed by Y. T. Lee and co-workers,2 and the relationships between the dynamics and potential energy surface (PES) for this reaction were considered. More recently, important crossed molecular beam studies (Bielefeld/Madrid/ Stuggart) reported angular distributions of LiF for a range of temperatures and collision energies.6 In 1980 a theoretical three-dimensional potential energy surface (PES) for the Li + HF reaction was reported at the configuration interaction (CISD) level.7 This extensive work qualitatively confirmed previous predictions that there exists an entrance attractive well8−11 but gave a more reliable geometry (bent structure with the angle of 114°) and a more accurate dissociation energy of 4.6 kcal/mol. Subsequently, different fitting procedures based on the ab initio PES of ref 7 were adopted to generate potential energy functions for dynamical studies.12−14 In fitting these functions, the CI barrier (6.4 kcal/ mol after zero-point correction) was recommended by Chen and Schaefer to be scaled to 4 kcal/mol, due to higher order correlation effects.7 In 1993−1995, Aguado et al. reported a PES using a multireference single and double excitation © 2013 American Chemical Society

configuration-interaction (MRDCI) method and presented a new global analytical fit of the PES.15,16 Their results were fitted to use in further quasi-classical trajectory (QCT) studies, and the results reported were in broad agreement with experiment. In 2001−2003, Truhlar and co-workers used the MRDCI variant of the multireference configuration interaction method to provide LiHF potential energy surfaces for the ground state and several excited states.17−19 In their first two papers,17,18 a product complex with a shallow well is reported, and in their third paper19 a second transition state was found between the exit complex and the product LiF + H. Their ground state potential surface for the Li + HF → H + LiF reaction was used to study state-to-state, state-specific, and cumulative reaction probabilities.19 Because the dynamics can be sensitive to small changes of the potential surface, and the reaction probability depends in part on the quasibound states of the van der Waals potential,15 a more accurate potential energy surface is needed. This concern is confirmed by the experimental conclusions of Loesch, Stienkemeier, and co-workers.20,21 In their 2011 paper, these authors state “To date, all threshold energies deduced from ab initio potentials and zero-point vibrational energies are at variance with our results.” In this study, we will adopt highSpecial Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: January 16, 2013 Revised: April 5, 2013 Published: April 15, 2013 10027

dx.doi.org/10.1021/jp400541a | J. Phys. Chem. A 2013, 117, 10027−10033

The Journal of Physical Chemistry A

Article

Figure 1. Li + HF → H + LiF optimized geometries for the reactants (1), reactant complex (2), first transition state (3), first product complex (4), second transition state (5), second product complex (6), and products (7). The upper distances were predicted by the CCSD(T) method with the Basis-1 basis sets, i.e., cc-pVQZ basis set for H and F, and cc-pCVQZ basis set for the Li atom. The middle distances by the analogous level but with Basis-2, i.e., cc-pV5Z for the F atom. The lower distances with Basis-3, i.e., aug-cc-pVQZ for the F atom.

The core orbital for the Li atom is not frozen, because corecorrelation effects involving the Li atom are significant. For the H and F atoms, the basis sets used in our computations begin with the robust correlation-consistent polarized valence quadruple-ζ basis sets (cc-pVQZ).25 For the Li atom, because the core is not frozen, the corresponding correlation-consistent polarized core−valence quadruple-ζ basis set (cc-pCVQZ) is used.26 The latter basis set, named Basis-1 in this paper, is denoted H[6s3p2d1f/4s3p2d1f], F[12s6p3d2f1g/5s4p3d2f1g], and Li[15s9p5d3f1g/8s7p5d3f1g]. The same method CCSD-

level ab initio methods including the CCSDT method with up to core-correlated cc-pV5Z basis sets to study the Li + HF → H + LiF reaction.

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THEORETICAL METHODS The stationary points for the Li + HF reaction have been initially optimized using single and double excitation coupled cluster theory with perturbative triple excitations CCSD(T).22−24 Only one core orbital (F atom 1s) was frozen (doubly occupied) in the present coupled cluster computations. 10028



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Figure 2. Schematic illustration of the energies (kcal/mol) for the Li + HF reaction. The blue lines represent CCSD(T) energies obtained with the basis set H(cc-pVQZ), Li(cc-pCVQZ), and F(aug-cc-pVQZ). The red lines apply zero point vibrational energies to the above classical results.

energetic relationships between these stationary points are presented graphically in Figure 2. For the reactant hydrogen fluoride molecule, the bond distance was predicted to be re(H−F) = 0.932 Å by Chen and Schaefer in 1980 with their CISD method.7 In 2003, it was predicted to be re(H−F) = 0.917 Å by Jasper and Truhlar.19 In the present paper (Figure 1), we find the bond distance to be re(H−F) = 0.916 Å with the CCSD(T)/Basis-1 method, re(H− F) = 0.917 Å with the CCSD(T)/Basis-2 method, and re(H−F) = 0.918 Å with CCSD(T)/Basis-3, all of which are in good agreement with the experimental value re(H−F) = 0.9168 Å.33 For the reactant complex (2), the early CISD geometry was re(H−F) = 0.942 Å, re(Li−F) = 1.947 Å, and θ(Li−F−H) = 114°.7 Truhlar’s 2003 geometrical predictions were re(H−F) = 0.926 Å, re(Li−F) = 1.885 Å, and θ(Li−F−H) = 110°.19 In the present research the CCSD(T) method predicts re(H−F) = 0.933 Å, re(Li−F) = 1.872 Å, θ(Li−F−H) = 109.0° with Basis1; re(H−F) = 0.934 Å, re(Li−F) = 1.876 Å, and θ(Li−F−H) = 109.0° with Basis-2; and re(H−F) = 0.934 Å, re(Li−F) = 1.875 Å, and θ(Li−F−H) = 108.8° with Basis-3 (Figure 1 and Table 1). Our CCSD(T) geometry parameters are in reasonable agreement with Truhlar’s results in their 2001 and 2003 papers,17,19 but the θ(Li−F−H) angle in their 2002 paper (107.0°)18 seems a bit small (Table 1). The Li−F distance predicted early by the CISD method (1.947 Å)7 is too long by ∼0.07 Å (Table 1). Figure 1 and Table 1 also report the optimized geometry of the first transition state (3) for the Li + HF reaction. The CCSD(T) method predicts re(H−F) = 1.290 Å, re(Li−F) = 1.667 Å, θ(Li−F−H) = 72.2° with Basis-1; re(H−F) = 1.283 Å, re(Li−F) = 1.670 Å, θ(Li−F−H) = 72.5° with Basis-2; and re(H−F) = 1.281 Å, re(Li−F) = 1.672 Å, θ(Li−F−H) = 72.6° with Basis-3. These geometric parameters are encouragingly similar to the CISD values obtained in 1980, re(H−F) = 1.291 Å, re(Li−F) = 1.699 Å, and θ(Li−F−H) = 74° (Table 1).7 The present predictions are also comparable to Truhlar’s 2003

(T) but with the two larger basis sets for the F atom were also used in this research. The first one is cc-pV5Z for F atom, named Basis-2,27 and the second one is aug-cc-pVQZ for the F atom, named Basis-3. To obtain more reliable relative energies, single point energies for each stationary point were further evaluated by using the coupled-cluster method with all triple excitations, not just perturbative triples, i.e., the CCSDT method.28−30 Restricted open-shell Hartree−Fock (ROHF) orbitals were employed in the construction of all wave functions. All computations were performed with the Mainz-Budapest-Austin version of the ACES II package.31

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RESULTS AND DISCUSSIONS Geometrical Structures. As early as 1980, Chen7 studied the potential energy hypersurface for the Li + HF → LiF + H reaction at the self-consistent field (SCF) and configuration interaction (CISD) levels of theory with medium-sized basis sets. Chen found four stationary points on the reaction pathway, namely the reactants Li + HF (1), products H + LiF (7), reactant complex Li···F−H (2), and the transition state Li···F···H (3). Between 2001 and 2003, Truhlar and coworkers,17−19 reported more reliable potential energy surfaces with the MRDCI/6-311G(3d2f,3p2d) method. In their first two papers,17,18 they found a product complex (4), which is a shallow van der Waals well,32 lying only 0.6 kcal/mol below the products (7). In the 2003 paper,19 Truhlar reported one more stationary point, a second transition state (5) with a very small barrier separating the product complex (4) from separated H + LiF (7). Thus, six stationary points were located on the ground state potential energy hypersurface for the Li + HF reaction. In the present research, we adopt the CCSD(T)/Basis-1, CCSD(T)/Basis-2, and CCSD(T)/Basis-3 methods to study the ground state potential energy hypersurface, and we have now located seven stationary points, displayed in Figure 1. The 10029



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Table 1. Comparison of the Geometrical Parameters (Distances in Å; Angles in deg) of the Stationary Points for the Li + HF → LiF + H Reaction basis sets

Basis-1

first transition state (3)

reactant

product

method

re(H−F)

re(Li−F)

re(H−F)

reactant complex (2) re(Li−F)

θ(Li−F−H)

re(H−F)

re(Li−F)

θ(Li−F−H)

ref 7 ref 17 ref 18 ref 19 CCSD(T)

0.932 0.915 0.915 0.917 0.916

1.605 1.566 1.566 1.563 1.564

0.942 0.926 0.931 0.926 0.933

1.947 1.884 1.884 1.885 1.872

114 110.0 107.0 110.0 109.0

1.291 1.286 1.386 1.282 1.290

1.699 1.672 1.640 1.667 1.667

74 72.3 72.8 73.3 72.2

CCSD(T)

0.917

1.566

0.934

1.876

109.0

1.283

1.670

72.5

CCSD(T)

0.918

1.567

0.934

1.875

108.8

1.281

1.672

72.6

exp33

0.9168 1.5639 first product complex (4)

Li: cc-pCVQZ H: cc-pVQZ F: cc-pVQZ Basis-2 Li: cc-pCVQZ H: cc-pVQZ F: cc-pV5Z Basis-3 Li: cc-pCVQZ H: cc-pVQZ F: aug-cc-pVQZ

basis sets

Basis-1

second transition state (5)

second product complex (6)

method

re(H−F)

re(Li−F)

θ(Li−F−H)

re(H−F)

re(Li−F)

θ(Li−F−H)

re(H−F)

re(Li−F)

θ(Li−F−H)

ref 7 ref 17 ref 18 ref 19 CCSD(T)

1.762 2.064 1.755 2.069

1.582 1.577 1.586 1.581

69.7 68.4 69.2 66.6

2.384 2.643

1.565 1.566

87.8 107.3

2.682

1.565

178.1

CCSD(T)

2.069

1.583

66.9

2.630

1.568

109.2

2.682

1.567

178.1

CCSD(T)

2.051

1.585

67.1

2.603

1.569

111.7

2.652

1.569

179.0

Li: cc-pCVQZ H: cc-pVQZ F: cc-pVQZ Basis-2 Li: cc-pCVQZ H: cc-pVQZ F: cc-pV5Z Basis-3 Li: cc-pCVQZ H: cc-pVQZ F: aug-cc-pVQZ

results19 re(H−F) = 1.282 Å, re(Li−F) = 1.667 Å, and θ(Li−F− H) = 73.3°, and the similar results in their 2001 paper.17 However, the results in the 2002 Truhlar paper are somewhat different: re(H−F) = 1.386 Å, re(Li−F) = 1.640 Å, and θ(Li− F−H) = 72.2° (Table 1).18 Unlike the 1980 potential hypersurface paper, a product complex (4) is found in the present paper with the CCSD(T) method (Figure 1), and the geometrical parameters are predicted to be re(Li−F) = 1.581 Å, re(H−F) = 2.069 Å, θ(Li−F−H) = 66.6° using Basis-1; re(Li−F) = 1.583 Å, the re(H−F) = 2.069 Å, θ(Li−F−H) = 66.9° using the larger Basis2; and re(Li−F) = 1.585 Å, the re(H−F) = 2.051 Å, θ(Li−F− H) = 67.1° using Basis-3. Structure 4 lies above the reactants by 1.64 kcal/mol, and shows a very shallow valley, only 0.97 kcal/ mol below the products with the CCSD(T)/Basis-3 method. Structure 4 was also found by Truhlar and co-workers in all three of their papers.17−19 The Li−F distance (∼1.58 Å) and ∠Li−F−H angle (∼69°) in those three papers are in good agreement with our CCSD(T) results, but among the H−F distances in their three papers (Table 1), only the distance

predicted in their 2002 paper (2.06 Å)18 is close to our CCSD(T) results. For the Li + HF reaction, a second transition state (5) with lower barrier is reported in Figure 1. This transition state (5) lies above the reactants by 2.23 kcal/mol, which is ∼2.3 kcal/ mol lower than the earlier first transition state (3). However, because the reactants must first get over TS(3), the second transition state does not dominate the reaction rate. Our CCSD(T) geometrical parameters of structure 5 are re(Li−F) = 1.566 Å, re(H−F) = 2.643 Å, θ(Li−F−H) = 107.3° with Basis1; re(Li−F) = 1.568 Å, re(H−F) = 2.630 Å, θ(Li−F−H) = 109.2° with Basis-2; and re(Li−F) = 1.569 Å, re(H−F) = 2.603 Å, θ(Li−F−H) = 111.7° with Basis-3 (Figure 1 and Table 1). In their 2003 paper, Truhlar et al. discovered this second transition state between the product complex (4) and the products (7), lying above the products (7) by 0.32 kcal/mol. However, in the present study, this transition state (5) lies slightly below the products by 0.38 kcal/mol, and there must be another energetically low-lying minimum after this transition state. 10030



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Table 2. Comparison of Different Theoretical Predictions for the Relative Energies (ΔEe, in kcal mol−1) of the Seven Stationary Points for the Li + HF → LiF + H Reactiona basis set

Basis-1 (Li: cc-pCVQZ H: cc-pVQZ F: cc-pVQZ) Basis-2 (Li: cc-pCVQZ H: cc-pVQZ F: cc-pV5Z) Basis-3 (Li: cc-pCVQZ H: cc-pVQZ F: aug-cc-pVQZ) a

reactants

reactant complex

TS1

second complex

TS2

product complex

method

1

2

3

4

5

6

products 7

ref 7 ref 16 ref 17 ref 18 ref 19 CCSD(T) CCSDT

0.00 0.00 0.00 0.00 0.00 0.00 0.00

−4.6 −6.43 −4.87 −5.56 −4.87 −6.96 −6.98

10.0 5.37 8.12 5.70 8.12 4.23 4.20

0.44 4.93 3.46 3.94 1.69 1.62

5.23 2.29 2.30

2.25 2.26

2.9 1.89 4.91 4.04 4.91 2.60 2.63

CCSD(T) CCSDT

0.00 0.00

−6.19 −6.22

4.49 4.48

1.69 1.64

2.28 2.31

2.27 2.30

2.61 2.64

CCSD(T) CCSDT

0.00 0.00

−6.06 −6.09

4.50 4.47

1.64 1.57

2.23 2.24

2.22 2.23

2.61 2.64

The CCSDT results are single-point energies based on the CCSD(T) optimized geometries.

lower than the early theoretical results (Table 2) except for that from Aguado.16 To further refine the energetics for this reaction, we report single point energies, as described above. With full triple excitations, the CCSDT/Basis-1 method predicts the relative energies of structures 2−7 with respect to structure 1 to be very similar to the CCSD(T)/Basis-1 results (Table 2). The differences between these two methods are less than 0.07 kcal/mol (=1.69 − 1.62 kcal/mol for structure 4), and the deviations for the other stationary points are less than 0.03 kcal/mol. With the larger basis set Basis-2 with cc-pV5Z for the F atom, the relative energies have almost no change for the stationary points on the product side (structures 4−7) but predict higher energies for structures 2 and 3. The energy increases for structures 2 and 3 relative to the reactants indicate that the basis functions on the F atom are more important for the reactant (HF molecule), which has a single H−F covalent bond. However, these changes (0.8 and 0.2 kcal/mol) are not excessive, compared with the difference between our CCSD(T) results and the previous theoretical results.7,16−19 As for the single point energies with full triple excitations, the CCSDT/ Basis-2 method predicts the relative energies are very similar to the CCSD(T)/Basis-2 results, within 0.05 kcal/mol (Table 2). Table 2 also shows that, with diffuse functions added to the cc-pVQZ basis on the F atom, i.e., Basis-3, the relative energies for the stationary points in the product side (structures 4−7) are similar to those without the diffuse functions (within 0.06 kcal/mol). However, similar to the Basis-2 results, those for reactant complex (2) and TS1 (3) have higher relative energies with respect to reactants (1) by 0.9 and 0.3 kcal/mol, respectively. Again, based on the single point energies with the CCSDT/Basis-3 method, the relative energies are similar to the CCSD(T)/Basis-3 results within 0.07 (= 1.64−1.57) kcal/ mol (Table 2). Figure 2 shows the reaction pathway with the present results (with and without the ZPVE corrections). Our present potential surface is different from the previous CI results.7 The first difference is that three stationary points 4, 5, and 6

Accordingly, we found another product complex (6), which was not reported earlier.7,17−19 Structure 6 lies above the reactants by 2.22 kcal/mol, and lower than the second transition state (5) by only 0.01 kcal/mol with the CCSD(T)/Basis-3 method. However, the latter energy difference is sufficiently small that one can only state with certainty that the PES is very flat in this region. Our CCSD(T) geometric parameters of 6 are predicted to be re(Li−F) = 1.565 Å, re(H− F) = 2.682 Å, θ(Li−F−H) = 178.1° with Basis-1; re(Li−F) = 1.567 Å, re(H−F) = 2.682 Å, θ(Li−F−H) = 178.1° with Basis2; and re(Li−F) = 1.569 Å, re(H−F) = 2.652 Å, θ(Li−F−H) = 179.0° with Basis-3 (Figure 1 and Table 1). The Li−F distance in 6 is very slightly shorter than that in 5, and very close to that for the product (LiF). For the products (7) LiF + H, the CCSD(T) method predicts the bond distance re(Li−F) = 1.564 Å with the “Basis1”, 1.566 Å with the “Basis-2”, and 1.567 Å with the “Basis-3”, all of which are in good agreement with the experimental result re(Li−F) = 1.5639 Å,33 and close to that from Truhlar’s research (Table 1). The LiF distance predicted in Chen’s 1980 paper (1.605 Å) appears to be 0.04 Å too long.7 Classical Energetics. The relative energies of the stationary points, including those in the earlier research,7,16−19 are reported in Table 2. For the reactant complex (2), our CCSD(T)/Basis-1 energy lies below the reactants (1) by 6.96 kcal/mol, which is lower than the early CI result (4.6 kcal/ mol),7 also lower than those from Truhlar (4.87−5.56 kcal/ mol),17−19 but close to Aguado’s theoretical result.16 We see that higher levels of theory preferentially favor the reactant complex (2). For the primary transition state (3), our classical energy barrier of CCSD(T)/Basis-1 is 4.23 kcal/mol, much lower than that predicted by the 1980 CISD method,7 and also lower than those predicted by Truhlar et al.,17−19 but also close to Aguado’s 1997 result.16 For the products LiF + H (7), our theoretical relative energy (2.60 kcal/mol) is slightly lower than the CISD result (2.9 kcal/mol) in 1980,7 and those (4.04−4.91 kcal/mol) reported by Truhlar,17−19 but somewhat higher than Aguado’s 1997 result.16 Our CCSD(T)/Basis-1 relative energies for the other stationary points (4, 5, and 6) are 10031



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Table 3. Theoretical Harmonic Vibrational Frequencies (Listed as Unscaled/Scaled, in cm−1) for the Seven Stationary Points of the Li + HF Reaction Predicted by the CCSD(T)/Basis-1 Methoda

a

HF, reactant

2

3

4

5

6

LiF, product

4162/3996

366/351 399/383 3816/3663

1080i 688/661 942/904

152/146 364/350 884/849

39i 132/127 913/877

17/16 144/138 914/877

918/881

The scale factor is 0.96.

vibrational frequency (39i cm−1). Because this second transition state lies below the primary transition state (3) by 2.3 kcal/mol and corresponds to a very small barrier (0.6 kcal/mol) with respect to the product complex (4), this second transition state should have little significance for the reaction rate.

obtained with the present coupled-cluster method were not reported with the early CI method,7 and structure 6 has not been reported in any theoretical study. Our barrier height 4.50 kcal/mol for the primary transition state (3) is much lower than Chen’s early CI result7 of 10.0 kcal/mol, and it is also somewhat lower than those reported in Truhlar’s research (Table 2). Vibrational Frequencies and Zero-Point Vibrational Energies. The harmonic vibrational frequencies at the CCSD(T)/Basis-1 level of theory are reported in Table 3. The primary transition state (3) has an imaginary vibrational frequency of 1080i cm−1, and the imaginary vibrational mode reveals the simultaneous Li−F formation and F−H bond breaking as the reaction proceeds toward LiF formation. Compared with the experimental f undamental frequency (3961 cm−1) for HF,34 our harmonic frequency predicted by the CCSD(T)/Basis-1 method (4162 cm−1) is too large, and a scaling factor for HF is 0.952. Similarly, a scaling factor for LiF is 0.974, based on the experimental vibrational frequency.35 The scaled frequencies with an average scaling factor of 0.96 for all stationary points are listed in Table 3 and will be used for evaluating the zero-point vibrational energies (ZPVE). Thus, the ZPVE values for the seven structures are 5.71 (1), 6.29 (2), 2.24 (3), 1.92 (4), 1.43 (5), 1.47 (6), and 1.26 (7) kcal/mol, respectively, and these ZPVE corrections are consistent with those from Truhlar’s 2003 research.19 Consequently, after ZPVE corrections, the relative energies with the CCSD(T)/ Basis-3 method for the seven stationary points are 0.00, −5.49, +1.03, −2.15, −2.05, −2.03, and −1.84 kcal/mol (Figure 2), respectively. It is notable that the ZPVE corrected barrier of the primary transition state (3), compared with the reactants (1), is reduced to 1.03 kcal/mol. Another notable point is that the reaction becomes slightly exothermic (with reaction heat of −1.84 kcal/mol) after the zero-point corrections. This is because the LiF vibrational frequency and ZPVE are so much lower than that for HF.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: H.F., [email protected]; H.F.S., [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported in part by the National Natural Science Foundation of China (Grant No: 11204244 and 11074204), the Program for New Century Excellent Talents (Grant No: NCET-10-0949), the Youth Foundation (Grant No: 2012JQ0055) of the Department of Science and Technology, China. Research in Georgia was supported by the U.S. Department of Energy, Offices of Basis Energy Sciences, Division of Chemistry, Grant DE-FG02-97ER1474. HFS thanks Professor Takeshi Oka for many helpful discussions over the years, especially involving the infrared spectra of molecular ions.

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REFERENCES

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CONCLUDING REMARKS The Li + HF → LiF + H reaction has been studied using highlevel ab initio methods, up to full CCSDT single point energies with the CCSD(T) optimized geometries. The stationary point relative energies are very sensitive to the level of theory. With these high-level methods, we have found three intermediate complexes and two transition states for the Li + HF reaction. The entrance complex (2) has a low energy with a strong interaction between Li and the HF molecule. The primary transition state (3) displays a single imaginary vibrational frequency at 1080i cm−1. The classical barrier lies above the Li···HF complex by 10.6 kcal/mol, whereas the classical barrier with respect to the reactants (Li and HF) is 4.5 kcal/mol. The latter classical barrier is significantly reduced by zero-point vibrational energiesthe ZPVE of the transition state (3) is much less than that for diatomic HF. We also have found a second transition state (5) with a very small imaginary 10032



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NOTE ADDED IN PROOF We regret to have omitted references to four papers.36−39

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New Potential Energy Surface Features for the Li + HF â LiF + H

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New Potential Energy Surface Features for the Li + HF â LiF + H