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Potential energy surfaces of HgH2
CHEMICAL PHYSICS LETTERS
Volume 134, number 3
21 February 1987
POTENTIAL ENERGY SURFACES OF HgHZ Anne BERNIER and Philippe MILL16 CEA/IRDI/DESICP,
Dkpartement
de Physico-Chimie,
CEN/Saclay,
91191 Gif-sur-Yvette Cedex, France
Received 5 November 1986; in final form 8 December 1986
Potential energy surfaces for HgHz have been calculated using a nonempirical relativistic effective core potential incorporating configuration interaction by means of the CIPSI algorithm. Core valence polarization and correlation energy are included via a perturbative treatment. Spin-orbit coupling is introduced through an effective Hamiltonian. These theoretical results are used to discuss the experimental results of Breckenridge, Jouvet and Soep for the reaction Hg(3P1) + Hz + HgHc2 8+) + H.
1. Introduction
potential energy surfaces for the HgH, system. Because Hg has a large number of electrons all-electron calculations for the HgH, system would be very expensive. Using a relativistic effective core potential allows us to consider the mercury atom as a twoelectron system. Computational methods have been tested on the HgH molecule and good agreement obtained with the experimental spectroscopic constants for low-lying states [3]. Consequently, we have undertaken the exploration of the potential energy surfaces of the HgH2 system. We present theoretical results obtained for the Hg t H2 potential surface (C,, and C,, geometry), for the insertion reaction Hg + H2 + H-Hg-H (C,, geometry) and for the abstraction reaction Hg t H2 + H + HgH(2Z+) (C,, geometry). The different behaviour of the two van der Waals complex states Hg(3P1) t H, is discussed.
The Hg(3P1) t H2 system has recently been studied experimentally by Breckenridge, Jouvet and Soep [ 1] who carried out selective laser excitation of the van der Waals complex HgH, . The molecular product HgH(2 X+) was detected and rotationally analyzed. The two electronic configurations X and II of the complex Hg(3P1) + HZ, which correspond approximately to axial and perpendicular orientations, respectively, of the 6p orbital (see table 1) with respect to the freely rotating H2 molecule exhibit different behaviour. The reaction leading to HgH via the Il complex is direct, i.e. occurs within 0.1 ps and forms HgH(u = 0) with a rotational distribution peaked at J = 19. In contrast, the X complex forms HgH indirectly, i.e. the reaction occurs on a time scale greater than 2 ps. Furthermore, the HgH(u = 0) rotational distribution from the Z: complex is bimodal, with a major component similar to that from the n complex but a minor component definitely present at low J. Similar rotational distributions in the mercury hybride molecule produced by collision of Hg(3P,) with H,, HD or D, have been otained by Bras et al. 123. Breckenridge et al. [l], in their original paper, have discussed possible explanations for their experimental results with the help of theoretical results obtained for the isoelectronic systems MgH, and BeH,, but a better understanding of the processes by which reactants are converted into products requires theoretical 0 009-26 14/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
2. Computational method The mercury atom is considered as a two-electron system within a relativistic non-empirical effective core potential. Two component orbitals are derived from relativistic all-electron atomic calculations according to the method proposed by Barthelat et al. [4]. The nodeless one-component pseudo-orbitals and corresponding pseudopotentials are obtained following the B.V.
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Volume 134, number 3
CHEMICAL PHYSICS LETTERS
method of Barthelat and Durand [S] . Effective spinorbit (SO) operators acting on pseudo-orbitals are derived in order to reproduce the effect of the true SO operator on all-electron valence orbitals [6]. The Gaussian-type basis set used was a 5sSp3d set contracted to 3s4p3d for mercury and 5s2p contracted to 3s2p for hydrogen. The pseudopotential parameters and basis set details are reported in ref. [3] along with the results obtained for the HgH molecule. Configuration interaction was carried out using the CIPSI algorithm with a three class selection of determinants [7]. In order to obtain a relatively small generator space, the calculation should be started with molecular orbitals describing as well as possible the active orbitals of the low-lying states of the system. Consequently our initial orbitals were obtained from SCF and MC SCF calculations. Since the mercury atom exhibits the same valence configuration as the magnesium atom, we have used the molecular orbitals and state correlation diagrams reported by Chaquin et al. (figs. 7 and 8 of ref. [S]). In the C,, insertion reaction Hg + H, + H-Hg-H the electronic configuration of the 1A, state for large Hg-H2 distances is lat2af and for short distances la: lb;. We thuscarried out an MC SCF calculation with two configurations (la:2af--la!lbi) for the 1A, state. For the 3 B state we used a two-configuration iz (laf2al lb,-2b22a1 lb,) MC SCF, in order to describe correctly the H-H bond dissociation by introducing the OH2 + 0; excitation. A set of molecular orbitals was obtained for each geometry from these MC SCF molecular orbitals and the occupied SCF orbitals of the lowest 3A1, 3A2, 3 B, and 1 A2 states. Similar considerations were applied for other molecular geometries. With these molecular orbital sets, the generator space included less than 200 determinants and 1000-1500 determinants were considered up to infinite order of perturbation. A second-order perturbation treatment recovers 5 to 10% of the total correlation energy. Core valence polarization is included via a secondorder perturbative treatment [9]. Spin-orbit coupling is introduced through an effective Hamiltonian in a basis of LS states [6]. The potential energy for the HgH2 system has been calculated at 200 different geometries in C,, C-v, C, and D,, symmetry.
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27 February 1987
3. Results and discussion 3.1. The ground state of the Hg-Hz system The ground state of HgH2 has D,n symmetry. The optimized bond length is found to be 1.64 A; this is smaller than the equilibrium bond length for the HgH(2Z+) molecule (1.76 A) and the binding energy is much larger for H-Hg-H (3 .15 eV) than for HgH (0.46 eV). Similar results have been obtained for MgH2 by Chaquin et al. [8] + 3.2. The approach of Hg and H2 (dH_H = 0.7414 A) On the basis of the qualitative considerations reported by Chaquin et al. [S] we assume that the behaviour of the ground state of the HgH, system is dominated by a repulsive four-electron interaction between the Hg(6s2) and OH2 orbitals. This repulsion is greatest in Czv symmetry due to the larger overlap of these orbitals. Moreover, the pv (b2) orbital occupied in the B2 state is stabilized by interaction with the u& orbitals. In contrast, the pZ (al) and pX (bl) orbitals are expected to lead to purely repulsive states Al and B,. The 3P and IP states are thus expected to split according to B2 < Bl < Al (C, geometry) and II < Z: (C,, geometry). These considerations are corroborated by the calculated potential energy surfaces (PESs) shown in fig. 1. The lB2 PES exhibits an energy minimum of about 0.43 eV in C, geometry at a distance of 1.85 A between Hg and the middle of the constant H-H bond (d(H-H) = 0.7414A). The 3B2 PES is very slightly attractive (with an energy minimum of about 0.22 eV at a distance of 2.0 A from H2) and so are the 3 II and 1B PESs in C, v geometry. Other potential energy curves are repulsive when the Hg-H2 distance decreases. For Hg-H2 distances greater than 2.25 A, minimum energies are obtained for a H-H distance practically equal to the equilibrium bond length in H2 (d = 0.7414 A). For smaller Hg-H2 distances, the variation of the potential energies observed when the H-H distance increases does not change the repulsive or attractive character of the different potential energy curves shown in fig. 1.
Volume 134, number 3
Q%
CHEMICAL PHYSICS LETTERS
21 February 1987
0
ng ______~
Hg______H,H
t
H -“A
cll-
czv
-2
Cdl
t
‘A,
FL I
-4
\ 1
2.
I
2.5
z
+
2.
R(R) Fig. 1. The approach of Hg + Hz in Czv and C, d(H-H) = 0.7414 A. SO coupling not included.
symmetry
3.3. The insertion reaction (Hg + H2 + H-Hg-H) C2, symmetry
in
3.3. I. Potential energy curves The MO correlations reported by Chaquin et al. (ref. [8], fig. 7) show a change in the nature of the MO for the lA, state of HgH, when the distance between Hg and the middle of the H-H bond decreases. The ground state Hg(' S) + Hz correlates to the ground state of H-Hg-H(lXi) via a large potential energy barrier. The lA1 PES may cross the 3 B2 and 1B, PESs. The existence of such crossings can have important effects on the mechanisms of the reaction of Hg(3P) or Hg(lP) with Hz. (The ‘A, state is coupled via SO interaction with the 3& and 1 B, states.) The C,, potential energy surfaces have been investigated in the expected crossing region of these lowlying states. About 30 points have been calculated for selected angles (Y,and for different Hg-H bond lengths. Fig. 2 shows the potential energy curves for a Hg-H bond length equal to 1.64& the L H-Hg-H angle varying from 26” @(H-H) = equilibrium distance of H2) to
Fig. 2. Bneding potential energy curves in C2, symmetry d(Hg-H) = 1.64 A. SO coupling not included.
180”. The 3B2 and lB2 PESs show a minimum for 01 ’ = 80”) a strongly bent geometry as suggested by Breckenridge et al. [l] . The IA1 PES is firstly strongly repulsive when (Yincreases (as expected) with a maximum energy for 50°
27 February 1987
CHEMICAL PHYSICS LETTERS
Volume 134, number 3
activation barrier. A large bending vibrational excitation of the ground state is then obtained, which probably leads to a large rotational excitation in the HgH(2.Z+) product as observed by Breckenridge et al. [l]. But the 3B2 state can also dissociate to HgH t H through the 3A’ state (C, symmetry). This 3A’ state is correlated to the 3 B2 state in Czv symmetry and to the dissociative 3E+ state in C,, symmetry (see fig. 3 and table 1). Such a pathway has been proposed by Simandiras and Handy [ 11 J for the reaction Ca(3P) t H2 + CaH(*E+) t H.
1
1.5
I
,
2.
I
2.5
The importance of this second process has not yet been evaluated. We hope that dynamical studies using classical trajectories, actually in progress, will enable us to determine the rotational distribution of the molecular product of the Hg(3P1) t H2 -+ HgH(2X+) + H reaction and of the Hg(3P1) + HD + HgD + H and Hg(3P1) + D, + HgD + D isotopic reactions. These results, when compared with experimental [ 1,2] should enable us to determine the relative importance of these two different pathways.
I
3.
3.5
D (a)
Fig. 3. The abstraction reaction H-Hg-H SO coupling not included.
-+ H + HgH(*Z+).
3.4. The abstraction reaction (Hg + Hz + HgH + H) in C,, symmetry
to complete dissociation to Hg t H t H. As noticed by Callear and McCurk [lo], the formation of HgH may occur via two alternative pathways. Firstly through SO coupling, the strongly bent HgH2 (3 Bz) state resulting from the Hg(3P1 ) t H, approach in C,,, symmetry can lead to the formation of HgH2(lA,) without any
The experiments of Breckenridge et al. [l] have shown that the reaction Hg(3P1) + Hz -+ HgH + H via the ZZstate of the HgH2 complex is relatively slow. This is consistent
with the repulsive
Table 1 HgH2 van der Waals complex states
W-H,
-ground Hg(%) state + Hz Hg(“P,)+H,
B
00
n
8
0 -____ 248
3X:+
3A’
H2
3n
3A’
Hz
3n
3A”
H2
3A 1
3B2
3B1
character
of the
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CHEMICAL PHYSICS LETTERS
3A, state which correlates to the X complex state in C,, symmetry (see table 1). In C,, symmetry the MO and correlation diagrams reported by Chaquin et al. (ref. [83, fig. 9) lead us to expect that the 3 Z+ state might have a slight energy barrier and thus might lead to the formation of HgH via tunneling. Potential energy surfaces have been investigated for different H-H and Hg-H bond lengths. Equipotential lines in C,, symmetry for the .Q = 1 state (dissociating to Hg(3P1) + H2 in Z: complex states) are shown in fig. 4. It can be seen that the minimum energy path has a small activation barrier at Hg-H, =
27 February 1987
1.85 A and a H-H distance of 1.06 8, of about 0.62 eV above the dissociative limit Hg(3P1) + Hz. A qualitative evaluation of the tunneling effect through this energy barrier gives a probab~ty of about 1 to 5%. For Hg(3P1) f H2(u = 0) reaction therefore occurs on a 10 to 50 ps time scale in good agreement with the experimentally observed reaction time scale (between 2 ps and 1 ns) [l].
4. Conclusion Use of relativistic pseudopotentials enables us to consider the HgH2 system as a four-electron system. The methods employed are convenient for the evaluation of potential energy sufaces for the HgHz system. The different behaviour of the two electronic configurations I: and II for the HgH2 van der Waals complex in the Hg(3P,) t H, + HgH (KS’) t H reaction is confirmed. The L: complex state forms HgH by tunneling through an energy activation barrier, in a linear geometry. The II complex state reacts more efficiently in C2v (or quasi-C2v symmetry) and two alternative pathways leading to HgH(2E’) are possible. We hope that dynamical studies actually in progress will lead to a better underst~ding of the mechanism of the Hg(3P1) + H2 reaction. A very different behaviour for the Hg(lPr ) t H, complex is expected and more experimental work is required to confirm this. This study represents a benchmark in the use of pseudopotential methods to reduce the calculations for a heavy atom to the valence electrons only. Trajectory calculations require good quality potential energy surfaces and SO coupling elements. They will be a good test of the quality of our PES and spin-orbit coupling treatments.
1:5
2:
215 DISTANCE Hg - H
Acknowledgement Fig. 4. Equipotential lines for the R = 1 state in C, symmetry. The zero equipotential line corresponds to the Hg + H + H energy. The distance between two equipotential lines is 0.005 au (0.136 eV). Note: at large Hg-H distances, the potential energy curves are dominated by the H2 potential energy curves. Since the transition energy Hg(’ So)-Hg(3Pr) is of the same order of magnitude as the Hz binding energy, crossing between the two 3.X*states Hg(3Pr) + H2t1Zg3 and Hg(‘So) + Hz(~Z$) occurs at a H-H bond length of 1.2 A. This explains why the equipotential lines at large Hg-H distances exhibit a maximum energy for &H-H) = 1.2 A.
The authors thank F. Spiegelmann, C. Jouvet, B. Soep and I. Nenner for helpful discussions. The calculations were done in part on CIRCE (Orsay) computers.
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CHEMICAL PHYSICS LETTERS
References [l] W.H. Breckenrldge, C. Jouvet and B. Soep, J. Chem. Phys. 84 (1986) 1443. [2] N. Bras, J. Buteaux, J.C. Jeannet and D. Perrin, J. Chem. Phys. 85 (1986) 280. [3] A. Bernier, P. Millie’and M. Pelissier, Chem. Phys. 106 (1986) 195. [4] J.C. Barthelat, M. Pelissier and P. Durand, Phys. Rev. A21 (1980) 1973. [5] P. Durand and J.C. Barthelat, Theoret. Chim. Acta 38 (1975) 283.
2.50
21 February 1981
[6] C. Teichteil, M. Pelissier and F. Spiegelmann, Chem. Phys. 81 (1983) 273. [7] S. Evangelisti, J.P. Daudey and J.P. Malrieu, Chem. Phys. 75 (1983) 91. [8] P. Chaquin, A. Sevin and H. Yu, J. Phys. Chem. 89 (1985) 2813. [9] G. Jeung, J.P. Daudey and J.P. Malrieu, J. Phys. B16 (1983) 699. [lo] A.B. C’allear and J.C. McGurk, J. Chem. Sot. Faraday Trans. II 68 (1972) 289. [ 1 I] E.D. Sinrandiras and NC. Handy, J. Chem. Sot. Faraday Trans. II 82 (1986) 269.
Volume 134, number 3
21 February 1987
POTENTIAL ENERGY SURFACES OF HgHZ Anne BERNIER and Philippe MILL16 CEA/IRDI/DESICP,
Dkpartement
de Physico-Chimie,
CEN/Saclay,
91191 Gif-sur-Yvette Cedex, France
Received 5 November 1986; in final form 8 December 1986
Potential energy surfaces for HgHz have been calculated using a nonempirical relativistic effective core potential incorporating configuration interaction by means of the CIPSI algorithm. Core valence polarization and correlation energy are included via a perturbative treatment. Spin-orbit coupling is introduced through an effective Hamiltonian. These theoretical results are used to discuss the experimental results of Breckenridge, Jouvet and Soep for the reaction Hg(3P1) + Hz + HgHc2 8+) + H.
1. Introduction
potential energy surfaces for the HgH, system. Because Hg has a large number of electrons all-electron calculations for the HgH, system would be very expensive. Using a relativistic effective core potential allows us to consider the mercury atom as a twoelectron system. Computational methods have been tested on the HgH molecule and good agreement obtained with the experimental spectroscopic constants for low-lying states [3]. Consequently, we have undertaken the exploration of the potential energy surfaces of the HgH2 system. We present theoretical results obtained for the Hg t H2 potential surface (C,, and C,, geometry), for the insertion reaction Hg + H2 + H-Hg-H (C,, geometry) and for the abstraction reaction Hg t H2 + H + HgH(2Z+) (C,, geometry). The different behaviour of the two van der Waals complex states Hg(3P1) t H, is discussed.
The Hg(3P1) t H2 system has recently been studied experimentally by Breckenridge, Jouvet and Soep [ 1] who carried out selective laser excitation of the van der Waals complex HgH, . The molecular product HgH(2 X+) was detected and rotationally analyzed. The two electronic configurations X and II of the complex Hg(3P1) + HZ, which correspond approximately to axial and perpendicular orientations, respectively, of the 6p orbital (see table 1) with respect to the freely rotating H2 molecule exhibit different behaviour. The reaction leading to HgH via the Il complex is direct, i.e. occurs within 0.1 ps and forms HgH(u = 0) with a rotational distribution peaked at J = 19. In contrast, the X complex forms HgH indirectly, i.e. the reaction occurs on a time scale greater than 2 ps. Furthermore, the HgH(u = 0) rotational distribution from the Z: complex is bimodal, with a major component similar to that from the n complex but a minor component definitely present at low J. Similar rotational distributions in the mercury hybride molecule produced by collision of Hg(3P,) with H,, HD or D, have been otained by Bras et al. 123. Breckenridge et al. [l], in their original paper, have discussed possible explanations for their experimental results with the help of theoretical results obtained for the isoelectronic systems MgH, and BeH,, but a better understanding of the processes by which reactants are converted into products requires theoretical 0 009-26 14/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
2. Computational method The mercury atom is considered as a two-electron system within a relativistic non-empirical effective core potential. Two component orbitals are derived from relativistic all-electron atomic calculations according to the method proposed by Barthelat et al. [4]. The nodeless one-component pseudo-orbitals and corresponding pseudopotentials are obtained following the B.V.
245
Volume 134, number 3
CHEMICAL PHYSICS LETTERS
method of Barthelat and Durand [S] . Effective spinorbit (SO) operators acting on pseudo-orbitals are derived in order to reproduce the effect of the true SO operator on all-electron valence orbitals [6]. The Gaussian-type basis set used was a 5sSp3d set contracted to 3s4p3d for mercury and 5s2p contracted to 3s2p for hydrogen. The pseudopotential parameters and basis set details are reported in ref. [3] along with the results obtained for the HgH molecule. Configuration interaction was carried out using the CIPSI algorithm with a three class selection of determinants [7]. In order to obtain a relatively small generator space, the calculation should be started with molecular orbitals describing as well as possible the active orbitals of the low-lying states of the system. Consequently our initial orbitals were obtained from SCF and MC SCF calculations. Since the mercury atom exhibits the same valence configuration as the magnesium atom, we have used the molecular orbitals and state correlation diagrams reported by Chaquin et al. (figs. 7 and 8 of ref. [S]). In the C,, insertion reaction Hg + H, + H-Hg-H the electronic configuration of the 1A, state for large Hg-H2 distances is lat2af and for short distances la: lb;. We thuscarried out an MC SCF calculation with two configurations (la:2af--la!lbi) for the 1A, state. For the 3 B state we used a two-configuration iz (laf2al lb,-2b22a1 lb,) MC SCF, in order to describe correctly the H-H bond dissociation by introducing the OH2 + 0; excitation. A set of molecular orbitals was obtained for each geometry from these MC SCF molecular orbitals and the occupied SCF orbitals of the lowest 3A1, 3A2, 3 B, and 1 A2 states. Similar considerations were applied for other molecular geometries. With these molecular orbital sets, the generator space included less than 200 determinants and 1000-1500 determinants were considered up to infinite order of perturbation. A second-order perturbation treatment recovers 5 to 10% of the total correlation energy. Core valence polarization is included via a secondorder perturbative treatment [9]. Spin-orbit coupling is introduced through an effective Hamiltonian in a basis of LS states [6]. The potential energy for the HgH2 system has been calculated at 200 different geometries in C,, C-v, C, and D,, symmetry.
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27 February 1987
3. Results and discussion 3.1. The ground state of the Hg-Hz system The ground state of HgH2 has D,n symmetry. The optimized bond length is found to be 1.64 A; this is smaller than the equilibrium bond length for the HgH(2Z+) molecule (1.76 A) and the binding energy is much larger for H-Hg-H (3 .15 eV) than for HgH (0.46 eV). Similar results have been obtained for MgH2 by Chaquin et al. [8] + 3.2. The approach of Hg and H2 (dH_H = 0.7414 A) On the basis of the qualitative considerations reported by Chaquin et al. [S] we assume that the behaviour of the ground state of the HgH, system is dominated by a repulsive four-electron interaction between the Hg(6s2) and OH2 orbitals. This repulsion is greatest in Czv symmetry due to the larger overlap of these orbitals. Moreover, the pv (b2) orbital occupied in the B2 state is stabilized by interaction with the u& orbitals. In contrast, the pZ (al) and pX (bl) orbitals are expected to lead to purely repulsive states Al and B,. The 3P and IP states are thus expected to split according to B2 < Bl < Al (C, geometry) and II < Z: (C,, geometry). These considerations are corroborated by the calculated potential energy surfaces (PESs) shown in fig. 1. The lB2 PES exhibits an energy minimum of about 0.43 eV in C, geometry at a distance of 1.85 A between Hg and the middle of the constant H-H bond (d(H-H) = 0.7414A). The 3B2 PES is very slightly attractive (with an energy minimum of about 0.22 eV at a distance of 2.0 A from H2) and so are the 3 II and 1B PESs in C, v geometry. Other potential energy curves are repulsive when the Hg-H2 distance decreases. For Hg-H2 distances greater than 2.25 A, minimum energies are obtained for a H-H distance practically equal to the equilibrium bond length in H2 (d = 0.7414 A). For smaller Hg-H2 distances, the variation of the potential energies observed when the H-H distance increases does not change the repulsive or attractive character of the different potential energy curves shown in fig. 1.
Volume 134, number 3
Q%
CHEMICAL PHYSICS LETTERS
21 February 1987
0
ng ______~
Hg______H,H
t
H -“A
cll-
czv
-2
Cdl
t
‘A,
FL I
-4
\ 1
2.
I
2.5
z
+
2.
R(R) Fig. 1. The approach of Hg + Hz in Czv and C, d(H-H) = 0.7414 A. SO coupling not included.
symmetry
3.3. The insertion reaction (Hg + H2 + H-Hg-H) C2, symmetry
in
3.3. I. Potential energy curves The MO correlations reported by Chaquin et al. (ref. [8], fig. 7) show a change in the nature of the MO for the lA, state of HgH, when the distance between Hg and the middle of the H-H bond decreases. The ground state Hg(' S) + Hz correlates to the ground state of H-Hg-H(lXi) via a large potential energy barrier. The lA1 PES may cross the 3 B2 and 1B, PESs. The existence of such crossings can have important effects on the mechanisms of the reaction of Hg(3P) or Hg(lP) with Hz. (The ‘A, state is coupled via SO interaction with the 3& and 1 B, states.) The C,, potential energy surfaces have been investigated in the expected crossing region of these lowlying states. About 30 points have been calculated for selected angles (Y,and for different Hg-H bond lengths. Fig. 2 shows the potential energy curves for a Hg-H bond length equal to 1.64& the L H-Hg-H angle varying from 26” @(H-H) = equilibrium distance of H2) to
Fig. 2. Bneding potential energy curves in C2, symmetry d(Hg-H) = 1.64 A. SO coupling not included.
180”. The 3B2 and lB2 PESs show a minimum for 01 ’ = 80”) a strongly bent geometry as suggested by Breckenridge et al. [l] . The IA1 PES is firstly strongly repulsive when (Yincreases (as expected) with a maximum energy for 50°
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CHEMICAL PHYSICS LETTERS
Volume 134, number 3
activation barrier. A large bending vibrational excitation of the ground state is then obtained, which probably leads to a large rotational excitation in the HgH(2.Z+) product as observed by Breckenridge et al. [l]. But the 3B2 state can also dissociate to HgH t H through the 3A’ state (C, symmetry). This 3A’ state is correlated to the 3 B2 state in Czv symmetry and to the dissociative 3E+ state in C,, symmetry (see fig. 3 and table 1). Such a pathway has been proposed by Simandiras and Handy [ 11 J for the reaction Ca(3P) t H2 + CaH(*E+) t H.
1
1.5
I
,
2.
I
2.5
The importance of this second process has not yet been evaluated. We hope that dynamical studies using classical trajectories, actually in progress, will enable us to determine the rotational distribution of the molecular product of the Hg(3P1) t H2 -+ HgH(2X+) + H reaction and of the Hg(3P1) + HD + HgD + H and Hg(3P1) + D, + HgD + D isotopic reactions. These results, when compared with experimental [ 1,2] should enable us to determine the relative importance of these two different pathways.
I
3.
3.5
D (a)
Fig. 3. The abstraction reaction H-Hg-H SO coupling not included.
-+ H + HgH(*Z+).
3.4. The abstraction reaction (Hg + Hz + HgH + H) in C,, symmetry
to complete dissociation to Hg t H t H. As noticed by Callear and McCurk [lo], the formation of HgH may occur via two alternative pathways. Firstly through SO coupling, the strongly bent HgH2 (3 Bz) state resulting from the Hg(3P1 ) t H, approach in C,,, symmetry can lead to the formation of HgH2(lA,) without any
The experiments of Breckenridge et al. [l] have shown that the reaction Hg(3P1) + Hz -+ HgH + H via the ZZstate of the HgH2 complex is relatively slow. This is consistent
with the repulsive
Table 1 HgH2 van der Waals complex states
W-H,
-ground Hg(%) state + Hz Hg(“P,)+H,
B
00
n
8
0 -____ 248
3X:+
3A’
H2
3n
3A’
Hz
3n
3A”
H2
3A 1
3B2
3B1
character
of the
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CHEMICAL PHYSICS LETTERS
3A, state which correlates to the X complex state in C,, symmetry (see table 1). In C,, symmetry the MO and correlation diagrams reported by Chaquin et al. (ref. [83, fig. 9) lead us to expect that the 3 Z+ state might have a slight energy barrier and thus might lead to the formation of HgH via tunneling. Potential energy surfaces have been investigated for different H-H and Hg-H bond lengths. Equipotential lines in C,, symmetry for the .Q = 1 state (dissociating to Hg(3P1) + H2 in Z: complex states) are shown in fig. 4. It can be seen that the minimum energy path has a small activation barrier at Hg-H, =
27 February 1987
1.85 A and a H-H distance of 1.06 8, of about 0.62 eV above the dissociative limit Hg(3P1) + Hz. A qualitative evaluation of the tunneling effect through this energy barrier gives a probab~ty of about 1 to 5%. For Hg(3P1) f H2(u = 0) reaction therefore occurs on a 10 to 50 ps time scale in good agreement with the experimentally observed reaction time scale (between 2 ps and 1 ns) [l].
4. Conclusion Use of relativistic pseudopotentials enables us to consider the HgH2 system as a four-electron system. The methods employed are convenient for the evaluation of potential energy sufaces for the HgHz system. The different behaviour of the two electronic configurations I: and II for the HgH2 van der Waals complex in the Hg(3P,) t H, + HgH (KS’) t H reaction is confirmed. The L: complex state forms HgH by tunneling through an energy activation barrier, in a linear geometry. The II complex state reacts more efficiently in C2v (or quasi-C2v symmetry) and two alternative pathways leading to HgH(2E’) are possible. We hope that dynamical studies actually in progress will lead to a better underst~ding of the mechanism of the Hg(3P1) + H2 reaction. A very different behaviour for the Hg(lPr ) t H, complex is expected and more experimental work is required to confirm this. This study represents a benchmark in the use of pseudopotential methods to reduce the calculations for a heavy atom to the valence electrons only. Trajectory calculations require good quality potential energy surfaces and SO coupling elements. They will be a good test of the quality of our PES and spin-orbit coupling treatments.
1:5
2:
215 DISTANCE Hg - H
Acknowledgement Fig. 4. Equipotential lines for the R = 1 state in C, symmetry. The zero equipotential line corresponds to the Hg + H + H energy. The distance between two equipotential lines is 0.005 au (0.136 eV). Note: at large Hg-H distances, the potential energy curves are dominated by the H2 potential energy curves. Since the transition energy Hg(’ So)-Hg(3Pr) is of the same order of magnitude as the Hz binding energy, crossing between the two 3.X*states Hg(3Pr) + H2t1Zg3 and Hg(‘So) + Hz(~Z$) occurs at a H-H bond length of 1.2 A. This explains why the equipotential lines at large Hg-H distances exhibit a maximum energy for &H-H) = 1.2 A.
The authors thank F. Spiegelmann, C. Jouvet, B. Soep and I. Nenner for helpful discussions. The calculations were done in part on CIRCE (Orsay) computers.
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