Potential energy surfaces for excited neon atoms interacting with water moleculesJohn Bentley Citation: The Journal of Chemical Physics 73, 1805 (1980); doi: 10.1063/1.440316 View online: http://dx.doi.org/10.1063/1.440316 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/73/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Chirality of weakly bound complexes: The potential energy surfaces for the hydrogen-peroxide−noble-gasinteractions J. Chem. Phys. 141, 134309 (2014); 10.1063/1.4897136 An exchange-Coulomb model potential energy surface for the Ne–CO interaction. II. Molecular beam scatteringand bulk gas phenomena in Ne–CO mixtures J. Chem. Phys. 132, 024308 (2010); 10.1063/1.3285721 An exchange-Coulomb model potential energy surface for the Ne–CO interaction. I. Calculation of Ne–CO vander Waals spectra J. Chem. Phys. 130, 244310 (2009); 10.1063/1.3157169 Ab initio intermolecular potential energy surfaces of the water-rare gas atom complexes J. Chem. Phys. 129, 184310 (2008); 10.1063/1.3009270 First-order intermolecular diatomics-in-molecule potentials. Potential energy surfaces, spectra, andfragmentation dynamics of the NeCl 2 complex J. Chem. Phys. 106, 10134 (1997); 10.1063/1.474059

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Potential energy surfaces for excited neon atoms interacting with water molecules

John Bentley

Radiation Laboratory. a) University of Notre Dame. Notre Dame. Indiana 46556 (Received 24 December 1979; accepted 9 May 1980)

A substantial body of experimental data on interactions of metastable rare gas atoms with water molecules exists. but models of the interaction process are lacking. In order to interpret experiments involving collisions of Ne* with H20. molecular orbital calculations with configuration interaction have been carried out for the six three-dimensional potential surfaces arising from interaction of Ne (2p '3s 1.3 P) with a rigid H 20 molecule. Basis sets of roughly double zeta and double zeta plus polarization quality have been used. An attraction of 0.25 eV is found between Ne* and H20 at a neon-oxygen distance of 2.S A. in good agreement with the structure calculated for a Na-H20 complex. Multipolar expansions of the lowest triplet potential surface are reported. Interpretation of Penning ionization electron spectra and some excitation transfer results is aided by the present surface. An electrostatic model is proposed to construct potential surfaces of the type presented here.

I. INTRODUCTION

The investigation of interactions of atoms and mole­cules in electronically excited states has long been a fruitful area of chemical physics, providing much in­formation on energy transfer mechanisms, nature of excited states, and so forth. 1 Many experiments have been performed involving quenching of reactant excited state fluorescence or observation of fluorescence from excited products. Recently molecular beam techniques have been used to examine interaction potentials by fluo­rescence time-of-flight appearance times. 2 Theoretical investigations have concentrated on diatomic and tri­atomic systems, such as the excited potential curves of rare gas oxides and halides, 3 and the Penning ionization systems, 4. 5 HeH* and HeH~. Relatively little attention has been paid to the class of processes in which elastic and inelastic scattering occurs without electronic deexcita­tion of the excited species. Such processes are usually in competition with quenching or reactive processes and tend to be more difficult to detect. If they can be stud­ied, however, they contain as much information on the nature of the interaction as the more dramatic processes involving electronic rearrangement.

An example of an excited state interaction in which in­elastic processes can be easily studied is the collision of metastable rare gas atoms with small, ground state molecules. The long lifetimes of the 3PO.2 states of neon through xenon, and the 2 1

• 3S states of helium, make them ideal for molecular beam studies. Excitation transfer and Penning ionization processes involving these species have been observed, but the cross sections for quenching of metastables are not generally so large as to obscure all the structure in the nonreactive differential cross sections. In addition, it has been possible to pursue the analogy between rare gas metastables and alkali atoms into the realm of dynamics. 6.7

One system that has been studied by a variety of meth-

a)The research described herein was sUpported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-2066 from the Notre Dame Radiation Laboratory.

ods is that of rare gas metastables plus water mole­cules. Clyne et al. 8 observed the emission from elec­tronically excited OH (OD) molecules following dissocia­tive excitation of HaO (D 20) by Ar*. They interpreted their results in terms of an excitation transfer process, followed by a dissociation:

Ar*+H20-Ar+H20* ,

H20* - OH* (A 26 +) + H .

(la)

(lb)

The observed lack of energy balance was taken to indicate that the kinetic energy of products of reaction (la) was large. The Penning ionization processes

Ne* +HzO-Ne+H20·+e-

He* + H20 - He + H20. + e- (78. 0%)

- He +OH+ +H +e- (17.8%)

- other ionic products (4.2%)

have been observed by mass spectrometric detection of ionic products by Sanders and Muschlitz. 9 Cermak and Yencha10 have studied the same systems by kinetic ener­gy analysis of the released electrons, reporting relative intensities and energy shifts for the production of HP+ in the 2B1 and 2AI states. They concluded that large wells were present in the excited state potential sur­faces and that ionization occurred over a wide range of intermolecular distances. In a flowing afterglow study of He* (2 3S) + H20, Yencha and Wull have shown that neutral dissociative excitation processes are competi­tive with Penning ionization. Absolute cross sections for quenching by water at thermal collision velocities have been reported for Kr* (115 11..2., Ref. 12), Ar* (107 11..2, Ref. 12), and He* (105 1\2., Ref. 13); that for Ne* can reasonably be assumed to be of the same order. Reaction of Xe* with H20 gives rise to an ultraviolet emission band14 that has been ascribed to XeOH*.

This large body of experimental data has not resulted in any specific description of the mechanism by which rare gas metastable-water reactions occur. In an at­tempt to attack the problem from the reactant direction. Manzanares, Bentley, Winicur, and Haaser have car­ried out presently unpublished differential (with respect

J. Chern. Phys. 73(4), 15 Aug. 1980 0021-9606/80/161805-09$01.00 © 1980 American Institute of Physics 1805

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1806 John Bentley: Neon atoms interacting with water

to angle) and doubly differential (with respect to angle and velocity) cross section measurements for the systems Ne* + H20 and Ar* + H20, observing in each case elastic and rotationally inelastic scattering of the rare gas by the water. Attempts to fit the data with simple van der Waals potentials were unsatisfactory, suggesting that the anisotropy of the interaction was more than a weak perturbation. This inference was strengthened by the appearance of molecular orbital calculations on com­plexes between alkali atoms and polar molecules, car­ried out by Trenary et al~ 15 They showed that adducts of lithium and sodium with ammonia, water, and hydrogen fluoride are bound by from 1 to 15 kcal/mole.

The studies by Trenary et al. imply that the Ne* +HP surface is highly anisotropic, but do not suggest how rigid the Ne-Q bond is likely to be. A complete po­tential surface for the Ne* + Hp interaction was con­sidered necessary for interpreting the scattering cross sections. It was also felt that such a surface would help to unify the other experimental data mentioned above. This paper reports molecular orbital-config­uration interaction calculations on the potential surfaces arising from interaction of 2p - 3s excited neon atoms with ground state water molecules and it offers some in­terpretations of various experimental findings.

II. COMPUTATIONAL PROCEDURE

Molecular orbital (MO) calculations were carried out for the ground state of the NeHp supermolecule, keep­ing the H:P geometry fixed at the nominal experimental geometry used by Aung et al. 16 in their H20 calculations and varying the position of Ne. Stevens' program POLYCAL 17 was used for the MO calculations. The basis set used in most of the calculations was essentially a double-zeta set of Slater-type orbitals (STO) plus a 3s STO on neon. Orbital exponents and their sources are given in Table I. This basis set was intended to meet the conflicting requirements of maximum accuracy and minimum computer usage. How well it managed will be indicated in Sec. IV B. The MO's from the ground state calculation were used to construct determinants for con­figuration interaction (CI) calculations on excited states

TABLE I. Orbital exponents.

Neon" Oxygenb Hydrogenb

15 9.63 15 7.65 Is 1. 33 25 2.18 25 1. 74 Is 2.47

25 3.49 25 2.90 2p 2.05 2p 1. 56 2p 4.67 2p 3.60 35 0.69 [3d 1. 66]d

[3p 0.691 c

"Neon exponents were taken from Table 40.1 of E. Clementi, IBM J. Res. Dev. 9. 2 (1965), supplement. except for the 15 exponent [E. Clementi and Raimondi, J. Chem. phys. 38, 2686 (1963)], and the 3s exponent (Ref. 28).

lHydrogen and oxygen exponents were taken from wave function II of Ref. 16.

cUsed only in basis sets III and IV. dUsed only in basis sets II and IV.

of the system. Since the 2p- 3s manifold of neon excited states lies around 16.7 eV and the first ionization po­tential of water is 12.6 eV. the excited states of interest are embedded in the continuum of Ne + H20' + e- states.

A commonly used computational strategy for calcu­lating discrete states in the ionic continuum is to per­form a CI calculation using a discrete orbital basis set and to select those CI eigenvalues whose density ma­trices contain the appropriate excitation. This is some­times referred to as the stabilization method. 18 The roots of the CI which lie above the ionization potential of the system describe both discrete and continuum states. However, the discrete states are satisfactorily described by the basis set used, whereas the continuum states are approximated by projecting continuum or­bitals onto the discrete basis set. Thus the discrete states are relatively insensitive to variations in basis set composition and CI expansion length, while the con­tinuum states fluctuate with such variations. This fea­ture proved useful for limiting the size of both the basis set and the CI expansion length. Using basis set I de­scribed in Table I, we determined the potential curves of the excited states of interest with a CI list containing all single and double excitations from the ground state involving MO's with orbital energies between + 2 and - 2 hartrees. The excited state energies obtained were very similar to those obtained when a substantial num­ber of double excitations were deleted from the list. The energies to be reported here were obtained with CI expansion lengths of from 90 to 200 determinants, de­pending on the symmetry of the supermolecule.

Indentification of the excited states of interest was usually straightforward. Unless the Ne-O internuclear distance was less than about 4 bohr, the determinant with the Single excitation Ne 2px.y. or.- Ne 3s generally had a CI coefficient greater than 0.98. At small inter­nuclear distances, the neon and water subsystems tended to lose the ir independent identities.

III. POTENTIAL SURFACES

Calculations were carried out at Ne-Q internuclear distances of roughly 1. 5-5 A, along eleven directions of approach of Ne to H20, corresponding to polar angles (from water's C2V axis) of 0°,45°,90°, 135°, and 180° and azimuthal angles (from water's nuclear plane) of 0°, 45°, and 90°. At each of 106 points, the eigenvalues were determined for the ground state and the three triplet and three singlet states arising from interaction of Ne* 3p and Ip, respectively, with Hp. The result­ing potentials V(R, e, ¢) were fit by a multipolar expan­sion about the center of mass of the water molecule,

V(R, e, ¢) = L: Vlm(R)pr(cose) cosm¢ . 1m

Multipolar expansions up to 1 = 4 were examined. The surface for the lowest excited triplet state appears in Fig. 1, and its radial coefficients Vlm(R) are given in Table II. The root-mean-square deviation is 13.50 mhartrees, or 367 meV, with the largest deviations at small intermolecular distances. If points with neon­oxygen distances less than 3.5 a. u. are omitted, the

J. Chern. Phys., Vol. 73, No.4, 15 August 1980

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John Bentley: Neon atoms interacting with water 1807

Nell+ ~O Lowest Triplet State

Molecular Plane

, I / I I /

L./ I I I -5IN/ I I ___ -=::::::::;:::::::~~ ,,/ / I

- 7 '" / I , ~- .... "" / / / \. /'" /./ I

\ ..... _- /,/ / " .... / / ~,--- ,,/',/ / ~ ...... ---~ ,," / ~.::::.~----.... "" " .:\, ........ _--..",/ ...,/ ." , ,,' ~\' -----~ \', /"" : \ ...... _--..,.,...

Bisector Plane FIG. 1. Lowest triplet potential energy surface for Ne* + H20, calculated with basis set I. contours begin at the values indi­cated and decrease by a factor of one half for each contour. The upper part of the figure represents in-plane and the lower part out-of-plane approach of neon.

rms deviation is 0.197 mhartree (5.36 meV). The omitted points are almost all well up the repulsive wall. The singlet and triplet surfaces parallel each other closely, so discussion will be restricted to triplets. The important features of the surface are (0 the strong attraction of neon for the oxygen end of the molecule and (ii) the lack of symmetry between in-plane and out­of-plane approach of neon to water. These features are

0.40...----------------,

0.20 Ip

0.00 ------3p

~ -0.20 >. ~ C&I -0.40 Iii '0

I -0.60

:~ o ----------------------

IS

2.0 3.0 4.0 5.0

Ne - 0 separation I .& FIG. 2. Potential curves for the ground and certain excited states of Ne* +H20, calculated with basis set I. Neon approaches the oxygen end along the C2v axis. Full curves have At sym­metry; dashed curves have B t symmetry; dotted curves have B2 symmetry.

present in all the excited state potentials calculated here.

Figure 2 displays potential curves for all the states considered, taken along the C 2• axis containing the po­tential minimum. The near identity of corresponding triplet and singlet state curves is readily apparent. The main point to be drawn from this figure is that the orientation of the 2p hole in neon has little effect on the potential surfaces until small'intermolecular distances

TABLE II. Multipole coefficients (in hartrees) for the lowest triplet state of He* + H2O, using bas is set I.

R (lJohrs) voo VIO V'O V 22 V 30 V 32 V'O v" v" ;l.30 o. O~~ 371i - O. 097301 0.003149 -0.022081 0.036723 0.008880 - 0.024387 - 0.002087 0.000110 3. 7.) 0.05208~ - O. 073 024 0.001639 - O. 015399 0.021938 0.005375 - O. 015 365 - O. 001304 0.000056 .1. 00 IJ. 031 706 - O. 055 551 - 0.000698 - O. 011 038 0.012641 0.003141 - O. 008 613 - O. 000 747 0.000021i ,f. ~5 0.019667 - O. 043 393 - O. 000204 -0.007696 0.007442 0.001846 - O. 005912 - O. 000498 0.000007 4. ;)0 0.0128·14 - O. 034 059 - O. 000476 -0.005367 0.004015 0.001074 - O. 003429 - O. 000 347 - O. 000 002 4. i5 0.009334 - O. 027 Ii 74 - O. 000 380 - O. 004173 0.002674 0.000704 - O. 002 511 - O. 000 232 - O. 000 002 :"i. 110 0.007402 - O. 022 545 - O. 000970 - O. 003 527 0.001709 0.000498 - O. 001296 - O. 000 117 0.000003 .J. 2.) O. OOS Til -0.018482 - O. 000616 - O. 002 737 0.001366 0.000357 -0.000941 - O. 000 085 0.000001 J.:>O 0.004821 -0.013615 - O. 000334 - O. 002 248 0.001357 0.000315 - O. 000 940 - O. 000 076 0.000000 J.7;) 0.004090 -0.013030 - O. 000309 - O. 001898 0.001050 0.000262 - O. 000619 - O. 000 054 0.000001 (i,OO 0.003334 -0.010775 - O. 000 535 - O. 001639 0.000780 0.000206 - O. 000 210 - O. 000 023 0.000001 li.20 0.002998 - O. 008 916 -0.000472 - O. 001347 0.000679 0.000168 - O. 000 151 -0.000015 0.000000 Ii. 50 0.OO23'i7 - 0.007379 - O. 000393 -0.001113 0.000582 0.000142 -0.000139 -0.000012 0.000000 li.73 0.002209 - O. OOG 130 -0.000301 - O. 000 927 0.000509 0.000127 - O. 000 147 -0.000014 0.000000 7.00 0.00191G - O. 005 107 - O. 000224 - O. 000 778 0.000473 0.000117 - O. 000183 -0.000017 0.000001 7. ~5 0.001 G07 - O. 004148 - O. 000 190 - O. 000634 0.000381 0.000093 -0.000141 - O. 000 014 0.000000 7.30 0.001343 - O. 003355 - O. 000 151 - O. 000 513 0.000316 0.000075 - O. 000 104 -0.000011 0.000000 7.7;) 0.001123 - O. 002 709 -0.000115 - O. 000415 0.000267 0.000060 - O. 000 075 - O. 000 009 0.000000 ~.OO 0.000934 - O. 002 189 -0.000087 - O. 000 335 0.000236 0.000048 - O. 000 056 - O. 000 008 0.000000 tl. ~5 0.0007H -0.001772 - O. 000 067 -0.000272 0.000218 0.000038 -0.000047 - 0.000007 0.000000 8.50 O. 000635 - O. 001435 - O. 000 054 - 0.000219 0.000197 0.000029 - O. 000 035 - O. 000 005 0.000000 8. 75 0.000514 - O. 001151 - O. 000 046 - O. 000 172 0.000160 0.000020 - O. 000 023 - O. 000 003 0.000000

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1808 John Bentley: Neon atoms interacting with water

are reached. The structure in the 8 2 states is due to mixing with nearby continuum eigenfunctions and can be displaced or removed by varying the basis set (vide infra).

Observe in Fig. 2 that the Al curve of either multi­plicity crosses both the Bl and B2 curves of the same multiplicity. Away from the C2v axis, where the sym­metry is lower, these crossings are avoided, and the full three-dimensional surfaces exhibit two (hyper)coni­cal intersections of the type discussed by Herzberg. 19

We need not dwell on this feature, however, because the ordering of states at small intermolecular distances is an artifact of the CI expansion list. Some configura­tions that make negligible contributions to the energy at 7 a. u., and which were therefore omitted from the list, become increasingly important at smaller distances. The present program cannot handle the large CI expan­sions necessary to establish unequivocally the ordering of states, but a limited search for important configura­tions suggests that the Al state is lowest in the region of the well and repulsive wall. This agrees with an argument based on electron repulsions: the Al state has less electron density in the neon core orbital with the largest overlap with water orbitals.

IV. DISCUSSION

A. Potential surfaces

It is obvious from Fig. 1 and Table II that most of the anisotropy of the interaction is accounted for by the di­pole component of the potential. However, multipoles up to I = 4 are needed to obtain a surface that gives a good fit to all the ab initio data. The bonding in systems of this type has been describedl5

•2o as that of Lewis acid­

Lewis base adducts, with water acting as the Lewis base. In this framework, the asymmetry between in-plane and out-of-plane neon approach is readily explained: The water orbitals that can act as electron donors are 3ab which points along the symmetry axis, and Ib l , the oxy­gen 2prr orbital. In-plane approach encounters 1b2 , a poor donor, and is energetically disfavored.

The potential surface of Fig. 2 bears a striking re­semblance to the electrostatic potential surface for water reported by Scrocco and Tomasi2l (see their Figs. 2 and 3 on p. 108 of Ref. 21). This similarity empha­sizes the electrostatic nature of the interaction between Ne* and Hp. Further confirmation is given by the elec­tron density difference plot for Ne* +HP eA l ) shown in Fig. 3. The enhanced polarity of water, the repulsive polarization around neon, and the absence of a covalent bond between Ne and 0 are all apparent.

As a by-product of computing the excited state poten­tials, a potential surface for the ground state interac­tion of neon and water has also been produced. This surface is slightly anisotropic, and exhibits a well of about 30 meV at a Ne-O distance of about 3.5 A. Ne + Hz<) has been studied by crossed molecular beams by Bickes et at. , 22 who used a spherical interaction model and obtained a well depth and location of 5.5 meV and 3.20 A, respectively. Self-consistent-field (SCF) mo­lecular orbital calculations on this system have been

----............. , /1 ..... / ----_/

-.2

\ \ I I

/

0.: .2

FIG. 3. Electron density differences map for 3At at Ne-O dis­tance of 5 bohr (2.65 X). calculated with basis set IV. The separated-molecule density function was approximated by the CI density function at Ne-O distance of 13 bohr (6.88 XL

carried out by Losonczy et al. ,23 who reported a favored hydrogen bond structure (O-H" . Ne) with a well depth and a Ne~ distance of 7.4 meV and 3.63 A, respective­ly. The present calculations reproduce neither the mag­nitude of the experimental well depth nor the anisotropy of the previous calculation, and the spread in pOSition of the well minimum is quite large. The present basis set is inappropriate for calculating long-range interactions, so these discrepancies are not surprising.

B. Effect of expanding orbital basis set

With a limited baSis set such as that of Table I, the possibility exists that important contributions to the in­teraction may have been neglected. In the present case, the features that determine the interaction strength are the polarity (or the electron-donor capacity) of H20 and the polarizability of Ne*. Two new basis sets were formed to deal separately with the effects of altering each of these features. Basis set II was formed by add­ing to basis set I (Table I) a set of 3d orbitals (exponent = l. 66) on oxygen, and basis set III added a set of 3p orbitals (exponent = 0.69) on Ne to basis set 1. A fourth basis set contained both additional orbitals. Calcula­tions were performed with basis sets II-IV for C 2v nu­clear configurations only. The results are shown in Fig. 4 for the 3Al state. The trends are repeated by the other excited states.

The addition of a 3d orbital on oxygen leads to a sub­stantial decrease of about 0.3 eV in well depths. This is not unexpected. It is known that double-zeta basis sets tend to overestimate molecular dipole moments and that addition of polarization functions brings calcu­lated dipole moments closer to experimental values. 24

In the present context, it seems that basis set I places too much electron denSity in the oxygen nonbonding or­bitals, exaggerating the electron donor ability of the water molecule and thus the strength of the bond. Ad­dition of the 3d orbital corrects this tendency, decreas-

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John Bentley: Neon atoms interacting with water 1809

TA BLE Ill. Well parameters for Ne* + H20, using basis set IV.

state

well depth (eVl Ne-O distance (Al

0.26 2.38

0.24 0.22 2.45 2.65

0.25 0.20 2.45 2.59

0.21 l.ti5

ing the strength of the interaction. Note also that the well minimum and repulsive wall are at distances about 0.2 A. larger. As an indication of the reduced molecu­lar polarity of basis set II, the SCF molecular dipole moments of water are 2.79 D (basis set I) and 1.95 D (basis set II).

It has been shown that the proper description of po­larizability and long-range interactions requires the presence of diffuse polarization functions in the orbital basis set. 25 The Ne 3p orbital of basis set III is a step in this direction. The increase in long-range attraction due to greater Ne* polarizability is evident in both the 8 = 00 and 1800 directions. Because the additional or­bital has little effect on the repulsive part of the curve, the wells are deepened (by about 70 meV) and shifted to slightly larger distances.

Both of these effects are included in baSis set IV, which is the most accurate calculation reported in this work. The final well parameters for the excited states appear in Table Ill. Basis set IV is the largest we can manage practically, and with it we are restricted to cal­culations on the C Zv axis, where symmetry holds down the size of the CI expansions. Further improvements in the orbital basis set and in the description of elec­tron correlation are certainly possible. The most im­portant present deficiency is the lack of 2p polarization functions on the hydrogen atoms. This probably leads to the overe~timation of repulsion in the approach of Ne* at the hydrogen end of the molecule. With this caveat, we believe that baSis set IV contains all the im­portant physics of the Ne* + H20 interaction.

Obviously the change from basis set I to IV has a con­siderable effect on the shapes of the potential curves in the C2v direction. We felt it was necessary to explore the less symmetric directions to assure ourselves that the overall surface had not been grossly changed by the basis set improvement. As mentioned above, computing

~ '6 ~

i

0.2

0.0

.. -0.2

J c ....

-0.4

-0.6 2~--~--~3~--~--~4----~~

Ne-O separation, a FIG. 4. Effect of basis set variation of 3At potential curves in the C2v directions. Neon approaches along the C2l> axis. At­tractive curves are for approach at oxygen end; repulsive at hydrogen end. The repulsive curve for basis set II is similar to that for basis set 1.

limitations preclude a thorough study with basis set IV. However, with the use of a smaller CI expansion (about 60 configurations) and a sparse grid of geometries, it was possible to obtain a multipole expansion represen­tation of the lowest triplet surface. This is given in Table IV. The rms deviation for this surface is 0.087 mhartree. There are no surprises. The monopole com­ponent is less repulsive than that of Table II, due to the long-range stabilization afforded by the Ne 3p orbital. The dipole component is notably weaker, due to the im­proved description of water's dipole moment in the ex­panded basiS set. Changes in the higher multipoles are generally small. The contour map corresponding to

TABLE IV. Multipole coefficients (in hartrees) for the lowest triplet state of Ne* + H2O, using basis set IV.

R(bohrs) Voo V10 V 20 V 22 V 30 V 32 V,o V'2

3.50 0.057922 -0.034752 0.006805 0.006184 0.008222 -0.001622 -0.018547 0.001064 4.00 0.028623 -0.034257 0.001873 0.006481 0.007805 - 0.001672 - O. 008 546 0.000497 4.50 0.0l4196 -0.028013 0.000260 0.005651 0.007478 -0.001394 -0.003583 0.000247 5.00 0.007993 -0.019205 -0.000575 0.004109 0.004620 -0.001064 - O. 001779 0.000158 5.50 0.004446 -0.013274 -0.000396 0.002933 0.003043 -0.000723 - O. 000933 0.000068 6.00 0.002910 -0.009157 -0.000427 0.001936 0.001940 -0.000439 -0.000636 0.000023 6.50 0.001848 - 0.006210 -0.000326 0.001303 0.001291 -.0.000285 -0.000539 0.000008 7.00 0.001283 -0.004264 -0.000259 0.000870 0.000910 -0.000189 - O. 000477 0.000006 7.50 0.0008Il -0.002868 -0.000242 0.000574 0.000662 -0.000107 -0.000325 0.000004 8.00 0.000501 -0.001960 -0.000238 0.000385 0.000521 -0.000052 -0.000179 0.000004 8.50 0.000313 -0.001328 -0.000221 0.000259 0.000404 -0.000025 -0.000098 0.000004 9.00 0.000205 -0.000792 -0.000161 0.000155 0.000232 - O. 000 025 -0.000122 -0.000001

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1810 John Bentley: Neon atoms interacting with water

Table IV resembles Fig. 1 closely, the main differences being that the well is shallower and the attractive re­gion in the bisector plane extends to larger angles from the CZu axis. Although the multipole expansions of Ta­ble IV certainly have less precision than those of Table II, the former are a better representation of Ne* + HP potential surfaces and are more suitable for scattering calculations on this system. (The smaller CI used in Table IV produced a well depth lC1fo smaller than that of Fig. 4 and a very similar CZu potential curve. )

C. Comparison with Na + H:P calculations

Trenary et al. 15 have determined the molecular struc­ture of the complex between a neutral sodium atom and a water molecule by using molecular orbital methods. They report a dissociation energy of 0.23 eV and an equilibrium Na~ distance of 2.38 A with the same CZu equilibrium geometry found here for Ne* +Hp. The more polarizable Ne* is expected to bind more strongly to water than sodium does. The present calculations with basis set IV are quite similar to the NaHzO calcu­lation, with differences attributable to different proper­ties of Na and Ne* and to the different composition of the orbital basis sets.

D. Spin-orbit interactions

All the calculations reported here have been carried out with the assumption of Russell-Saunders coupling of spin and orbital angular momentum. It is, however, well known that the neon 2p- 38 manifold is split by spin-orbit coupling into 3P2.1.0 and IPI states. 26 This splitting is bound to persist in the Ne* + HaD complex; although the strength of the coupling will probably vary.Z7 We do not think that the spin-orbit interaction will have an important effect on the present potentials, for the following reason. As shown in Fig. 2, the potentials that would be mixed by spin-orbit coupling are all quite similar to each other and would probably not be displaced much by the coupling. This is in contrast to the situa­tion in Ne:, for which Cohen and Schneider have reported MO-CI calculations. 28 In that system, the nuclear ex­change symmetry gives rise to attractive and repulsive potential curves, and the spin-orbit interaction leads to considerable mixing and displacement of states rela­tive to their Russell-Saunders precursors. The simi­larity between states of different spin and symmetry in the present study suggests that spin-orbit coupling would not change the qualitative description of the Ne* -HzO system presented in Sec. IV.

E. Penning ionization experiments

The present calculations shed some light on the Pen­ning ionization experiments of Cermak and YenchalO on the system Ne* (3PZ) + HaD. As illustrated in Fig. 5, the Penning process may be classically described as an excited state collision which auto ionizes at its classical turning point and jumps to the appropriate ionic poten­tial curve, with the balance of energy appearing as the motion of the released electron. Z9 The electron kinetic energy is equal to the difference between excited and ionic potential energies at the turning point:

VIR)

VIR)

---Ne·+~

R(I\O-Ne)

1-------Ne" +HzO

Ibl

H H

dr~ @ ~----- Ne +~12BI)

RI~-Ne)

FIG. 5. Schematic description of Penning ionization in Ne* + H20. The molecules collide on the upper surface, undergo a vertical transition, and recede on the lower surface.

E. '" V* (R,) - V ·(R,) .

Defining an asymptotic electron energy

Eo'" V*(oo) - V·(oo) ,

one can determine an energy shift

tl.E",E. -Eo,

(2)

which is obviously related to the shapes of the potential curves involved. Cermak and Yencha reported that the Penning ion HzO· was produced in the zB l and zA I states with shifts of -70 and - 350 meV, respectively. The 2Al signal was several times more intense than that for zB l • They drew the conclusions that the excited state potential has a well deeper than can be accounted for by van der Waals and dipole-induced dipole attractions and that Penning ionization takes place over a wide range of intermolecular distances. We are now in a position to expand on these remarks.

In the Penning process, the orbital on water that is most likely to be ionized is that which penetrates the Ne 38 orbital and encounters the 2p hole. If neon approaches along the CZu axis, this will be the 3al orbital; if neon is above the molecular plane, it will be the Ib} orbital. These will result in zA} and 2Bl ions, respectively. No other states of HzO· are energetically accessible at ther­mal collision energies.

The Penning ionization energy shifts depend on the ionic as well as the excited potential surfaces r see Eq. (2)]. However, we shall argue that the ionic surfaces are sufficiently isotropic, and their attractive regions sufficiently weak, that the features of Penning ionization are essentially determined by the excited surfaces. The ionic surfaces consist of a short-range overlap repulsion term and long-range induction and dispersion terms,

V·(R) '" V· (R) -~ CiNo R-4 - 2J..LH~O. CiNoR-5 cosB + o (R-6) ,

rOP ~ (3)

J. Chem. Phys., Vol. 73, No.4, 15 August 1980

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John Bentley: Neon atoms interacting with water 1811

where a Ne is the polarizability of neon and j.J. H20. is the dipole moment of the water cation. We might approxi­mate the repulsive term by the repulsive ground state neutral interaction, ~.,(R), which would overestimate somewhat the strength of the repulsion. As a refine­ment on this, we might add the appropriate orbital ei­genvalues, i. e., apply Koopman's theorem30

:

V;.,(R) = ~ep(R) + E::r(R) .

E::r is the eigenvalue corresponding to either the 3a1 or 1b1 orbital in the water molecule. The induction terms in Eq. (3) are readily computed if one assumes J.L H 20.

'" J.L H20' Since electrons have been removed from or­bitals with most of their density around oxygen, the ion's dipole moment (relative to the center of mass) ought to be slightly less than the neutral molecule's, so the as­sumption is reasonable.

With either approximation for V;.P' the result is that the ionic potential surfaces are rather isotropic (much more so than the excited state surfaces) and not very attractive (with wells less than 80 meV in all models). Thus, in the classical picture of Penning ionization de­scribed previously, the determining feature is the turn­ing point R t on the excited state surface. This distance is about half an angstrom less for C 21J approach (2A1 product) than for out-of-plane approach (2B1 product). Thus 2A 1 products are produced higher up the repulsive part of the ionic potential energy curve and have larger energy shifts. The difference in R t also helps to ex­plain the observed intensity differences in ionic products. Since, in the calculations performed to date, 4,5 the cou­pling of excited to ionic channels [autoionization width r(R)] decreases exponentially with increasing molecule­rare gas distance, 2A1 ion production is more probable. A quantitative discussion of Penning ionization in this system must await the calculation of ionic potential sur­faces and of the auto ionization width as a function of Ne* poSition.

The foregoing arguments suggest that a negative cor­relation between energy shifts and populations of differ­ent ionic product channels ought to be a general feature of Penning ionization of Lewis bases by rare gas meta­stables. This is borne out by Cermak and Yencha's study31 of Ne* interactions with molecules containing the cyano (-CN) group: populations of ions produced by loss of a lone-pair electron from nitrogen are 2.5 to 7 times greater than if a CN 7r electron is removed, and the O"-ion peaks have energy shifts 10 to 45 meV more negative than the 7r-ion peaks. From Kollman's calcu­lation32 of the electrostatic potential of HCN and the cal­culations of Trenary et ai. , 15 we expect the most at­tractive RCN ... Ne* configuration to be linear. Hotop et ai. 33 have reported energy shifts and intensity ratios for He* ionization of a group of molecules, none of which is a strong Lewis base. In this case, the negative cor­relation between I1E and intensity is not expected, nor does it occur.

F. Excitation transfer experiments

In flowing afterglow studies of OH (A 2~+) emission following collisions of Ar* with HP, Clyne et ai. 8 ob-

served that the energy did not balance, i. e., some of the 11. 54 eV transferred from Ar* to HP appeared neither in bond breakage nor in emission. This is plausible on a set of potential surfaces such as those of Figs. 1 and 2, as will be explained below. In Ar* + H20, Penning ionization is energetically inaccessible, but in He* + H20, Penning ionization is observed to compete with dissociative excitation of H20. 9,11 The same com­petition ought to be observable in Ne* + H20.

The exit channel in the excitation transfer process in­volves the system Ne + HP*, with HP* subsequently dis­sociating to HO* +H r cf. Reaction (1)]. Although nothing is known about the exit channel potential Vex, it seems reasonable to assume, since HP* is in a Rydberg state, that it resembles the ionic potential surface yo discussed in Sec. IV E. In the attractive parts of V*, it is possible for the Ne atom to penetrate much closer to the ° atom than it would on V .. with the same relative kinetic energy. In other words, at thermal kinetic energies a vertical transition at the classical turning point from V* to Vex would place the system rather high up the repulsive wall of V... Assuming that the system crosses from V* to Vox at the classical turning point (about 2 A for a Czv approach at 40 meV relative incident kinetic energy), and approximating V .. by YO, we find that the system has 0.2 to 0.8 eV of kinetic energy on Vex, depending on the details of V... On the other hand, a repulsive approach on v* has a distance of closest approach of about 4 A, and in this range V* and Vex are not dis­similar. If excitation transfer can occur in this ori­entation, release of large amounts of kinetic energy seems unlikely. This qualitative argument ignores the nature of the HP* state, its interaction with Ne, and the mechanism by which it is populated, none of which are established. Its point is Simply to show that, in systems with high-lying attractive states and lower-lying less attractive states, excitation transfer from the former to the latter is consistent with the release of amounts of kinetic energy on the order of half an electron volt. The energy imbalance reported by Clyne et ai. 8 for Ar* + HP was about O. 7 eV, some of which

is kinetic energy of HP* diSSOCiation.

G. Applications, extensions, and generalizations

With the potential surface in hand, the next step is to use it in differential cross section calculations, in order to aid the interpretation of the molecular beam data. This will be dealt with in a later paper. A complete theoretical description of nonreactive Ne* + HP scatter­ing requires a knowledge of the auto ionization probabil­ity r(R) as a function of Ne pOSition, so that competition with quenching processes can be included in the calcula­tion of elastic and inelastic cross sections. Hickman et ai. 5 have shown how r(R) can be calculated using only the Hamiltonian matrix elements required for the CI calculation. We are presently working to apply this ap­proximation to the Ne* + H20 system.

There have been rather few studies of interactions between rare gas metastables and polar molecules, and these have usually involved heavier systems (e. g., Ar* +HBr, Ref. 34) in which the electrostatic interactions

J. Chern. Phys., Vol. 73, No.4, 15 August 1980

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1812 John Bentley: Neon atoms interacting with water

.3

.2

.1

>. .0 ->-CJO a; i -.I ;g c:

i -.2

-.3

2 3 Ne-O

I I , I , , , I

4 2

, I \ \ \ \

'-

separation. "'-'oms

\ \ \ \ \

\ ........ -

3 4

.2

.I

.!i! C

.1 ~

-.1

o a.

FIG. 6. Comparison of calculated and semiempirical potential curves for Ne* + H20. The solid curves were calculated using basis set IV; the dashed curves by the model of Sec. III. The directions are (a) 6 = 0°, cf> = 0°; (b) 6 = 180°, cf> = 0°; (c) /I = 90°, cf> = 90°; (d) 6 = 45°, cf> = 0°; (e) /I = 90°, cf> = 0° (cf> = 00 is in the molecular plane of H20, cf> = 90° is in the bisector plane, 6 = 0° is at the oxygen end of H20). The point at the minimum in (a) is the minimum for Na + H20 calculated by Trenary et al. (Ref. 15).

discussed here are less pronounced. Corresponding investigations involving alkali atoms have also favored heavier systems and have been more concerned with the nature of the exit channel (reactive scattering) than the entrance channel. Thus highly anisotropic radical com­plexes of the sort discussed here and elsewhere15 have received practically no experimental characterization. [The only relevant study of which we are aware is the matrix ESR detection of Li(HP), Li(H20)2, and Li(NHa) by Meier et al. 35] As similar systems come under study, it ought to be easy to estimate qualitatively rea­sonable potential surfaces for them without recourse to the expensive calculations reported here. Trenaryet al. 15 have reported well depths and well locations for the interactions between Li or Na and the polar hydrides AH" (A = N, 0, F, P, S, Cl). If the base strength of the Lewis base is known relative to those of the hydrides (for instance, by applying the method of Kollman36), one may interpolate well characteristics from the tables of Ref. 15. The rest of the potential energy surface may be generated by supplying the angular behavior of the elec­trostatic potential energy map of the base, or of its con­stituent groups. Scrocco and Tomasiz1 give numerous examples of such maps.

The electrostatic potential is proportional to the strength of interaction of a point charge with the charge density of the molecule being studied. In going from a point charge to a incident atom, several changes occur. The incident atom carries its own electron cloud, giving rise to intermolecular electron repulsions which desta­bilize the interaction relative to that of the point charge. In addition, the presence of the electron cloud gives the atom an effective hard-sphere radius which prevents its penetrating as close to the molecule as the point charge

can. On the other hand, both the atom and the molecule are polarized by the field of the other, providing a sta­bilizing effect on the interaction which partially com­pensates for the effects of electron repulSion.

In the present scheme the effect of electron repulsion is approximated by shifting the electrostatic potential radially outward until its minimum is at the same dis­tance as that of the complex. The shift distance corre­sponds to an effective atomic radius. The shifted elec­trostatic potential is then multiplied by a factor to bring its minimum energy into agreement with that of the com­plex. The result of applying these shifts and scale fac­tors to the entire electrostatic potential is an approxi.­mate potential surface for the atom-molecule interac­tion.

To illustrate this procedure we have computed sec­tions of the potential surface of Ne* +HP (or, almost equivalently, of Na+Hp), using as input only Figs. 2 and 3 of Ref. 21 (the electrostatic potential maps of water) and the Na+Hp well parameters of Ref. 15. We scaled water's electrostatic potential curve for the C Zv

direction so that its minimum value was - 0.23 eV, and we shifted it so that its minimum occurred at 2. 38 A. The shift factor was 1. 3 A, in rough agreement with the radius of Na of 1. 7 A used to correlate beam scattering measurements. 37 (Of course, there are any number of definitions of the size of an atom, and that of Ref. 37 is not equivalent to the present one. We only mean to show that the present value is of reasonable magnitude.) These scale and shift factors were then applied to the electrostatic potentials in several other directions, with the results shown in Fig. 6. Such a crude model cannot be expected to be quantitative, but it does seem to de-

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John Bentley: Neon atoms interacting with water 1813

scribe the angular variation of the potential surface. The model's success in the attractive regions is perhaps due to the partial compensation of intermolecular elec­tron repulsion contributions by attractive polarization contributions mentioned previously. The large under­estimations of repulsive potentials suggest that, in these directions, polarization effects are relatively unimpor­tant and no such compensation occurs.

v. CONCLUSION

We have determined potential energy surfaces for the interaction of excited neon atoms (2p5 38 3,lp) with ground state water molecules. We find a strong attraction be­tween Ne* and the oxygen atom, which resembles that reported for the analogous Na + H20 system. The at­traction is electrostatic in nature. We believe that the surfaces reported here are appropriate for interpreta­tion of experimental data involving metastable neon­water collisions, and we have illustrated this point in a discussion of Penning ionization data and excitation transfer results. We have proposed an electrostatic model for generating potential surfaces for this class of complexes.

ACKNOWLEDGMENTS

I am grateful to Dr. Daniel M. Chipman for consider­able assistance with the molecular orbital program and for discussions of the chemistry involved. I also had profitable conversations with Professor Daniel Winicur and Professor Maurice Schwartz and Dr. Winifred Huo and Dr. John Hardwick regarding aspects of the mate­rial reported here. I am grateful to the referee for pointing out several obscure passages.

ISee, for instance, The Excited State in Chemical Physics, edited by J. W. McGowan, Vol. 28 of Advances in Chemical Physics (Wiley-Interscience, New York, 1977).

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5 A. P. Hickman, A. D. Isaacson, and W. H. Miller, J. Chern. Phys. 66, 1483 (1977).

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