111
J. Phys. Chem. 1993, 97, 11 1-1 19
Spin-Forbidden Predissociation of the Rovibronic Levels of OH+(clII)t David R. Yarkony Department of Chemistry, The Johns Hopkins Uniuersity, Baltimore, Maryland 21 218 Received: August 4, 1992; In Final Form: October 19, 1992
The line widths of the OH+(c'II,u,J,e/fl levels arising from spin-forbidden predissociation are studied. Electronic structure calculations based on large configuration state function expansions, 500 000-1 100 000 terms, are used to determine the relevant potential energy curves and interstate couplings. These data are used within a coupled electronic state Golden Rule model to determine the line widths of OH+(clII,u,J,e/fl for J = 1-10, u 5 3. It is found that the OH+(clII,u,JJ) levels decay principally by a direct coupling to the dissociative lsZstate, clII 15Z-,attributable to a combined first-order dipolar spin-spin and second-order spin-orbit interaction. For the OH+(clII,u,J,e) levels an additional indirect mechanism, c'n- b'B+-A311, discussed by Sarre and co-workers (Phys. Reu. Lerr. 1989,63, 2216) becomes preeminent as J increases. For u = 2 the line widths of the OH+(c111,u=2,J,e) levels depend linearly on J ( J 1). The u = 2 results are in excellent agreement with the experimental results of Sarre and co-workers.
-
+
65000,
I. Introduction The hydroxyl cation OH+, the isoelectronic analogue of the well-studied imidogen radical N H , has been observed in cometary spectra.' The charge-transfer reaction 0 + H+ O++ H is the initial step in the production of OH in interstellar space2 while the reverse reaction is of importance in the i~nosphere.~ This relevance of the OH+ system to both atmospheric- and astrochemistry has motivated treatments of the OH+(X3Z-) photodissociation cross ~ e c t i o nshape , ~ resonances in the X 3 Z A311 transitions and the above-noted charge-exchange reaction6 Detailed studies by electronic spectroscopy have previously been largely confined to the A311 X3Z- transition, including a careful study of A3II-blZ+ perturbations.' The relevant spectroscopic states of OH+ are illustrated in Figure 1, which is based on data to be reported in this work. In N H the cIII-alA and cIn-blZ+ transitions are of considerable importance in the detection of NH(alA,blZ+) produced in laboratory environments and are well studied.8-13 Such is not the case in OH+.Only two observed transitions have been tentatively assigned to the cl IIalA t r a n s i t i ~ n . The ~ first observation and assignment of the transitions in the clII-blZ+ system was reported in 1988 by Rodgers and Sarre,14 who analyzed the c111-b1Z+(3,0) band. Subsequently Levick, Masters, Rodgers, Sarre, and, Zhu (LMRSZ)IS studied the c111-blZ+(2,0) band and observed a remarkable fine structure dependence in the line width and decomposition products of the OH+(clII,u,J,p=e/j) rovibronic levels. Here udenotes thevibrational quantum number, Jdenotes the total angular momentum quantum number and the parity, p, is denoted as e if p = +(-l)J and as f if p = -(-l)J. The experimental line widths for the (c1n,u=2,J,e)levels were found to be linear in J(J 1). These levels decompose preferentially to O(3P) H+. The line widths for the (c111,u=2,JJ) levels, on the other hand, were found to be constant and determined by the Doppler widthof 100 MHz. These levels decompose exclusively to O+(4S) + H(2S). This difference in the line widths and decomposition products was attributed's to the competition between a direct predissociation c l n - lsZ- and an indirect predissociationI6 mediated by the bound b'Z+ state, that is c l n b'Z+-A311. By explicit numerical calculations LMRSZ were able to show that the clll-bIZ+-A3II pathway accounts, in a
I
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I
I
;',
9z-
4
-.
+
-
+
+
-
Supported in part by National Science Foundation under Grant No. CHE 91-03299. +
c
$€
3
25000 15000 1.5
'
I
2.0
"
2.5
'
I , '
3.0
'
3.5
'
I
4.0
: +
'
4.5
R(a&
Figure 1. Potential energy curves for the X3Z- (partly visible), a'A, b'Z+, A3n, c l n , I ? - , and 232-, states from CI wave functions shifted as described in text. Vibrational levels of the c'II state indicated on the potential energy curve. Solid lines lead to O(lD) + H+.Short dashed lines (should) lead to O(3P) H+. Long-short dashed lines (should) lead to O+(4S) H. Asymptotic limits are discussed in section 111.
+
+
semiquantitive manner for theobserved (clII,u=Z,J,e) linewidths. Their model reproduced the J(J + 1) line width dependence and predicted line widths within a factor of three of experimental measurements. This situation is in a sense similar to the predissociation observed in the clII state of NH/ND. In that predissociation, which has been the object of recent experimental and theoretical ~ o r k , ~ ~ , ~ ~ a competitionexists between the direct predissociation, c l n - 1Q-, induced by a combination of the first-order dipolar spin-spin and second-order spin-orbit interactions, and the indirect predissociation channel CIII-A~II- lS8-induced by successivespin-orbit couplings. There are however two significant differences between the situation in NH(clII) and that in OH+(clII). In N H the intermediate state in the indirect process is coupled to the cln state through a first-order, largely J-independent, spin-orbit interaction while in the OH+ system this interaction is attributable to the strongly J-dependent A-doubling interaction.I9 In addition in the N H system the predissociating electronic state is the same for the two paths, while for OH+ the direct and indirect processes lead (in the absence of significant product channel couplings) to chemically distinct fragments, OH+(AjII) O(3P) + H+while O H + ( ~ ~ Z - ) 0+(4s) + ~ ( 2 s ) . There have been several previous studies of the electronic
-
+
0022-3654/58/2097-0111%04.00/0 0 1993 American Chemical Society
112 The Journal of Physical Chemistry, Vol. 97, No. 1 , 1993
Yarkony
structure of OH+ using correlated wave f~nctions.~.20-2~ Of relevance in the present context is the work of Hirst and Guestz0 that reported reliable potential energy curves for many of the low-lying states of OH+ and the work of De Vivie et a1.2' that considered predissociation of OH+(blE+) induced by the A3II state. These studies were used by Sarre and c o - w ~ r k e r sto~ ~ analyze the c111-b1E+-A311pathway. However these studies do not report sufficient electronic structure data to fully address the predissociation of OH+(clII). It is the aim of this work to study the competing decay channels of OH+(dII) using a b initio electronic structure methods. Section I1 presents our theoretical approach. Section 111presents the results of our calculations. In this section it is shown that the c1II-blE+-A3II pathway in fact quite accurately accounts for the experimentally observed lifetimes. Section IV summarizes and concludes.
emerge that for the low-lying vibrational levels, u = 0-3, that are the object of this study, the direct mechanisms (ii) and (iii) are negligible. Thus this work will focus on a two channel model consisting of the direct path c l n - 1% and the indirect path c1II-b'C+-A3II. As noted in the Introduction, this model is analogous to that which is responsible for the predissociation of the isoelectronic NH(clII,u=O,l) states. The treatment of the predissociation espoused in this work parallels our previous successful treatment of NH(clII,u=O,l) predissociation.I7J8 A description of this treatment follows. (B)BolodstateWave F I " The nominal OH+(dIIpJ,e/ fl wave functions are developed in terms of the following boundstate expansion:
11. Theoretical Approach
From Figure 1 it is evident that many decomposition pathways exist for the clII state of OH+. Therefore it is appropriate to preface the detailed discussion with an overview, subsection A, of the possible decay channels. This is followed, in subsections B and C, by a mathematical description of the radiationless decay of the individual parity levels of the clII state, (cIII,u,J,e/j), based on a Golden Rule type approach.I6v22 Subsection D considers the mechanisms for radiative decay. These discussions are prerequisite to a description of the electronic structure treatment of the intersurface couplings presented in subsections E and F which is the principal computational task in this work. (A) Decay Mechanisms. The clII state can decay radiatively (spin-allowed, dipole-allowed) to the al A and blE+ states, denoted clII (alA,blE+). The clII state can predissociate only to channels correlating adiabatically, with O(3P) H+, on the A311 and X3E- potential energy surfaces, and with O+(4S)+ H(2S), on the 15E- and 23E- potential energy surfaces. Nonadiabatic interactions in the product channel can influence the distribution of the product ~tates,~-23 that is, the branching ratio O+(4S)/ O ( ~ P J ) .Nonadiabatic effects on the predissociation will be the subject of a future study. The essential point here is that while radiative decay is spin-allowed, radiationless decay, predissociation, is necessarily spin-forbidden. Predissociation can occur either by direct or indirect mechanisms.l6 The three principal channels for direct predissociation are as follows: (i) clII, l'E7: the clII state is coupled directly to the 1%- state, which correlates with O+(4S)+ H(*S), through the first-order dipolar spin-spin, and second-order spin-orbit, interactions; (ii) c'II, -23E;: the clII state is coupled directly to the 2jE- state, which also correlates with O+(4S) H(2S), through a first-order spin-orbit interaction; (iii) clIIl -A3€&: thecIII stateis coupleddirectly to theA3II state, whichcorrelates with O(jP) + H+, through a first-order spin-orbit interaction. Here the electronic state notation 2S+1An,with Q = A E, has been used. Direct predissociation of the dIII state by the X3E; state, c'II, - X3E;, is also possible but is negligible. Indirect processesinvolvecouplingtoeither thea' Aor blE+ states which are subsequently predissociated by the continuum of the A311state: (iv) c1III-b1E~+-A3II,+: the clII state is coupled by the A-doubling interaction L d 9 to the bl E+ vibronic levels which are then predissociated by the continuum levels of the A3II state through a first-order spin-orbit coupling interaction; (v) c1111-a1A2-A3112:the clII state is coupled by the A-doubling interaction LJ to the alA vibronic levels which are again predissociated by the continuum levels of the A3II state through a first-order spin-orbit coupling interaction. Note from Figure 1 that the blE+ and A3n states are quasidegenerate for a significant range of internuclear separations. For this reason and from the energetics indicated in Figure 1 it is anticipated and will be demonstrated that indirect mechanism (v) will be subordinate to indirect mechanism (iv). It will also
-
+
-
+
where Z = clII1, a'A2, blE:+. These wave functions consist of a rotational4ectronic (rotronic) term, \k;JP(r;R) that specifies, in addition to the Born-Oppenheimer electronic state, Z, the parity p and total angular momentum, J , and a vibrational term &(R) that depends parametrically on Z and J. The *Ep{r;R), taken as symmetrized Hund's case (a) basis functions, are in turn expressed as linear combinations of products of an electronic part *F(r;R), which is the Born-Oppenheimer electronic wave function in the body-fixed frame and will be denoted W(Z) when the coordinate dependence can be suppressed, and a nuclear rotation part \k:J (arguments suppressed) given by a normalized D m a t r i ~ ' ~with . * ~rotational quantum numbers J, Q (Mis suppressed). The \k;;,(r;R) 9 y ( Z ) , with the coordinate dependence suppressed, are given for t i e clII state by
* \ k y 1 r I - p y 1 p/ d=5 *(-1)J
\ k e y ' q ) = [\ke(lrIl)\k;'J JP
(2.2)
for the alA state by
*;('A2)
= [\ke(lA2)\k';'Jf \ke(1A-2)\k!'~l/fi p = &(-l)'+' (2.3)
and for the blZ+ state by
The nuclear vibration wavefunctions, &(R) and corresponding eigenvalues CLJ s G"J(Z),satisfy the case (a) vibrational Schr& dinger equation:
+
where the rotronic potential, E#(R), is given byI6
H;;J(R)= E;(R) +
h*[J(J+ 1) - n2+ S(S 2pR2
+ 1) - 221 (2.6)
is the reduced mass and Ej(R) is taken as the nonrelativistic Born-Oppenheimer electronic potential energy curve. The u? satisfy the matrix eigenvalue equation
[Her-EUP]aUP= 0
(2.7)
where qL'JpJ"Jp (x~~(R)~~~p(r;R)l~l*~;~(r;R)x~J(R))~,~ Subsequently to avoid complex subscripts it will be convenient to write M:,B = Mx(A,B). In eq 2.7 Her is the standard rotronic Hamiltonian operator19 so that the matrix elements of the blocks
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993 113
Rovibronic Levels of OH+(cIII) diagonal in the electronic state index Z are given by li;:Vp,luJp = G$,,u. The following nondiagonal elements are required:
for p = e (2.8a)
=0
f o r p = f (2.8b)
-
involving the A3&+ and A 3 n 2 electronic states, cln, blZ:+-A-’no+ and clIIl-a1A2-A3112. Similarly the 15Z; and 23Z; states each provide a direct dissociation channel, c l n l 15Z; and ~ l I I ~ - 2 ~ 2 ;It. is important to observe that each of these electronic manifolds, 15Z-,PZ-, and A3n,can predissociate both e l f symmetry levels. Thus the significant symmetry distinguishing interaction is that provided by eq 2.8.15 The radiationless decay rate of the individual rovibronic levels, OH+(clII,u,J,p) is given within the Golden Rule approximationZ2 by AP‘(c’rI,u,J,p) =
= p‘(C’n,u,J,p;K)
(2.13 b)
K
where &(R) = (qk:(r;R)lL:(r,R)l~~(r;R) ),. Again to avoid complex subscripts, it will be convenient to write M;,#(R) 5 Mx(A,B) when the coordinate dependence of M&(R) can be suppressed without ambiguity. Here L:(r,R) = L:(r,R) + iL;(r,R) and Le(r,R) is the total electronic orbital angular momentum operator relative to the center of mass of 1601H+. Since eq 2.1 involves a summation over (Z,u), only (J,p) are in principal good quantum numbers. However in practice it will emerge that a given L is dominated by a single (Z,u) term. Thus it will be appropriate to speak of (Z,u,J,p) levels and the notation (L,J,p) and (I,u,J,p) will be used interchangeably. Further, parity is a good quantum number. Thus from eq 2.8a the e symmetry levels may contain contributions from both Z = clnI and b’Z:+. This gives rise to the indirect predissociation type (iv) mechanism. However, for the f symmetry levels this mixing is not possible and therefore this mechanism does not exist for the f symmetry levels. This is not the case for predissociation mediated by the a1A2state. From eq 2.9, the a’Astate can perturb both the e and f components of the clII state. (C) hedissociation. Radiationless decay will be discussed in terms of three interrelated quantities, the decay rate APr and the lifetime 7 p r in the time domain, and the line width Tpl in the frequency domain, with APT= = 27rcTpr. The rovibronic levels of the above described bound states are predissociated by coupling to three electronic states, the dissociative 15Z;, 23Z; states and the AXI2,1.0+state. The relevant rotronic functions are, for the A311 state
*
q ; ( 3 ~=2[)~ ( ~ n , ) e ee(3n-2)e:{1/fi ;~ p= (2.10a)
eey3nI) JP = [ ~ ( ~ n , )*e~‘ (; ~ . ~n _ , ) e : ; ] / f i p = *(-lf’ e;(3n0+)=
ee(3no*)9;J p = +(-1)J
whereZ’= c l n l , aIA2, blZ:+, APr(clII,u,J,p;K) is thecontribution to the rate associated with the Kth decomposition channel, K = A ~ V ~ +A,~ I I ~A, ~ I I ~ 232;, , Pz;, HBP(Z’U’J~;K,E,J~) = ( x S ~ ( R ) ( H ~ ~ ( R ) I X)R, ~ ~xi,@) (R) is the energy normalized continuum nuclear “vibration” wave function corresponding to electronic state K with asymptotic kinetic energy E, and HfL(R) (=HBP(Z,K) when the R dependence is suppressed) is the Breit-Pauli induced coupling between the electronic states K and Z and is discussed in subsection E. Within this approximation, which is expected to be entirely adequate for the present situation in which the distribution of the product channel states is not an i ~ s u e , the ~ 3 predissociation rate or line width is the sum (over K ) of contributions for the different decay channels. Note however that because of the form of eq 2.13a within each channel interference effects (sum over Z’J? are possible.16 Intrachannel interference is not included in the previously noted model used by LMRSZ to analyze the c’n,-b’Z:+-A3no+ decay channel. (D) Radiative Decay. The OH+(cln,u’,J,p) levels can decay radiatively into the a l Aand blZ+electronic states. The radiative decay rate for a transition (cln,u,J) (Z”,u”,J) was calculated as A(c~~,u’~J;I’’,u’’,J)= 2.149 X 1010(hv)3p(c1~,u,J;Z”,u”,J)~ where hv = G,J(CIII)- G u , t ~ ( Z ”and ) p(Z’,u’,J;Z,u,J) = ( x::J(R)I~~,,(R)Ix~~(R))R is the vibrationally averaged electronic transition moment. Here hv and p are expressed in atomic units and the radiative decay rate is given in s-l. The electronic dipole transition moment, p,,,(R) is given by pl,,(R) = (qk:~r;R)Ip:(r,R)l\kk:(r;R) ), and is abbreviated p(Z’,Z) when the R dependence can be suppressed. &(r,R) = --[p:(r,R) ip;(r,R)] / d 2 , where pe(r,R) is the standard electronic dipole moment operator. Only transitions between levels with the same J a r e considered in this standard case (a) model and consequently the total radiative decay rate from a particular rovibrational level (cIn,u,J) is given as
-.
+
(2.10b) (2.10c)
for the 1% state
q ~ ( ~ 2=; [) s ~ ~ z J i~ ee(52~l)q:;1/fi ‘;.~ p = *(-l)J-1 (2.1 1) and for the 2%- state q 3 3 2 ; )= [ q e ( 3 ~ ~ i )ee(3z:l)9:;]/fi ~;.J
p = i ( - l ) J (2.12) In the present case (a) approximation three distinct A311 dissociation channels are possible, a direct channel involving the A3111electronic state, cln, -A3111, and two indirect channels
Arad(clII,u,J) = ~A(c’II,”;I”,u’’,J)
(2.14)
I‘’*u”
(E) Electronic Structure Aspects: Interstate Couplings. From the discussion in subsections B-D three classes of interstate couplings are required: (i) transition dipole moments connecting the c l n state with the alA and b l Z + states, p(a1A2,c1111),p(clIIl,blZi+), (ii) the L-coupling matrix elements L+(a1A2,c1nl),L+(c’n,,b’Z~+), and (iii) the relativistic couplings for the pairs of states (cl11,,2~Z;), (clIIl,A3111), (A3110+,b1Z,+,), (A3112,atA2),and (c111,,15Z;). In this work the relativistic couplings are evaluated within the full microscopic Breit-Pauli approximation25326 using the dipolar spin-spin operator, Hss, and spin-orbit operator, Hso(both the one-electron spin-orbit and two-electron spin-other orbit contributions) and we write HBp = Hso HSs.
+
114
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
For those matrix elements for which the first-order spin-orbit interaction is nonvanishing the dipolar spin-spin contribution is neglected, so that HBp(~'n,,231;;)= (\ko(~1n,)~H"ol\k0(232;)) (2.15) (2.16) HBP(c'III,A3II,)= (\ko(c'~,)~HSo~\ko(A3111)) H B P ( A 3 ~ , + , b '= I ; ~( ~0(A3110+)lH"oJ!Vo(b'I;~+)) +) (2.1 7) HBP(A311,,a'A,) = (\ko(A3112)1EFol\ko(a'A,)) (2.18) Here \kp(r;R) = W(1) is the zeroth-order electronic wave function for state Z and the R dependence of HBp(Z,K)has been suppressed. These matrix elements will also denoted q ( Z , K ) to more clearly indicate the origin of the coupling. Thecoupling interaction HBp(c'II,,l'2;) is considerably more difficult to evaluate in a reliable manner. In this case the firstorder spin-orbit interaction is zero by symmetry. To obtain accurate results it is necessary to evaluate the dipolar spin-spin interaction to first order and the spin-orbit interaction to second ~ r d e r , l ~ that . ~ ~ is- ~ * H B P ( ~n,, I 152;) =
n,) l ~ " s l \ k o ( 1 5 ~ ; )) + i / 2 G ( c I I I I ,1'2;)
(2.19)
where, using a van Vleck transformationI6 e ( c ' n , , 1 3 ; ) = (\k' (c' n,)lH""l\k0(1'1;;) )
+
( ~ o ( c ~ n , ) ( H s o ( \151;;)) k'(
(2.20)
and to first order in Hso, W(Z) = \ko(Z) + Ql(Z). Because the A3111state can directly predissociate the cl II state, it is necessary to use quasidegenerate perturbation theory to evaluate the perturbation \k'(Z).29J0 Through first order the electronic wave functions are given by
Yarkony contributions, O&(K;Z)for (1 - Q,K,Z) = ( A 3 ~ , , 3 ~ l , 1 5 Z ; ) , (A3111,3111,c1111), (O,'Z:,l'Z;), and (o,3z:,c'n,). In each case the wave functions were expanded in flexible second-order CSF spaces developed as follows. At each internuclear separation a common set of molecular orbitals for all wave functions was determined from a state-averaged multiconfiguration self-consistent field (SA-MCSCF)31-34procedure based on the extended ContractedGaussian basissets (9s7p3dlf) onoxygen and (6s3pld) en hydrogen used in a previous study of OH/OD(A2Z+) predis~ociation.~~ In the SA-MCSCF procedure the following partitioning of the molecular orbitals into core, (lu), and active [ ~ c T - ~ u ~ T -orbitals ~T] was used. The doubly occupied core orbital corresponds to the O(1s) orbital while the active space, which contains six electrons, includes the 0(2s,2p) and H( 1s) orbitals as well as two additional u and one T orbitals to account for active space "relaxation effects", the fact that a given orbital does not experience an equivalent environment in all states in question. Seven states were included in the state-averaging procedure, the X W , alA, blZ+, A311,d I I , 15Z-, and 23Z-states with weight vector w = (1,1,1,2,2,1,1). The above-noted zerothorder wave functions and first-order perturbation contributions were constructed in second-order CSF spaces relative to the above noted active space, with the highest occupied molecular orbital of u symmetry (the O(1s) correlating orbital) truncated. The dimension ofthesespaces (in Cz,symmetry) is asfollows: 3A2(32-) = 1 142 910, 'Ai('A,'Z+) 725 794, 3B~(311,) 1 157 844, 'B2('IIY)= 707 890, 5A2(5Z-) = 528 094, 3A~(31;+,3A)= 1 172 136. These are by far the largest CSF spaces used to date to consider relativistic effects in OH+ and will enable the first report of a second order spin-rbit interaction in a CSF space of over 1 million terms. The accuracy of the present description will be discussed in the following section. 111. Results and Discussion
(A) Bodppenheimer Potential Energy Curves. The potential energy curves for the X3Z-, a ' A, b12+,A3II, clII, l Q-, and 232states are reported in Table I and plotted in Figure 1. Using \zI'(~z:;c'II,) (2.21a) these data and the corresponding C,,(Z) (see eq 2.5), spectroscopic constants, re, we, a d e ,and Te were determined and are reported in Table 11, where they arecompared with theexperimentalvalues and the most complete previous theoretical treatment, that of Here \k$K;Z) is the first-order perturbation contribution to state Hirst and Guest.20 The present theoretical results are seen to be I belonging to symmetry Kand is evaluated in the subspace defined in very good agreement with the experimental data when available by Q, which in this case represents the orthogonal complement and the theoretical results of Hirst and Guest when no experiof \k0(A311). (When Q is absent the entire symmetry space is mental data exists. The excitation energy O(1D)-O(3P) of assumed available.) Thus 16 000 cm-I, derived from the A311and alA potential energy curves at R = 10.Oao,is in good agreement with the experimental z q ( c i n l ,1 5 ; ) = ( \ k k ' ( 3 8 : ; ~ l n , ) l ~ 0 1 ~5z;)) o(i value 15 867 cm-1.36 Similarly the excitation energy O+(ZD)O+(4S)of -27 700 cm-I, obtained from the tabulated data for (\k~(3n,;c'n,)lH""I\kO( 152;)) the 1 9 - state and that for the 13Astate which is not tabulated, (\ko(c'n,)~H"o~\k'(32:;1~z;)) + is in good agreement with the experimental value 26 808 cm-1.36 Note however from the R = 1O.Oao results that the O+(4S) (\k~(c'n,)~Hs~~\k,b(~n,;l~z;)) (2.20') H(2S) (X3Z-,15Z-) asymptote is found to be 1700 cm-' lower where the perturbative contributions satisfy than the O(3P) + H+ (A3II, PZ-) asymptote although experimentally these asymptotes are known to be nearly degenerate.36 [Ho- Z?(Z)]!V'(K;Z) = - H s o \ k o ( ~ (2.22a) This deficiency in the description of the atomic oxygen ionization potential is common to all previous treatments of the OH+ system4J0-2'and results in the reversing of the character of the (2.22b) [@ - Z?(r)]\k,b(K;I)= -QH""\k0(Z) X3Z- and 23Z- states a t large R. On the basis of the predicted T,'s this deficiency is only partially reflected in the molecular Equations 2.22 are solved exactly with a given configuration region and the incorrect asymptotic correlation is not of consestate function (CSF)space using an approach discussed in ref quence here. 30. In this approach the exact contribution to the perturbed wave function from each zeroth-order eigenstate is obtained The predissociation line widths may be sensitive to the relative without having to compute any of the eigenstates explicitly. positions of the potential energy curves. Thus the available Te(s, (F) Electronic Structure Aspects: Computational ConsiderTe(a1A)37and Te(A311),7 and Ton's,T O O ( X ~ Z - , ~ I Zand +)~ ations. From the above discussion two classes of electronic wave To3(b1Z+,c111),14 were used to uniformly shift, S(Z), the Ith, a b functions are required, zeroth-order wave functions W(Z) for Z initio potential energy curve as follows: S(alA) = -346.8 cm-], = X3Z-, aIA, blZ+, A3II, c l n , 1% and first-order perturbation S(blZ+) = -521 -2cm-1, S(A311) = -341.4 cm-l, S(clII) = -7 10.1 9 e ( c ' n , ) = \kO(c'n,)
+ \k33n,;c'n1) +
-
+
+
-
+
The Journal of Physical Chemistry, Vola97,No. I, 1993 115
Rovibronic Levels of OH+(c'II)
TABLE I: Energies from CI Wave Functions' R 1.50 1.75 1.87 1.95 2.00 2.13 2.25 2.37 2.50 2.75 3.00 3.25 3.50 3.75 3.80 4.00 4.50 5.50 6.50 10.0 Ab
XQ-
alA
bl2+
A3n
Cln
14016.0 1935.6 259.5 0.0 94.8 1015.1 2 453.1 4 222.5 6 337.1 10 555.8 14 599.8 18 282.1 21 556.5 24 432.8 24 962.8 26 942.3 31 014.3 36 257.5 38 906.2 40 553.7
31 623.5 19 551.3 17 898.3 17 660.2 17 770.6 18 739.3 20 232.0 22 065.4 24 259.1 28 655.1 32 900.5 36 794.7 40 275.8 43 338.6 43 902.3 46 001.5 50 243.8 55 220.6 57 152.4 58 267.1
43 194.3 31 018.6 29 319.3 29 050.1 29 140.8 30 056.0 31 495.1 33 269.0 35 389.2 39 607.7 43611.8 47 178.8 50 221.8 52711.2 53 142.6 54 652.7 57 087.2 58 560.1 58 678.3 58 470.7
47 820.1 33 369.2 30 456.6 29 352.9 28 915.8 28 450.3 28 624.0 29 160.6 29 989.8 31 914.4 33 906.4 35 748.3 37 345.8 38 664.8 38 895.0 39 707.8 41 081.3 42 090.5 42 259.9 42 224.1
68 284.1 51 580.1 47 711.1 46 022.4 45 241.8 43 964.1 43 490.0 43 473.4 43 803.8 45 035.0 46 636.4 48 338.9 50001.7 51 546.2 51 836.6 52 928.7 55 136.3 57 451.3 58 073.9 58 190.4
+
o ( ~ D )+ H+
o ( 3 ~ ) H+
o ( ~ D )+ H+
+
o ( 3 ~ ) H+
152163 076.3 128 897.4 115 333.5 107 227.6 102 533.1 91 606.1 83 041.2 75 775.8 69 182.4 59 540.9 52 923.1 48 43 1.2 45 417.4 43 423.1 43 116.4 42 126.7 40 799.5 40 247.1 40 335.8 40 558.5
O(lD) + H +
0+(4s)
+H
232172 283.8 143 996.0 132 453.0 125 163.7 120 801.1 110 288.5 101 752.0 94 337.9 87 476.5 77 161.1 69 731.3 64 279.0 60 128.7 56 826.3 56 241.2 54 103.1 49 902.0 45 014.4 42 924.1 42 234.8 074s)
+H
Energies in cm-I relative to E ( X 3 Z - ) = -75.181 393 81 au, at R = 1.95~0.R in ao. Potential energy curves are shifted as described in text. Asymptotic correlations based on experimental data. As discussed in text computed X3Z-and 2)Z- limits are reversed due to inadequate description of differential G O +correlation. (1
TABLE I V Characteristics of the Vibrational Levels of alA, bB+, and clII States'
TABLE 11: Spectroscopic Constants from CI Wave Functions' ~ _ _ _
~
state
re
x3z-
PWb HGC
alA
PW HG
b'Z+
PW HG PW HG E PW HG
Ed
1.0324 1.0328 1.0289 1.0305 1.0364
E A'Jl
cln
1.033 1 1.0398 1.1399 1.147 1.1354 1.2258 1.2382
~~~
Te 0.0 18 002.8 19 043 17 656 29 571 .O 28 772.9 29 350 28 431.5 44 151.1 45 023
We
UeXe
3124.0 3104. 3113.37 3164.1 3 122.
72.1 77.8 78.515 68.9 76.6
3127.4 3132 2157.5 2187 2133.65 1797.3 1825
70.9 89. 78.4 87.6 79.55 52.4 49.3
re in A, Te,we, and wexe in cm-I. Present work. Theoretical results from ref 20. Experimental result.
rr in
UO,
1.980 3.120 3.275 3.968 3.456 3.495b
29 150 34 820 48 400 54 430 49 700
E, in cm-I relative to E e ( X 3 Z - ) . Reference 20.
cm-I. The effect of these relatively modest, uniform shifts of the potential energy curves is discussed below. The vibrational level dependence of the direct predissociations c'II, 1'2; and c'II, -2jZ; reflects the location, r,(I,K), of and the energy, E,(I,K), at the crossing of the states ( I , K ) for ( Z , K ) = (15Z-,c111) and (23Z-,c111). These r, and E,, obtained from the data in Table I, are reported in Table 111 together with the corresponding values for the A)II-a'A, AjII-blZ+, and clnb'Z+ crossings. The E,(Z,c'II) are to be compared with the G,J(c~II)reported in Table IV. From Tables 111 and IV (or Figure 1) it is seen that the 1 5 2 - 4 I I crossing occurs in the vicinity of the (clII, u = 3) level while the 23Z--clllcrossing occurs in the vicinity of the (c'II, u = 6) level. While the direct predissociations are sensitive to E,(Z,clII) the indirect predissociations reflect the (c'll,u)-(blZ+,u'j or (cIII,u)(aIA,u? energy separations since this influences the size of the blZ+-c'II or al A-clII mixing induced by the interactions 2.8 and
-
0 1 2 3 4 5 6 7 8 9
IO 11 12 13 14 15
19158 22 181 25066 27 789 30338 32725 34970 37091 39100 41 001 42800 44501 46 106 47617 49035 50361
30597 33579 36420 39097 41 600 43937 46 124 48 171 50081
44284 45974 47559 49044 50434 51 731 52 934
347(5)h 150(6) 612(7) 873 (7) 353(8)
217(11)" 132(12) 58 (13) 9 (14) 73 (15)
A,(blZ+)
112873 719.4 140583 1456.9 159692 2106.1 172043 2646.7 178496 3064.2
All energies in cm-l relative to E e ( X 3 2 - ) ,A in s-l, G , ( K ) G , J ( K ) , tl.(K,u') c,j(K,u'), A , ( K ) A(cln,u,$K,J). G,j(K), frJ(K,u')and A(c1Jl,u,J;K,J) evaluated for J = 2. u'given parenthetically.
TABLE 111: Curve Crossings' (A3n,b' Et) (A3n,a1A) (c'n,i52-) (cIlT,232-) (cIn,blZ+)
u G,(alA) G,(blZ+) G,.(cIII) c,(blZ+,u? c,(alA,u? A,(aIA)
2.9. To help quantify this dependence, define for a given (clII,u,J) the quantity C~,J(K,U') = IGU,~(clII) - G,,,j(K)I where (K,u',J) is the level for which the smallest difference obtains. The G , j ( I ) and eu,~(K,u?are summarized in Table IV for I = (alA, b'Z+, clII) and K = (aIA, biz+). From this table it isseen eo,2(blZ+,u3 is by far smallest for u = 1, with (bIZ+,u' = 6,J = 2) and that eu,2(alA,u? is by far smallest for u = 3 with (alA,u'= 14,J = 2) and represents an approximate accidental degeneracy. These observations will'provide considerable insight into the radiationless decay rates to be discussed subsequently. ( B ) Interstate Interactions. The interstate couplings d c lIII ,b' E,'+), p(a' A& II I ) r L+(clII,,blE,'+), t + ( aI A2, clII,), ~ ( c ' I I , , ~ ~ Z ;q(c111,,A311,), ), fl(A3110+,b1Z&), q(A3112,a1A2),and HBP(c'IIl,l5Z;)are plotted in Figures 2 and 3, and the data that are key to the present work L+(clIIl, blZ,'+), q(A3110+,b'Z,'+), and HBP(c'III,l5Z;)are also given in Table V. The HBP(c111,,15ZJinteraction is broken down into its dipolar spin-spin and second-order spin-rbit contributions. From this table it is seen that in the vicinity of r,(c111,15Z-) = 3.275~0,HBP(c'III,l5Z;) 1.7 cm-I and exhibits only a modest R dependence. In this region approximately 20% of HBP(c'II,,lsZ;) is attributable to the second-order spin-orbit interaction. This is over twice the size of the second-order spin-
-
Yarkony
116 The Journal of Physical Chemistry, Vol. 97,No. 1 , 1993
components of the degenerate O(lD) + H+ asymptote for large R. On the other hand over the entire range of R,L+(a1A2,c1111)
4 2.33
L'C'D'
-0.200
+
1.50
1.5
3.5
2.5
5.5
4.5
6.5
7.5
Wag)
Figure 2. w(c,b) p(c'II,,b'Z&), L(c,b) = L+(c'II,,b'Z;&),dashed lines and p(a,c) = p(a'A2,c'IIl),L(a,c) = L+(a1A2.lII1)solid lines, all in au. L is evaluated relative to the center of mass of I6O1H. 100
" ' I ' ' " 1 ' " ' L " " "
-Y
-'6
-I
20
L-
m
=
.I
HSo(A,a)
60 c
Yz
-20
-1
-60
-100
1' 1.5
' ' '
' ' ' '
2.5
'
' ' ' '
3.5
'
' '
4.5
a
'
'
' ' ' '
5.5
1 6.5
Wag)
Figure 3. Breit-Pauli interstate couplings in cm-I: H~o(c,232-) 2 ~ ; " ( c 1 1 1 , , 2 ' 2 ; ) , Hso(c,A) a fl(c1111,A3111), Hso(A,b) = fl(A'II,+,b12&), Hso(A,a) fl(A'II,,alA,), HBP(c,l5Z-) = H~~(c~~,,~~z;).
TABLE V Interstate Coupling Interactions from CI Wave Functions' R L+(c,b) 1.50 1.75 1.87 1.95 2.00 2.1 3 2.25 2.37 2.50 2.75 3.00 3.25 3.50 3.75 3.80 4.00 4.50 5.50 6.50 10.00
-1.638 76 -1.64924 -1.651 95 -1.653 40 -1.65427 -1.656 76 -1.65971 -1.663 87 -1.670 30 -1.690 17 -1.722 33 -1.76895 -1.831 79 -1.908 66 -1.925 15 -1.99487 -2.159 76 -2.36408 -2.431 88 -2.45091
fl(A,b)
fl(i5Z-,c)
k!3lSZ-,c)
HBp(15Z-,c)
-73.978 -73.613
-0.392 -0.764
-0,031 -0.107
-0.424 -0.871
-73.315
-1.009
-0.157
-1.166
-72.645
-1.155
-0.193
-1.348
-71.195 -68.524 -64.247 -57.983 -49.377 -38.382 -35.883 -25.417 1.808 35.633 46.949 55.144
-1.245
-0.240
-1.485
-1.336 -1.353 -1.353
-0,327 -0.372 -0.414
-1.663 -1.725 -1.767
-1.332 -1.300 -1.174 -0.739 -0.355 -0.018
-0.458 -0.477 -0.497 -0.355 -0.175 -0.009
-1.789 -1.778 -1.671 -1.094 -0.531 -0.027
R in 00. L+ in au relative to center of mass of I6O1H+,Breit-Pauli interactions in cm-I.
orbit contribution to the analogous interaction in the isoelectronic N H system.'* The A-doubling interaction L+(clII,,biz,',) increases by approximately 30% from its near-equilibrium value 1.65 au to its expectedI9 asymptotic value - d 6 , given by [L(L+ 1) - A(A + l)]I/* with L = 2, A = 0 since the clII and blZ+ states become
-
is approximately equal to its expected asymptoticvalue -2, given by [L(L 1) - A(A 1)]lI2, with L = 2, A = 1, since the alA state also becomes a component of the degenerate O(lD) H+ asymptote. (C) Radiative Decay. The radiative decay rate of the (clII, u = 0-3) levels was obtained using eq 2.14, together with the electronic transition moment data presented in Figure 2. The A(clII,u,&I",J) s ~,,,A(ciII,u,J;I",u",J) are reported in Table IV, for J = 2, I" = alA and blZ+. From this table it is seen that A(clII,uJ;alA,J) >> A(clII,u,&blZ+,J) although theabsolute rates are comparatively small (contributing less than 1 MHz to the line width). The radiative decay rates exhibit only a limited J dependence, changing by less than 25% for J = 2-10. (D)Radiationless Decay. The interstate couplings presented in subsection IIIB enable a critical assessment of the radiationless decay pathways discussed in section 11. As suggested in that section forcln, u < 4 it will emerge that only thedirect mechanism clIIl 1'2; and indirect c I I I I blZl+ A3110+ must be considered to interpret the experimental results of LMRSZ discussed in the Introduction. Then within the Golden Rule formulation espoused in section I1 the radiationless decay rate of the (clII,u,J)fsymmetry levels arises only from the direct term APr(clII,u,JJ) = APr(c1~,u,Jf;l5Z3.The decay rate of the e symmetry levels on the other hand is the sum of this rate and the indirect contribution arisingfrom c I I I I blZ:+ A3110+so that APr(clII,u,J,e) = Apr(c1II,u,J,e;A3II~+) + APr(c1II,v,J,e;l5Z;), with APr(~111,u,J,e;52J= APr(c111,u,Jf;15Z;).i5~18 In our previous treatmentsofthe NH(clII)I7JSand NH(A3II)38 predissociations the location (but not the shape) of the 1% potential energy curve was established with the help of accurate lifetime data.38 It is thus useful to estimate the accuracy of experimental data that would be required in this regard. To this end and to determine the sensitivity of the predictions of this subsection to uncertainties in the electronic structure data, the predissociation calculations were repeated with the potential energy curves shifted with respect to the data in Table I as follows. The 1%- potential energy curve was uniformly lowered by 710 cm-I, giving the cln-1 Y - crossing obtained from the unaltered electronic structure calculations. From Tables IV and V or Figures 1 and 3 it is seen that HBP(15Z:-,c111)exhibits only a limited geometry dependence in the vicinity of the lSZ--clII curvecrossing. Thus this shift of the 1%state principally affects APr(clII,u,Jf;lSZ;)through the vibrational overlaps. This situation should be contrasted with that in the recently studied 4Z--induced predissociation of OH(A2Z+,u= 3,J,e/j).35 In that case q(A2Z+,14Z-) changes by almost a factor of 2 in the vicinity of the A2Z+-14Z- crossing. The Apr(c111,u,J,e;A3110+) are expected to be most sensitive to changes in e,,J(blZ+,u'). However when compared with the cl II and 1%- potential energy curves the relative positions of the b i z + ,A311,and clII potential energy curves are subject to much smaller uncertainties. This is a consequence of the incorporation of the spectroscopic data cited in section IIIA. Consequently these decay rates were recomputed with the cl II potential energy curve uniformly translated by f30, +140, and +160 cm-1 with the latter two values chosen to emphasize the close proximity of the (b'Z+,u = 6) and (clII,u = 1) levels (see Table IV). The computed line widths are presented in Figures 4-7, which, following LMRSZ, plot Pr(c'II,u,Jf;15Z;) and Pr(c1II,u,J,e;A3II0+) vs J(J l ) , J = 1-10. for u = 0, 1, 2, and 3, respectively. The analysis begins with the (c'II,u = 2,J,e/f) levels (Figure 6) which were the object of the experimental study of LMRSZ. In a qualitative sense the results of LMRSZ are reproduced quite well. Pr(clII,u = 2,J,e;A3110+)is seen to be linear in J(J 1) and Pr(cIII,u = 2,JA is largely independent of J , in accord with the measurements of LMRSZ. However, the
+
+
-
-
-
- -
+
+
Rovibronic Levels of OH+(clII)
The Journal of Physical Chemistry, Vol. 97, No. I , 1993 117 600
I
l
l
/
I
I
I
I
I
i
I
t
t OH+(v-0)
I 2
2
2 5 1
I
F
300
F
rl
200 100
0 20
0
40
100
80
60 J(J+l)
120
To.
240
r
I
I
I
I
I
I
I
''
140
90
+
+
II
i
15000
-
1
-; *,+
0
20000
I
b $ ;8 l
190 -
20
40
60
100
80
r!
loooo
120
J(J+l)
Figure5 Same as Figure4 except for u = 1. 0 and a T(e) data,connected by dashed lines, use the right-hand scale. All other T(e) and both T ( f ) data use left hand scale. T(e) label is omitted for clarity.
200
.I
4
r^ 150
E
100
50
0 0
20
40
60 J(J+l)
20
40
60
80
100
120
J(J+l)
Figure 4. Line widths: 'Ipr(clrl,u = 0,J,e;A3rlo+)= T(e) and P r ( c l I I , T(e): Solid line (and solid circles) for c ' r l = 0,Jf;l'E;) = potential energy curve given in Table I. The i,0,a symbols denote T(e) results with clrl potential energy curve shifted *30, +140, and +160 cm-l, respectively. The 0 data is omitted from the u = 0, 2, 3, plots for clarity. T ( f ) : Solid line (and open circles) for 15Z-potential energy curve given in Table I. The I symbol (usually within the open circles) denotes T ( f )results with 1% potential energy curve shifted -710 cm-I.
u
0
80
100
120
Figure 6. Same as Figure 4 except for u = 2.
line widths in Figure 6 are uniformly smaller than those of LMRSZ. This is a consequence of the instrumental contribution to the measured line widths which to a first approximation adds a uniform contribution of 90-100 MHz to these ~ a l u e s . 3 ~ Subtracting this contribution from theexperimental results yields the Pr(cIII,u = 2,J,e;A3IIo+) results reported in Figure 6 to approximately within experimental error. This agreement provides strong support for the theoretical approach espoused in this work. The smaller Tpr(cIII,u = 2 , J d are more difficult to determine experimentally. Our present estimate based on the ab
Figure 7. Same as Figure 4 except for u = 3.
-
initio data reported in this work is Pr(clII,u = 2,Jf) 6-12 MHz [T(c~II,u= 2,Jf) 28-14 ns]. This is comparable to the 65-ns lifetime for the NH(dII,u = 1,J = 1-6,e/f) which is also attributable to a direct clII- 15Z-interaction arising principally from the dipolar spin-spin interacti~n.~~,I* The results with the shifted potential energy curves are also presented in Figure 6. Pr(clII,u = 2,Jf;15Z;), which now ranges from 8 to 15 MHz, is seen to be largely insensitive, in an absolute sense, to the -710-cm-l translation of the 1% potential energycurve. Similarly Tpr(cIII,u = 2,J,e;A3&+) is littlechanged by f30, +140, and +160 cm-I shifts in the clII potential energy curve. This is most likely attributable to the relatively large value of ~2,~(bIZ+,7) = 612 cm-I reported in Table IV. Figures 4, 5, and 7 report TPr(c1II.u,J,e;A3n~+)and Pr(c1II,u,JS;l5Z;) for u = 0, 1, and 3, respectively. It is interesting to observe that the linear dependence of Pr(clII,v,J,e;A3IIo+)on J(J+ l), which contributed to LMRSZ proposing the c l n -blZl+wA3110+ ~ pathway, is only predicted for u = 2 (and approximately for u = 3) using the present model. Pr(c111,u,Jf;15Z;) increases monotonically with u for fixed J reflecting the fact that E,(c1II,l5Z-) isclose toGj(clII);see Figure 1 or Tables 111 and IV. However for Pr(clII,u,J,e;A311~+), we find for each J considered Pr(clII,u = 3,J,e;A3110+)> Pr(c1II, u = 1,J,e;A3110+)> Tpr(clII,u = 2,J,e;A3110+)> P r ( c 1 n , u = 0,J,e;A3110+).The anomalous behavior for u = 1 is attributed to the small value of t1,2(b1Z+,6)= 150 cm-I. From Figures 4, 6, and 7 it is seen that the qualitative J dependence of Pr(clII,u,J,e;A3111) for u = 0, 2, and 3 is not altered by the f 3 0 , +140, and +160 cm-I translations of theclII potential energy curves noted above. However this is not the caseforu = 1. Thesmallvalueoft1,2(b1Z+,6)makes the Pr(clII,u = l,J,e;A3110+)sensitive to the accuracy of the blZ+ potential energy curve. The line widths with the clII potential energy curve shifted +140 and +160 cm-I are significantly (approximately 50 times) larger than even the largest Pr(c1II,u = 3,J,e;A3~o+) and exhibit markedly different Jdependences than the Pr(cIII,u = 1,J,e;A3110+)obtained with the unshifted curve; see Figure 5. In this regard it is significant to note that in the experiments ofSarre and co-worker~'~~~5c~II-b~Z+(2,0) and dIIb1Z+(3,0)transitions have been observed using laser photofragment spectroscopy. However transitions originating in c l n , u = 1 manifold have not in general been observed indicating that these levels are significantly broader than the u = 2 or 3 levels. From the above discussion the predictions for Pr(cIII,u,J,e; ATIo+),u = 0,2, and 3 and Pr(c111,0,Jf;152;), u = 0, 1 , 2 , 3 are expected to be quite reliable, with error estimates provided by the range of Pr given in the figures. However in view of the large sensitivity of Pr(cIII,u = 1,J,e;A3110+)to changes in the location of the higher, particularly u = 6, levels of the blZ+ state the Pr(cIII,u = 1,J,e;A3no+) presented here must be viewed as illustrative. To address the question of the line widths of the (cln,u = 1 ,J,e) levels in a more detailed manner requires very
118 The Journal of Physical Chemistry, Vol. 97, No. 1 , 1993
Yarkony
accurate clII and blZ+ potential energy curves. In this regard a combination of additional experimental and theoretical work is desirable. FromTableIVitisseenthatforthecIII,~ = 3 levelc3,2(a'A,14) = 9 cm-l. Thus it is significant to inquire whether the indirect decay mechanism clII1 -a1 A2w3112 is important for this level. To this end the L+(a1A2,clIIl)and v(A3112,a1A2) coupling data from Figures 2 and 3 wereused todetermine Pr(c111,u,J,e;A3112). For low J , Pr(clII,u = 3,J,e;A3&) is found to be several orders of magnitude larger than Pr(clII,u # 3,J,e;A3112)although the line width are only fractions of a megahertz. As J increases, J > 7, Pr(clII,u = 2,J,e;A3n2)becomes comparable to, and even exceeds, Pr(ciII,u = 3,J,e;A3&) becoming almost 10 MHz for Pr(clII,u = 2,J = 8,e;A3112). The otherwise generally small magnitude of Pr(ciII,u = 2,J,e;A3112) is attributed to the small Franck-Condon overlaps between the relevant vibrational levels. Thus these results indicate that this mechanism is unlikely to contribute significantly to the decay of the clII state except in the case of a very close accidental degeneracy at a particular rotational level. Potential energy curves of cm-I accuracy over a wide range of vibrational levels and a more complete treatment of the nuclear rotation in the A311 continuum-for example, Hund's case (b)-would be required to further quantify this point. Finally the direct decay channels c ' I I I - A ~ I I ~and c'II,23C; were considered using the fl(c1111,A3111) and ~ ( c ' I I , , ~ ~ Zgiven ; ) in Figure 3. Pr(c111,u,J,e/f;A3111)is generally between 1 and 2 MHz for u = 1-3 and J = 1-10, Thus while the efficacy of this decay channel exceeds that of the radiative decay channel it is completely subordinate to the Pr(ciII,v,J,e/f;lSZ;) channel. Similarly the Pr(cllI,u,J, e/f;23Z;) is completely negligible for u I4. For u = 5 this channel begins to become significant as J increases, being approximately 20 MHz for J = 10. A more complete discussion of this mechanism using a multichannel quantum scattering formalism will be the subject of a future publication.
line widths on J ( J + 1) is not predicted for u = 0, 1. For u = 1 enhancement of the decay rate due to the proximity of the (blZ+,u = 6 ) and (clII,u = 1) levels is found. This work provides considerable insight into factors influencing the spin-forbidden radiationless decay of OH+(clII,u,J,e/fi. However there remain many avenues for additional study. The role of the 23Z- channel in the predissociation of the higher vibrational levels needs to be considered. The reduced lifetime of the (clII,u = l,J,e) levels predicted here to be due to the proximity of the (blZ+,u= 6 ) and (clII,u = 1) levels is potentially quite important. In fact in Sarre's laboratory transitions to (clII,v = 1,J,e) levels are, in general, not observed. This is attributed totheaccidental degeneracy with (blZ+,v = 6).39 A similar effect involving the clIIl -alA2-A3112 pathway may be observable. Quantitative numerical studies of these effects will require more precise potential energy curves than those used in this work. A more complete treatment of rotational effects in the dissociative c o n t i n u ~ m may ~ ~also ~ be ~ ~required. ~ ~ ~ It will be interesting to consider the potential for nonadiabatic interactions in the exit channel23 to influence the detailed distribution of O(3P~)states formed in the predissociation. Additional work along these lines is Dlanned.
IV. Summary and Conclusions The focus of this work is the spin-forbidden predissociation of the OH+(clII,u= &3,J,e/j3. A Hund'scase (a) model was used. Both direct predissociations c'II, lsZ;, C I I I , N ~ ~ Z ;and , c l I I l-A3111 and indirect predissociations c'II, -b'Z;+A3110+and clIIl-a1A2-A3112, were considered. Electronic structure calculations based on large configuration state function (CSF) expansions, 500 000-1 100 000 terms, were used to determine the relevant potential energy curves and interstate couplings. All relativistic interactions were treated using the full microscopic dipolar spin-spin and spin-orbit operators. The electronic structure data were used within a coupled electronic state Golden Rule model to determine the line widths ofOH+(clII,u,J,e/fl foru I3. It is found that theOH+(c'II,u,JJ) levels decay principally by the direct coupling to the dissociative lsZ-state, clII1-lsZ;. The coupling matrix element, of magnitude approximately 1.7 cm-I, is attributable principally to the dipolar spin-spin interaction with a subordinate contribution from the second-order spin-orbit interaction. The present treatment of the second-order spin-orbit interaction in C S F spaces of greater than 1 million terms is the most extensive treatment of this effect reported to date. Line widths as large as 40 MHz (for u = 3, J = 10) are predicted for this mechanism. This mechanism is also operative for the OH+(clII,u,J,e) levels. For the OH+(cl II,u,J,e) levels an additional indirect mechanism c'II,-b1Z&-A311,+ discussed by Sarre and co-workers's becomes preeminent as J increases. For u = 3 line widths as large as 550 MHz for J = 10 are predicted. For u = 2 the line widths of the OH+(clII,u = 2,J,e) levels depend linearly on J(J + 1). Theu = 2 results are in excellent agreement with the experimental results of Sarre and co-workers. The linear dependence of the
-
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