- Email: [email protected]
Structure and stability of the HFF and FHF radicals
of Molecular Structure, 40 (1977) 117-126 8Elsevier Scientific Publishing Company, Amsterdam -
JOWML
Printed in The NetherIan&
STRUCTURE AND STABILITY OF .THE HFF AND FHF RADICALS RODERICH,PREUB,
SIGRID
D. PEYERIMHOFF
Lehtitiihl fiir’Theotit&ch& Chemie. Bonn, 53 Bonn (W: Germany) (Received 4 November
and Institut
and ROBERT
fiir Physikalische
3. BUENKER*
Chemie
der Uniuersitiit
1976)
ABSTRACT The structure and stability of the HFF and FHF isomers in their two lowest electronic states is studied by means of ab initio SCF and CI calculations employing a double-zeta basis plus various polarization functions. Both complexes can be essentially described by an HF dipole (exhibiting a standard HF bond length) attracting a fluorine atom, with an FF distance of 5.14 bohr calculated for the HF - - F ground state and an H - - F bond of 4.3 bohr for,the most stable FHF species. The HF, radical is found to prefer a bent structure in its zE+- ‘A’ ground state with an extremely flat potential curve, while the fast very low-lying excited state of HF, as well as both components of the ground (in this case ‘n) state of the. FH - - F complex are calculated to be linear. The symmetric FHF structure exhibits optimal bond lengths at approximately 2.1 bohr but is considerably. less stable than the asymmetrical arrangement of nuclei. With respect to dissociation into HF + F the HF, form is’ found to be stable in both (‘x:’ - A’) and 91 states while the conformer FH - - F shows a minimum only for the ‘II g-round state; the exdthermicity of the H + F2 - HF + F reaction is calculated to be 104.6 kcal mol-’ in good agreement with the experimental quantity of 102.5 2 2.8 kcal mol-‘. Comparison with the negative ions HF,-and FHF- is made whenever appropriate. INTRODUCTION
The study of the HF, and FHF radical systems has gained increased interest in recent years as a result of the development of the HIPl laser [l] and because .of a number. of experimental and theoretical investigations of the isovalent s@kies containing heavier halogen elements [ 2-4 1. The indication from theoretical calculations carried out on this subject [ 5-81 ~isthat.&he&ound~states .of both HF2 and FHF are only slightly bound with resp&t-to dissociation .into HF + -F. Because of the fact that the fluorine .atom po’ssessesa Spatially degenerate (‘P) ground state it seems clear that moth t&m Ia’smgle electionic state is important for such weakly bound moleculA~~~c&ipleq$s~,notably a,,2E+.and.a 211species in each system, and th&@$&ion thus&ises.which- of these (four) statespossesses the most stab!_i?.-~,~_~_~um:structure ,and;what the respective optimal geometrical pzir+me+-are in-e.~h_dase,:as-well:as:whether all of them are bound with -r&p&t to:dissociation.int& HF +. F. *Pieseiit:sd~~~~Fachbereich Chemie, Gesamthochschule _W;_Germany.
’ W,up$$&EB&fletd,
Wuppertal, GauOstr. 20,
Existing calculations have generally assumed that linear equilibrium geometries are preferred for such systems, although species vvith only one less electron such as FOH [Q] are well known to possess strongly bent structures. Especially given the weakly bound character .of .the HF, and FHF radicals there would thus appear to be a possibility that non-linear geometries are also important in these cases for one or more of their lowlying states. Since relatively small energy differences are involved in all these calculations it also would seem to be necessary to.consider effects of electron correlation in devising theoretical treatments of sufficient flexibility to allow for an ?ccurate determination of the pertinent pot+ial.energy surfaces in each case; in addition it is desirable that the AO-basis set employed contain various polarization functions and hence go beyond the conventional double-zeta level. With these considerations in mind the present study reports a series of SCF and CI calculations for the potential surfaces of HF, and FHF in which secular equations,of order 3000 to ,500O are solved and polarization effects are accounted for in the AQ basis through the inclusion of various bond-centered species as well as hydrogen 2p functions. PRELIMINARY STUD~.OF HF, AND BASIS SET The first series of calculations carried out employs a double-zeta A0 basis for fluorine and hydrogen given by Whitten’ [lo, 111 ;-the hydrogen functions (decomposed into two groups) tie scaled relative to the neutral atom by a factor of v2 = 2.60. The molecule ia then placed in the Xy.plane, with the F-F bond being collinear with the z axis.- With this b,asisminimal (SCF) energy is obtained for the lowest ‘A’ (. . . 2~“~8cz’) state .of,the HF,system for RHF = 1.73 bohr, RFF = 4.96 b o h r and LHFF’i 140°, whereby the angular potential curve is found to be extremely shallow (0.03 kcal mol-‘ depth). The lowest-lying *A” ( . . . 8ar22a”) species is found to lie only 0.0039 hartree above the ground state at this geometry. exhibiting a minimum for the linear arrangement of nuclei. Various polarization functions are then optimized for a linear HF, structure at roughly the above bond length values. The greatest effect noted comes upon addition of a hydrogen 2~.primitive-(a,,, = .0;8278), causing a lowering of the SCF energy by 0.01.7+rtree; Adding a smgies gaussian: (a 0Pr = 1.60) at the center of the HF-b&id yields anaddi‘ti‘onal energy lowering of 0.005 hark&e; whikuse of tie I&& &b-of @38bond-cent@d s and pn primitives, with.optimum ekponentkof0.35 tid.0.08 for the s gaussians and 0.30 and’0.045for. thep.!AO~s.respecti~~y;.is found:$&be.. much less purposeful (total low&g &ie’.t,o &:six :fnnc-~ons:~~_o_~y..d;oO3~. hartme). The fin’& bask, iniAu&ig all_the,aforemen~~~ediAO?~~(~2:~_~~~~~ yields a ground state .SCF eh‘e~‘of.~l99~4420~4.h~~:,~~bis“b_~~~~~~~.~. hartree lower than: the-double-zeta’val~~~~tr6~~~d:
119
The small energy difference between the lowest two states of HF, is easily recognized as reflecting the almost dissociative character of this radical, which approximates very nearly to a closed-shell HF molecule and a fluorine atom in their respective (I Z+ and ‘P) electronic ground states. In a linear field the lowest fragment state of this system splits into 2X+ and 211components; in bent geometries the Ill in turn correlates with both ‘A? and 2A” while the 2C’ species assumes 2A’ symmetry. The ground state at weak field strengths favors an electronic configuration in which the F atom po is only singly occupied while the correspondingpn species is a closed shell This state of affairs can be rationalized by viewing the po as a strongly polarized u* MO, which is slightly less stable than the correspondingpn (n?) species, an ordering which of course agrees at least qualitatively with what one finds in F2 itself. The magnitude of the 2A’ 2A” or2C+‘II splitting is thus seen to be a direct measure of the strength of the interaction between the HF dipole and the fluorine atom, and as such is expected to vary strongly with the FF distance in this system but much less so for the other two internal coordinates. In the double-zeta basis, for example, the 2z+ - 211SCF splitting changes from 0.0039 hartree to 0.0047 hartree in going from RFF = 4.9 to RFF = 4.7 bohr (with RnF held fixed at 1.75 bohr) while the energy of the 2X+ and ‘ll states themselves changes by only 0.00030 and 0.00107 hartree respectively as a result of the same decrease in RFF bond length. OPTIMIZEti
HF: EQUILIBRIUM
GEOMETRY
The double-zeta plus polarization (DZP) basis described above is used to reoptimize the nuclear geometry of the two lowest states of HF1 as well as the ground state of HF2-, again using the SCF approach exclusively (Table 1). In both HF, states the HF bond length is calculated to be 1.706 bohr in very close agreement to the value observed for isolated HF, namely 1.733 bohr [12] or 1.728 bohr [ 131, again pointing out the essential characteristics of HF, as an HF,molecule plus a weakly attached fluorine atom. The respective TABLE
1
Cakulated equilibriuni parameters (in bohr) for the HF, (HF - * F) radical obtained from SCF &kulations u&g the small double-kta’basis and the larger one including polarization functions
ax+ _fiz&..:.
z2
DiPb& -<
‘n.;:?&&e DZ b&i&__. :=Dzp-&&.
R(H-F)
R(&F)
LHFF
Energy (hartree)
1.73 1.706.
4.96. ‘!I%14
i40” 135O
-199.3945 ‘-199.4201
1173 .1:706
4.98 5.28
ia00
-199.3905 -199.4176
-s&t,
155”.
FF distancesare somewhat .differe& inthe two states;.namely 514. bohr.for the ‘A’ - zZ+ ground state and.5.28.bohrfor theczA”- ‘Il spa&& This resultagainappears to be consistent with the interpretationof th&:highest two orbitalsas polarizedTF*'guxh?-species respectively.-In the-?A'ground state the more strongly antib,ondingof the two (D*) is only singly occu&ied. and thus in this view +ou.ld. be expeCtedto prefer a slightly smallerRrF : value than.the 'A" excited state;.in which this species contains two electrons*. The calculationsindicate furthermorethat (linear).HFz- wiWthe present HF distanceof 1.7 bohr is not-bound at all, .a finding which seems reasonable in light of the unfavorableorientationof the HF’dipofe relative’to the Fion. The angularpotential curvesfor both HF2 states show very shallow minima away from the lineargeometry ineach case (0.17 kcaf.mol-” for ‘A! 3nd 0,016 kcal mol-i for ‘A”-), in contrast to results reported in earliercalculations;in the latter w.ork[ 7 3 the HFF angle was optimized employing relatively small R FF.valuesbetween 2.92 and 3.32 bobr, however.-Inview. of the fact that suchsmall energy differences are apparentlyinvolved it was then decided to consider the same angularvariationsusing CI techniques &lF = 1.70 and RFF = 5.10 bohr). All singly and doubly-excited configurationsrelativeto the leading(SCF) term* for each of the.two lowestlying I-IF,statesare accounted for (14541 symmetry-adaptedfunctions in all) in this treatmentvia an energy extrapolation schemediscussed elsewhere [ 141; the estimatedaccuracyof the resultingCI eigenvalues (i.e. compared to what would be obtained if the CI matrix were diagonalized explicitly) rangesfrom 1.0 X IO-$ to 4.0 X lo-’ hartree. The resulting potential curve data are given in Table 2; the averageCI energylowering is 0.197 hartree. (The selection thresholdemployed is 1.0 X 10e6 hartreein thiscase; seculru equationssolved are of order up to 4864.) From these data it is clearthat there is very nearly free rotation of the HF dipole in the field of the neutralF atom in both of the HF2 states considered. The indicationis that the.?l’l - 2A)’ excited state does show its~mmimum energy(-199.6146 hartree)for the lineargeometry .but the ?A’+ 2Z+. groundstate is calculated to be some 0.0004 hartree (1QO cm-‘) more stable for a bent structure(-199.6175 hartree)thti in its linearnucf&r arrangement.(Because of the errorsin the energy @$apolfttiO~ _~~oced~~. possible to give.$e op~~.~~F~_v~u~ to.yee_fiigh accur&y but it appears to be in the 100--121[) deg&e range.) The ~~c~a~d-~n~n~;. frequency is only 70 cm-’ at this point. horn: which it is .&n that ody &a-a::-.
it is not
TABLE
2
Calculated CI energies (b’artree) for the ‘A’ and. ‘A” states of HF, as a function of the HFF bending angle; thecorresponding SCF value for HF; are also given (RFH = 1.7 hohr, RFF = 5.1 bohr, zero of energy is -199.00 hartree) LHFF (degree)
7A’(HF,)
‘A”( HF,)
‘A’(HF,-).
180 176 170 157.5
-0.61711 -0.61715 -
-0.61460 -0.61454
-0.43521 -0.43523 -0.43531 -
-0.61733
+I.61436 -0.61393 -
-0.43614 -0.43695 -0.43813 -0.44211 -0.44706
:
150 140 130 110 95
-0.91735 -0.61757 -0.61756
SCF
single vibrational level actually lies below the barrier height obtained for the linear structure. While it is obviously true that such results may change somewhat upon further improvement in the A0 basis employed it still seems likely that the results of Table 2 are at least qualitatively correct, that is, the HF, ground state does prefer a bent equilibrium structure in contrast to what has generally been assumed for it in the past. Finally, HF2- is seen to prefer a much more strongly bent nuclear arrangement (SCF results only), undoubtedly as a consequence of the attraction between F and the hydrogen terminus of the HF dipole. CALCULATIONS
FOR THE ASYMMETRIC
FH -a F COMPLEX
Given the relatively weak FF bond for the HF2 radical and particularly the extreme flatness of its angul& potential curves in both ground and excited states, it is already clear that geometrical arrangements of the FH- F type should possess similar stability. To study this question an equivalent DZP basis is employed in SCF and CI calculations for such species. Again low-lying ‘E* and 2ll species are found and both are seen to correlate with the ground state dissociation. products HF (‘I: ‘) and F(‘P), but clear differences relative to the’HF, case are readily noted, in particular in the energy ordering of the FH-: F states. For a linear nuclear arrangement and HF distanceS of 1.70 and 4.40 bohr respectively, for example, SCF calculations find the.211state to be 0.0030 hartree more stable than 2Z*, whereas in HF, the ‘Il is always predicted to lie above the 2E”~S&&. Sinde,only Small energy-differences are involved it is difficult to -say with certainty why this mt+r$umge:of states takes place between these two conforr@io~,. but at least one factor seems to be that the po A0 of the more weakly bound F-atom is m.a better position to bind with the hydrogenic species in FH- -.F than are its pn counterparts. This rationale isnot only con&t&%&h the.observatitin that the po2pa3 2~ electronic l
I_
122
~dbnfiguration.s~oul'd:beqao~'sta;~e.~an 'ZT.(in 7Rhich~,u]~.o~y::s~,~~ occupied) butalsd‘ with: the c~alciula’ted.finding:tbat”only’~e.more.stable. state is act;ially;~l_+id+ith j_e+&$+&ss;ia~oninhqIF& ~F_(Tabl~_3,j$t RAF = i. Ol..-~~ .l._b. &.&&. ~av~.=~i~~~~~~~~~..:~~~~~~~~~~-~~~~~~~r~ smaller separations.,_ co~pon~g~~;;~r;tial~:~~es:$ee~~~~~sd~~~.__~I:-:_ diverge, with.the:~n?s~~-reac~ing,a-~nimum .a~~;3.~~~~“~~~~bih~~-~ energy of otiy‘O.0012 hart&e (0;75.k&l ~oi-l~--the::~T~~d~tial.~~e. .. ... .. . :_;-‘_ is strictly repulsive in :,theGme~ region;’ hd%Gever.~- . Since the amount &bin&g is so :,smallin the .FH -.~-.~F.-.~omple‘x.it -Q:not. surprisingthat the’sh&:gII aistance:~~foun;cilto.be.ve~..n~arly,e~al to the bond distance in HF-itself (Table 3); Similarly. the’corresponding angular potential curves (both SCF.-an$ C1):donforn-i to a. fairly~.classical model of the bonding inthisjsystem, sho&g sim~lyth&i&both corn? ponents of the ‘li state the most fav,otible ‘mbdeof~,$@pr~o&chis .linea&, whereby the ;separation of .thd positive’terrninus of th&HF dipole is .n&imized relativeto the approaching.Fiatom (Tablei5)~.lrhe:steepness.of:.theangular potential curves is relatively_minor, again .emphas~ng,th~.small:,amount-,of binding involved; but -the.ne&ive: ion system FH :.-: KY $hoF.a-mu& stronger preference for the.linear :orientation;-ag&as ,wouldbe.exp.ected from simple. electrostatics. In-‘other words, of all the. v&ous states :of- H& and FHF the only species which.appeais to prefera bent str&~e:is.the *Z+ ground state of the former s~stem~(Sect. 31. -Fir&v it is found that.
CaltulS?d%C.3~energy fix Uie sand a function of the H- - - F distance (F zero of energy = -199.00 bartree).
R(H- -F) 1.7 2.5 3.2 4.0 4.4 5.0 6.0 7.0 TABLE 4
tg (+j:--. -0.26640 1-0.38167 -0.406OT -0.41332 -0.41458. a41ii53 -0.41.6$$ '-_o.416$g
=ll states of=- - tititiil the ‘2 state of i?HF- & = l.?‘bbbr; eneeiti hkrt&k;--di&&‘in%bhi;
‘.‘~~@~i)_~:~ +;.‘@iI+ ,. _‘^ .. _--o_ti4.sii~;*.4io&i: : 1-0.3$138 +0;41361. --0.41_?45 -+417;52 +O,:$q22’ ';oi+1674' +&.6'ij~~
--0_5qi344~ ._0.60371~ +Lqsg73_ -~;fS79SQ '$;ri.@6. y;g6$&j -%dSS't&
123 TABLE
5
‘&k&ted dI’e&gies (hartree) for the ‘n and *z* states of FH - - F as a function of the bending angle; the corresponding SCF values for the negative ion are also given (Rm = 1.7 bohr, RH?. F_7 4.4 bohr;zero of energy is -199.00 hartree) LFkF(degk)
‘A’ (&ij
1’80 170 150 130 110
-0.61244 -0.61241 -0.61236 -0.61182 -0.611Q3
zA-* (‘fl) -0.61244 -0.61241 -0.61228 4.61186 ,.--0.61063
‘A’ (‘Z*,‘FHF-) -0.4 7959 -0.47924 -0.47643 -0.47043 -0.46050
the optimal symmetric FHF.structure corresponds to an FH distance of about 2.1 bohr (Fig. l), but the’SCF energy at this point is 45 kcal mol-* higher in the present treatment than for the most stable (asymmetric) FH : - F. conformation indicated in Table 4. This result clearly emphasizes that by- far the best description .of the FHF equilibrium structure is a weakly bound FH + F complex. A schematic diagram indicating the calcuJa~,d~~equil~briu geometries of the various HF F and F-H - - F species treated-may bc found in Fig. 2. l
[F,ii -Eimrg
l
[ FHF]-
t!artmaI
bmtroa 1
- 199.2 . -.199.21
-199.40
:; - 199.21
- 199.42
-199.u .,‘..
-199. b4
-1sp.q :
-199.46
-l&r
-199.48
-199.50 ; 199.52 -.
(vp7ocm~ H
H-F
100120’
Ground ‘jt&:.
-----m-F
0.903
2~
Excited State
2z:’
F-H
2.79
. . .. .. . F
0.91
Fig. 2. Schema& diagram showing the calculated equilibriuk various HF, and FHJ? species considk-ed in this w.ork.
ENERGY RELATIOlhWP PRODUCTS
BETWEEN
FH-,iF
&ID
replilsive parameters (in A) of the
HF.--F-AND
DISSOCIATION
For the.purpose of studying chemical reactions of such-HF, species:it is useful to have equivalent calculations for the two importkt’sets ‘of dissociation products HF (‘Z:‘) + F(2P) and H(‘S) +--F*(!Cf). The CI calculations for FH -.-•F _ata very large FF distance (for example l’l,‘70 h&r) are sufficient for the description of the HF + F system, but for the other case it is clearly nec&s&y to carry out an analogous treatment for’the equilibrium conformation of F;. For this purpose an equivalent fluorine DZP basis as described in Setit. 2 is employed, except that the extraneous hydrogen-type species (including: the HF bond s function) are deleted therefrom. The SCF potential‘ciirve for the ‘Zp’ ground state of FLyields an optimal value for the FF. bond of 2.65 bohr and a total energy of -198.7020 h,artree; the calcukted .’ equilibrium bond dis mental value of 2.68 bo measurement and-calcula optimization at the Cl lev calculation at thd’ei$e+mental R -198.9436 hai-tree; while hartree, compared- to value obtained uniformally for th is clear that CI is quite impo (i.e. the differen& ircalculated~ The resulting CI energies for HF2 isomeric spe+s studied in .the+ Table 6;. these re,suItsare also c HP (!z;)_+ _F(2@ _&_&,-&~&sy Sect_
4 the
g+
s&-of
>_..._ ._., ____ _m ~ ~ F: .&&$~
125 TABLE
6
Summary of key energies for the various systxms obtained in the DZP basis employing the CI treatmenp System
Total energy (hartree)
HF -. F, ‘Xc (bent) ‘n FH- .F; ‘n 2x+ FH + F (‘Z+ + ;P) ti + F, (‘S + ‘Z;)
-199.6175 -199.6146 -199.6124 no minimum -199.6102 -199.4436
aIn general an HF value of 1.7 bobr was employed, (uniformally)slightly lower by using 1.72 bohr.
Relative energy (kcal mol-’ ) -4.6 -2.8 -1.4 0.00 104.6 although total energies would be
the F atom but the other three states treated show binding energies cf 1.4 to 4.6 kcal mol-‘. The electronic energy difference for the reaction HF + F + Fz + H is found to be 104.6 kcai mol-’ in the present Cl calculations. (The earher CI treatment of O’NeiI et al. [7] yields a value of 88.3 kcal mol-’ while the corresponding work with an improved A0 basis [S] gives 99.0 kcal mol-I.) The experimental value for this quantity can be obtained by subtracting the known D, values for F2 (38.8 f 2.3 kcal mol-’ according to [16] ) and HF (141.3 + 0.5 kcal mol-’ according to [17] ), yielding an estimate of 102.5 f 2.8 kcal mol-l; The present calculated result is thus seen to lie within the error’limits given for this quantity experimentaliy. ACKNOWLEDGEMENT
-The services and computer time made available by the University of Bonn computer center have been essential to this study and are gratefully acknowledged. REFJ&ENCES 1 J. c Airey, Int. J. Chem. Kinetics, 2 (1976) 65. .2P.‘fi. Noble’.and G. C. Pimeqtel, J. Chem Phys., 49 (1968) 3165; V. Bondybey, “. G.-C. Pimenti, P_ 8. &Ioble, J. Ch em_,Phys., 55 (1971) 54O;P. N. Noble. J. Chem. Phys.. :56(i972)-2088. t : ‘3 D. F. Mill&an and M.-E. Jacoq- +.Chem. Phys., 53 (1970) 2034; 55 (1971) 2550. 4 Di-G; Tqthlar, P. c.: Olso~.C. A Parr, J. Chem. Pbpa, 57 (1972) 4479. SP.~N.~Nobleand,RN. Kortzeborn,~J.,~em.Phys., 52 (1970) 5375. 6-S V;.‘G’fieilj D. F. St&efer~~~and’C. F..Be’nder. Proc. Nat. Acad. Sci. USA, 71 (1974) -,-l’o;l. 7-‘5:‘~._a’~~,~P~:~.,Pe~n’~d H; F_‘S&aefer Ii& J_-Chem. Phys., 58 (1973) 1126. ‘S k$L.F_;B&der; C. W. -~uechticher &i-&d H: .F. Schaefer III, J. Chem. Phys., 60 (1974) 3707.
9 10 11 12
R. J. Buenker and S. D. Peyerimhoff, J. Chem. Phys., 45 (1966) 3682. J. L. Whitten, J. Chem. Phys., 44 (1966) 359. S. D. Peyerimhoff; R. J. .Buenket and L. C. Allen, J. Chem. Phys., 45 (3966)734, D. E. Mann, B. A. Thrush. D. R_Lide, J. J. Ball and N. Acquista, J. Chem. Phys, 34 (1961) 420. 13 L. E. Sutton (Ed.), Chem. Sot. (London), Spec. Publ., ll(1958); 18 (i965). 14 R J. Buneker and S. D. Peyerimhoff, Theor. Chim Acta, 35 (1974) 33; 39 (1975) 217. 15 A. Andrychuk, Can. J. Phys., 29 (1951) 151. 16 J. J. DeCorpo, RrP. Steiger, J. L. Franklin and J. L. Margrave, J. Chem.,.Phys. 53 (1970) 936. 1’7 W. A Chupka and J. Berkowitz, J. Chem. Phys., 54’(1971) 5126.
JOWML
Printed in The NetherIan&
STRUCTURE AND STABILITY OF .THE HFF AND FHF RADICALS RODERICH,PREUB,
SIGRID
D. PEYERIMHOFF
Lehtitiihl fiir’Theotit&ch& Chemie. Bonn, 53 Bonn (W: Germany) (Received 4 November
and Institut
and ROBERT
fiir Physikalische
3. BUENKER*
Chemie
der Uniuersitiit
1976)
ABSTRACT The structure and stability of the HFF and FHF isomers in their two lowest electronic states is studied by means of ab initio SCF and CI calculations employing a double-zeta basis plus various polarization functions. Both complexes can be essentially described by an HF dipole (exhibiting a standard HF bond length) attracting a fluorine atom, with an FF distance of 5.14 bohr calculated for the HF - - F ground state and an H - - F bond of 4.3 bohr for,the most stable FHF species. The HF, radical is found to prefer a bent structure in its zE+- ‘A’ ground state with an extremely flat potential curve, while the fast very low-lying excited state of HF, as well as both components of the ground (in this case ‘n) state of the. FH - - F complex are calculated to be linear. The symmetric FHF structure exhibits optimal bond lengths at approximately 2.1 bohr but is considerably. less stable than the asymmetrical arrangement of nuclei. With respect to dissociation into HF + F the HF, form is’ found to be stable in both (‘x:’ - A’) and 91 states while the conformer FH - - F shows a minimum only for the ‘II g-round state; the exdthermicity of the H + F2 - HF + F reaction is calculated to be 104.6 kcal mol-’ in good agreement with the experimental quantity of 102.5 2 2.8 kcal mol-‘. Comparison with the negative ions HF,-and FHF- is made whenever appropriate. INTRODUCTION
The study of the HF, and FHF radical systems has gained increased interest in recent years as a result of the development of the HIPl laser [l] and because .of a number. of experimental and theoretical investigations of the isovalent s@kies containing heavier halogen elements [ 2-4 1. The indication from theoretical calculations carried out on this subject [ 5-81 ~isthat.&he&ound~states .of both HF2 and FHF are only slightly bound with resp&t-to dissociation .into HF + -F. Because of the fact that the fluorine .atom po’ssessesa Spatially degenerate (‘P) ground state it seems clear that moth t&m Ia’smgle electionic state is important for such weakly bound moleculA~~~c&ipleq$s~,notably a,,2E+.and.a 211species in each system, and th&@$&ion thus&ises.which- of these (four) statespossesses the most stab!_i?.-~,~_~_~um:structure ,and;what the respective optimal geometrical pzir+me+-are in-e.~h_dase,:as-well:as:whether all of them are bound with -r&p&t to:dissociation.int& HF +. F. *Pieseiit:sd~~~~Fachbereich Chemie, Gesamthochschule _W;_Germany.
’ W,up$$&EB&fletd,
Wuppertal, GauOstr. 20,
Existing calculations have generally assumed that linear equilibrium geometries are preferred for such systems, although species vvith only one less electron such as FOH [Q] are well known to possess strongly bent structures. Especially given the weakly bound character .of .the HF, and FHF radicals there would thus appear to be a possibility that non-linear geometries are also important in these cases for one or more of their lowlying states. Since relatively small energy differences are involved in all these calculations it also would seem to be necessary to.consider effects of electron correlation in devising theoretical treatments of sufficient flexibility to allow for an ?ccurate determination of the pertinent pot+ial.energy surfaces in each case; in addition it is desirable that the AO-basis set employed contain various polarization functions and hence go beyond the conventional double-zeta level. With these considerations in mind the present study reports a series of SCF and CI calculations for the potential surfaces of HF, and FHF in which secular equations,of order 3000 to ,500O are solved and polarization effects are accounted for in the AQ basis through the inclusion of various bond-centered species as well as hydrogen 2p functions. PRELIMINARY STUD~.OF HF, AND BASIS SET The first series of calculations carried out employs a double-zeta A0 basis for fluorine and hydrogen given by Whitten’ [lo, 111 ;-the hydrogen functions (decomposed into two groups) tie scaled relative to the neutral atom by a factor of v2 = 2.60. The molecule ia then placed in the Xy.plane, with the F-F bond being collinear with the z axis.- With this b,asisminimal (SCF) energy is obtained for the lowest ‘A’ (. . . 2~“~8cz’) state .of,the HF,system for RHF = 1.73 bohr, RFF = 4.96 b o h r and LHFF’i 140°, whereby the angular potential curve is found to be extremely shallow (0.03 kcal mol-‘ depth). The lowest-lying *A” ( . . . 8ar22a”) species is found to lie only 0.0039 hartree above the ground state at this geometry. exhibiting a minimum for the linear arrangement of nuclei. Various polarization functions are then optimized for a linear HF, structure at roughly the above bond length values. The greatest effect noted comes upon addition of a hydrogen 2~.primitive-(a,,, = .0;8278), causing a lowering of the SCF energy by 0.01.7+rtree; Adding a smgies gaussian: (a 0Pr = 1.60) at the center of the HF-b&id yields anaddi‘ti‘onal energy lowering of 0.005 hark&e; whikuse of tie I&& &b-of @38bond-cent@d s and pn primitives, with.optimum ekponentkof0.35 tid.0.08 for the s gaussians and 0.30 and’0.045for. thep.!AO~s.respecti~~y;.is found:$&be.. much less purposeful (total low&g &ie’.t,o &:six :fnnc-~ons:~~_o_~y..d;oO3~. hartme). The fin’& bask, iniAu&ig all_the,aforemen~~~ediAO?~~(~2:~_~~~~~ yields a ground state .SCF eh‘e~‘of.~l99~4420~4.h~~:,~~bis“b_~~~~~~~.~. hartree lower than: the-double-zeta’val~~~~tr6~~~d:
119
The small energy difference between the lowest two states of HF, is easily recognized as reflecting the almost dissociative character of this radical, which approximates very nearly to a closed-shell HF molecule and a fluorine atom in their respective (I Z+ and ‘P) electronic ground states. In a linear field the lowest fragment state of this system splits into 2X+ and 211components; in bent geometries the Ill in turn correlates with both ‘A? and 2A” while the 2C’ species assumes 2A’ symmetry. The ground state at weak field strengths favors an electronic configuration in which the F atom po is only singly occupied while the correspondingpn species is a closed shell This state of affairs can be rationalized by viewing the po as a strongly polarized u* MO, which is slightly less stable than the correspondingpn (n?) species, an ordering which of course agrees at least qualitatively with what one finds in F2 itself. The magnitude of the 2A’ 2A” or2C+‘II splitting is thus seen to be a direct measure of the strength of the interaction between the HF dipole and the fluorine atom, and as such is expected to vary strongly with the FF distance in this system but much less so for the other two internal coordinates. In the double-zeta basis, for example, the 2z+ - 211SCF splitting changes from 0.0039 hartree to 0.0047 hartree in going from RFF = 4.9 to RFF = 4.7 bohr (with RnF held fixed at 1.75 bohr) while the energy of the 2X+ and ‘ll states themselves changes by only 0.00030 and 0.00107 hartree respectively as a result of the same decrease in RFF bond length. OPTIMIZEti
HF: EQUILIBRIUM
GEOMETRY
The double-zeta plus polarization (DZP) basis described above is used to reoptimize the nuclear geometry of the two lowest states of HF1 as well as the ground state of HF2-, again using the SCF approach exclusively (Table 1). In both HF, states the HF bond length is calculated to be 1.706 bohr in very close agreement to the value observed for isolated HF, namely 1.733 bohr [12] or 1.728 bohr [ 131, again pointing out the essential characteristics of HF, as an HF,molecule plus a weakly attached fluorine atom. The respective TABLE
1
Cakulated equilibriuni parameters (in bohr) for the HF, (HF - * F) radical obtained from SCF &kulations u&g the small double-kta’basis and the larger one including polarization functions
ax+ _fiz&..:.
z2
DiPb& -<
‘n.;:?&&e DZ b&i&__. :=Dzp-&&.
R(H-F)
R(&F)
LHFF
Energy (hartree)
1.73 1.706.
4.96. ‘!I%14
i40” 135O
-199.3945 ‘-199.4201
1173 .1:706
4.98 5.28
ia00
-199.3905 -199.4176
-s&t,
155”.
FF distancesare somewhat .differe& inthe two states;.namely 514. bohr.for the ‘A’ - zZ+ ground state and.5.28.bohrfor theczA”- ‘Il spa&& This resultagainappears to be consistent with the interpretationof th&:highest two orbitalsas polarizedTF*'guxh?-species respectively.-In the-?A'ground state the more strongly antib,ondingof the two (D*) is only singly occu&ied. and thus in this view +ou.ld. be expeCtedto prefer a slightly smallerRrF : value than.the 'A" excited state;.in which this species contains two electrons*. The calculationsindicate furthermorethat (linear).HFz- wiWthe present HF distanceof 1.7 bohr is not-bound at all, .a finding which seems reasonable in light of the unfavorableorientationof the HF’dipofe relative’to the Fion. The angularpotential curvesfor both HF2 states show very shallow minima away from the lineargeometry ineach case (0.17 kcaf.mol-” for ‘A! 3nd 0,016 kcal mol-i for ‘A”-), in contrast to results reported in earliercalculations;in the latter w.ork[ 7 3 the HFF angle was optimized employing relatively small R FF.valuesbetween 2.92 and 3.32 bobr, however.-Inview. of the fact that suchsmall energy differences are apparentlyinvolved it was then decided to consider the same angularvariationsusing CI techniques &lF = 1.70 and RFF = 5.10 bohr). All singly and doubly-excited configurationsrelativeto the leading(SCF) term* for each of the.two lowestlying I-IF,statesare accounted for (14541 symmetry-adaptedfunctions in all) in this treatmentvia an energy extrapolation schemediscussed elsewhere [ 141; the estimatedaccuracyof the resultingCI eigenvalues (i.e. compared to what would be obtained if the CI matrix were diagonalized explicitly) rangesfrom 1.0 X IO-$ to 4.0 X lo-’ hartree. The resulting potential curve data are given in Table 2; the averageCI energylowering is 0.197 hartree. (The selection thresholdemployed is 1.0 X 10e6 hartreein thiscase; seculru equationssolved are of order up to 4864.) From these data it is clearthat there is very nearly free rotation of the HF dipole in the field of the neutralF atom in both of the HF2 states considered. The indicationis that the.?l’l - 2A)’ excited state does show its~mmimum energy(-199.6146 hartree)for the lineargeometry .but the ?A’+ 2Z+. groundstate is calculated to be some 0.0004 hartree (1QO cm-‘) more stable for a bent structure(-199.6175 hartree)thti in its linearnucf&r arrangement.(Because of the errorsin the energy @$apolfttiO~ _~~oced~~. possible to give.$e op~~.~~F~_v~u~ to.yee_fiigh accur&y but it appears to be in the 100--121[) deg&e range.) The ~~c~a~d-~n~n~;. frequency is only 70 cm-’ at this point. horn: which it is .&n that ody &a-a::-.
it is not
TABLE
2
Calculated CI energies (b’artree) for the ‘A’ and. ‘A” states of HF, as a function of the HFF bending angle; thecorresponding SCF value for HF; are also given (RFH = 1.7 hohr, RFF = 5.1 bohr, zero of energy is -199.00 hartree) LHFF (degree)
7A’(HF,)
‘A”( HF,)
‘A’(HF,-).
180 176 170 157.5
-0.61711 -0.61715 -
-0.61460 -0.61454
-0.43521 -0.43523 -0.43531 -
-0.61733
+I.61436 -0.61393 -
-0.43614 -0.43695 -0.43813 -0.44211 -0.44706
:
150 140 130 110 95
-0.91735 -0.61757 -0.61756
SCF
single vibrational level actually lies below the barrier height obtained for the linear structure. While it is obviously true that such results may change somewhat upon further improvement in the A0 basis employed it still seems likely that the results of Table 2 are at least qualitatively correct, that is, the HF, ground state does prefer a bent equilibrium structure in contrast to what has generally been assumed for it in the past. Finally, HF2- is seen to prefer a much more strongly bent nuclear arrangement (SCF results only), undoubtedly as a consequence of the attraction between F and the hydrogen terminus of the HF dipole. CALCULATIONS
FOR THE ASYMMETRIC
FH -a F COMPLEX
Given the relatively weak FF bond for the HF2 radical and particularly the extreme flatness of its angul& potential curves in both ground and excited states, it is already clear that geometrical arrangements of the FH- F type should possess similar stability. To study this question an equivalent DZP basis is employed in SCF and CI calculations for such species. Again low-lying ‘E* and 2ll species are found and both are seen to correlate with the ground state dissociation. products HF (‘I: ‘) and F(‘P), but clear differences relative to the’HF, case are readily noted, in particular in the energy ordering of the FH-: F states. For a linear nuclear arrangement and HF distanceS of 1.70 and 4.40 bohr respectively, for example, SCF calculations find the.211state to be 0.0030 hartree more stable than 2Z*, whereas in HF, the ‘Il is always predicted to lie above the 2E”~S&&. Sinde,only Small energy-differences are involved it is difficult to -say with certainty why this mt+r$umge:of states takes place between these two conforr@io~,. but at least one factor seems to be that the po A0 of the more weakly bound F-atom is m.a better position to bind with the hydrogenic species in FH- -.F than are its pn counterparts. This rationale isnot only con&t&%&h the.observatitin that the po2pa3 2~ electronic l
I_
122
~dbnfiguration.s~oul'd:beqao~'sta;~e.~an 'ZT.(in 7Rhich~,u]~.o~y::s~,~~ occupied) butalsd‘ with: the c~alciula’ted.finding:tbat”only’~e.more.stable. state is act;ially;~l_+id+ith j_e+&$+&ss;ia~oninhqIF& ~F_(Tabl~_3,j$t RAF = i. Ol..-~~ .l._b. &.&&. ~av~.=~i~~~~~~~~~..:~~~~~~~~~~-~~~~~~~r~ smaller separations.,_ co~pon~g~~;;~r;tial~:~~es:$ee~~~~~sd~~~.__~I:-:_ diverge, with.the:~n?s~~-reac~ing,a-~nimum .a~~;3.~~~~“~~~~bih~~-~ energy of otiy‘O.0012 hart&e (0;75.k&l ~oi-l~--the::~T~~d~tial.~~e. .. ... .. . :_;-‘_ is strictly repulsive in :,theGme~ region;’ hd%Gever.~- . Since the amount &bin&g is so :,smallin the .FH -.~-.~F.-.~omple‘x.it -Q:not. surprisingthat the’sh&:gII aistance:~~foun;cilto.be.ve~..n~arly,e~al to the bond distance in HF-itself (Table 3); Similarly. the’corresponding angular potential curves (both SCF.-an$ C1):donforn-i to a. fairly~.classical model of the bonding inthisjsystem, sho&g sim~lyth&i&both corn? ponents of the ‘li state the most fav,otible ‘mbdeof~,$@pr~o&chis .linea&, whereby the ;separation of .thd positive’terrninus of th&HF dipole is .n&imized relativeto the approaching.Fiatom (Tablei5)~.lrhe:steepness.of:.theangular potential curves is relatively_minor, again .emphas~ng,th~.small:,amount-,of binding involved; but -the.ne&ive: ion system FH :.-: KY $hoF.a-mu& stronger preference for the.linear :orientation;-ag&as ,wouldbe.exp.ected from simple. electrostatics. In-‘other words, of all the. v&ous states :of- H& and FHF the only species which.appeais to prefera bent str&~e:is.the *Z+ ground state of the former s~stem~(Sect. 31. -Fir&v it is found that.
CaltulS?d%C.3~energy fix Uie sand a function of the H- - - F distance (F zero of energy = -199.00 bartree).
R(H- -F) 1.7 2.5 3.2 4.0 4.4 5.0 6.0 7.0 TABLE 4
tg (+j:--. -0.26640 1-0.38167 -0.406OT -0.41332 -0.41458. a41ii53 -0.41.6$$ '-_o.416$g
=ll states of=- - tititiil the ‘2 state of i?HF- & = l.?‘bbbr; eneeiti hkrt&k;--di&&‘in%bhi;
‘.‘~~@~i)_~:~ +;.‘@iI+ ,. _‘^ .. _--o_ti4.sii~;*.4io&i: : 1-0.3$138 +0;41361. --0.41_?45 -+417;52 +O,:$q22’ ';oi+1674' +&.6'ij~~
--0_5qi344~ ._0.60371~ +Lqsg73_ -~;fS79SQ '$;ri.@6. y;g6$&j -%dSS't&
123 TABLE
5
‘&k&ted dI’e&gies (hartree) for the ‘n and *z* states of FH - - F as a function of the bending angle; the corresponding SCF values for the negative ion are also given (Rm = 1.7 bohr, RH?. F_7 4.4 bohr;zero of energy is -199.00 hartree) LFkF(degk)
‘A’ (&ij
1’80 170 150 130 110
-0.61244 -0.61241 -0.61236 -0.61182 -0.611Q3
zA-* (‘fl) -0.61244 -0.61241 -0.61228 4.61186 ,.--0.61063
‘A’ (‘Z*,‘FHF-) -0.4 7959 -0.47924 -0.47643 -0.47043 -0.46050
the optimal symmetric FHF.structure corresponds to an FH distance of about 2.1 bohr (Fig. l), but the’SCF energy at this point is 45 kcal mol-* higher in the present treatment than for the most stable (asymmetric) FH : - F. conformation indicated in Table 4. This result clearly emphasizes that by- far the best description .of the FHF equilibrium structure is a weakly bound FH + F complex. A schematic diagram indicating the calcuJa~,d~~equil~briu geometries of the various HF F and F-H - - F species treated-may bc found in Fig. 2. l
[F,ii -Eimrg
l
[ FHF]-
t!artmaI
bmtroa 1
- 199.2 . -.199.21
-199.40
:; - 199.21
- 199.42
-199.u .,‘..
-199. b4
-1sp.q :
-199.46
-l&r
-199.48
-199.50 ; 199.52 -.
(vp7ocm~ H
H-F
100120’
Ground ‘jt&:.
-----m-F
0.903
2~
Excited State
2z:’
F-H
2.79
. . .. .. . F
0.91
Fig. 2. Schema& diagram showing the calculated equilibriuk various HF, and FHJ? species considk-ed in this w.ork.
ENERGY RELATIOlhWP PRODUCTS
BETWEEN
FH-,iF
&ID
replilsive parameters (in A) of the
HF.--F-AND
DISSOCIATION
For the.purpose of studying chemical reactions of such-HF, species:it is useful to have equivalent calculations for the two importkt’sets ‘of dissociation products HF (‘Z:‘) + F(2P) and H(‘S) +--F*(!Cf). The CI calculations for FH -.-•F _ata very large FF distance (for example l’l,‘70 h&r) are sufficient for the description of the HF + F system, but for the other case it is clearly nec&s&y to carry out an analogous treatment for’the equilibrium conformation of F;. For this purpose an equivalent fluorine DZP basis as described in Setit. 2 is employed, except that the extraneous hydrogen-type species (including: the HF bond s function) are deleted therefrom. The SCF potential‘ciirve for the ‘Zp’ ground state of FLyields an optimal value for the FF. bond of 2.65 bohr and a total energy of -198.7020 h,artree; the calcukted .’ equilibrium bond dis mental value of 2.68 bo measurement and-calcula optimization at the Cl lev calculation at thd’ei$e+mental R -198.9436 hai-tree; while hartree, compared- to value obtained uniformally for th is clear that CI is quite impo (i.e. the differen& ircalculated~ The resulting CI energies for HF2 isomeric spe+s studied in .the+ Table 6;. these re,suItsare also c HP (!z;)_+ _F(2@ _&_&,-&~&sy Sect_
4 the
g+
s&-of
>_..._ ._., ____ _m ~ ~ F: .&&$~
125 TABLE
6
Summary of key energies for the various systxms obtained in the DZP basis employing the CI treatmenp System
Total energy (hartree)
HF -. F, ‘Xc (bent) ‘n FH- .F; ‘n 2x+ FH + F (‘Z+ + ;P) ti + F, (‘S + ‘Z;)
-199.6175 -199.6146 -199.6124 no minimum -199.6102 -199.4436
aIn general an HF value of 1.7 bobr was employed, (uniformally)slightly lower by using 1.72 bohr.
Relative energy (kcal mol-’ ) -4.6 -2.8 -1.4 0.00 104.6 although total energies would be
the F atom but the other three states treated show binding energies cf 1.4 to 4.6 kcal mol-‘. The electronic energy difference for the reaction HF + F + Fz + H is found to be 104.6 kcai mol-’ in the present Cl calculations. (The earher CI treatment of O’NeiI et al. [7] yields a value of 88.3 kcal mol-’ while the corresponding work with an improved A0 basis [S] gives 99.0 kcal mol-I.) The experimental value for this quantity can be obtained by subtracting the known D, values for F2 (38.8 f 2.3 kcal mol-’ according to [16] ) and HF (141.3 + 0.5 kcal mol-’ according to [17] ), yielding an estimate of 102.5 f 2.8 kcal mol-l; The present calculated result is thus seen to lie within the error’limits given for this quantity experimentaliy. ACKNOWLEDGEMENT
-The services and computer time made available by the University of Bonn computer center have been essential to this study and are gratefully acknowledged. REFJ&ENCES 1 J. c Airey, Int. J. Chem. Kinetics, 2 (1976) 65. .2P.‘fi. Noble’.and G. C. Pimeqtel, J. Chem Phys., 49 (1968) 3165; V. Bondybey, “. G.-C. Pimenti, P_ 8. &Ioble, J. Ch em_,Phys., 55 (1971) 54O;P. N. Noble. J. Chem. Phys.. :56(i972)-2088. t : ‘3 D. F. Mill&an and M.-E. Jacoq- +.Chem. Phys., 53 (1970) 2034; 55 (1971) 2550. 4 Di-G; Tqthlar, P. c.: Olso~.C. A Parr, J. Chem. Pbpa, 57 (1972) 4479. SP.~N.~Nobleand,RN. Kortzeborn,~J.,~em.Phys., 52 (1970) 5375. 6-S V;.‘G’fieilj D. F. St&efer~~~and’C. F..Be’nder. Proc. Nat. Acad. Sci. USA, 71 (1974) -,-l’o;l. 7-‘5:‘~._a’~~,~P~:~.,Pe~n’~d H; F_‘S&aefer Ii& J_-Chem. Phys., 58 (1973) 1126. ‘S k$L.F_;B&der; C. W. -~uechticher &i-&d H: .F. Schaefer III, J. Chem. Phys., 60 (1974) 3707.
9 10 11 12
R. J. Buenker and S. D. Peyerimhoff, J. Chem. Phys., 45 (1966) 3682. J. L. Whitten, J. Chem. Phys., 44 (1966) 359. S. D. Peyerimhoff; R. J. .Buenket and L. C. Allen, J. Chem. Phys., 45 (3966)734, D. E. Mann, B. A. Thrush. D. R_Lide, J. J. Ball and N. Acquista, J. Chem. Phys, 34 (1961) 420. 13 L. E. Sutton (Ed.), Chem. Sot. (London), Spec. Publ., ll(1958); 18 (i965). 14 R J. Buneker and S. D. Peyerimhoff, Theor. Chim Acta, 35 (1974) 33; 39 (1975) 217. 15 A. Andrychuk, Can. J. Phys., 29 (1951) 151. 16 J. J. DeCorpo, RrP. Steiger, J. L. Franklin and J. L. Margrave, J. Chem.,.Phys. 53 (1970) 936. 1’7 W. A Chupka and J. Berkowitz, J. Chem. Phys., 54’(1971) 5126.