- Email: [email protected]
Diatomics-in-molecules calculations of potential-energy surfaces for B+(3P) + H2(X 1Σg+)
Recriwd
16 May 1953: in final form 2S Srptcmhcr
Collisions
interpretation
19S3
B+(3P) with Hi(X “p’ ) have hrcn studied rcptlatedly uing molecular-hram of the results suffered from missing inform.ttion about the potentini-energy surfxes
of
reports on_ dinromics-in-molcules cnlcultttions for Q wids rttngc of minimum-mergy paths xc determined. Symmetrically orrhogotxdizsd differ only slightly nt the minimum-energy
path. The potmtinl-cnsrgy
surfaces or the 1 ‘A’ and ?‘A’
with the BHH angle. leading possibly to ndinbntic as well as non-adiabatic rlcmcntxy states are nexly degenerate for geometries ranging from the entmnce chxmel to the interxtion surfwxs arc those with_C,,
versions
states show dramatical
proccssrs. The 1 ‘A” and 1 3.4’
r&on.
The most f.tvourabIe
symmetry.
ties [4,6]. In the present paper, we recalculate
1. Introduction
ergy path WEp)
and fragment
information
To describe the DIM calculation, following three basis structures:
-~BH+(X.~Zf,A’n,B’Z+)+H
(1)
B+(‘S)
+ 2ti(ls),
(2)~ B*(3P)
+ 2H(ls),
: (3)
,
B(‘P)+H@s)+Ij+,~
em
1v-edefine the
__
from which the possible:symmetry-adapted 3A’ and 3Ay basis functions (SBFs) were constructed. These SBFs are characterized in table 1: _ The energy Jevels of the atomic species~ were
0301-0104/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland PhysicsPublishing Division) 1
~.
[Sl-
2. DIM calculation
+ H2(X’Zp’)
and its isotopic anhlogue with D, to occur prevailingly through a long-lived complex. The reader is referred to the literature for more detailed information on cross- sections [3], scattering -diagrams [4-61,. translational energy and angular distribu_tions of the products [5]. product internal -state distributions [7] as -well was translational exoergici_
the
PESs using more reliable input data, and determine the stationary points on the minimum-en-
In an earlier paper [l], we presented an approximation to the_lowest (BH,)’ potential-energy surfaces (PESs) within the diatomics-in-molecules (DIM) framework [2] in order to interprete recent molecular-beam data [3]. These measurements give evidence for the reaction B’(3P)
The rhrorericxl for this system. This paper kttiokq points one the
nuclenr geomelries. The and non-hcrmitcan diatomics-in-molecules
chnngs
configur.ttions of approach on thssr potcnkcnttrgy
tcch~niqurs.
-.
~.
-~
‘IS
E Schneider cl af. /
DIM
porenriaf enersr sur-aces
taken from ref. [9]_ The diatomic H,‘and H, inter:1L’t1Wl energies \vrre represented by extended Rfc>rsc curve fits [lo]. The same analytical form ha\ bscn uwi to drscribr the BH and BH‘ inter:tctwns. The BH -(S ‘1: -_ B ‘\“. A’n) potential~ncrgy curves (PECe) are fits to the results of XtRD Cl calculations [I I]. while the BH(a-‘IT) PE<‘ is a fit to GL’B results [12]. Whcrs availabis. the q-wnmcnt:~I valurs of r_ [13] have been used In the fits. The aho\-cmcntionrd diatornic states xs \LJI IS two other BH’ states (aJII. bJ\‘+) have hwn a~~umsd tO he “pure” states. u bile three further cxcitcd states BH *(7 ‘II. 3 ‘X-) and BH(c ‘I- ) have been trcittcd iiS -‘rnised exited >tatr’>” 1141. This concept nwans. that \vc did not ube the bcbt :~v:tilablr PEC inform:ttion [ 1 l-161 but rather interpolated curves brtk\vren several different excited states. The interpolated “miscd” CLI rv’c’s arc more appropriate for our restricted DI Xl bak The simplest straightforward clay to obtain such asmixed” PECs as \\~ll as mising coefficients of Jistomic states of the same symnh2try. c-e_ 131-I-( ‘I-: ) or BH ‘( -wv’). is to perform a VB typr calculation for the diatomic with a basis set reztrictsd CO the character of the Dlhl basis structurt’s (bv wmoving the third atom). For thrsc and ictrth sqL,IIr~L't st.ktrs 0f BH + we uad the AI,\1
off BH,)_
the. (OM). method [17.18] and obtained BH’(Z’IX a’II. 3’S’, b”Z’) and BH(c”S+) PECs and the mixing coefficients of BH’(‘LI) and BH’( ‘I’). The diatomic configuration mixing for the ‘II case has been formulated according to
(;r)=(::-:i)(;$
(1)
where 9, and +2 are the basis functions dissociating into B+(“P) + H(ls) and B(‘P) + H+. rcspectivcly. For the ‘Xc case. we put
A, is the B -( ‘S) + H( 1s) basis function. and the 9-1~. 9$ ( c, = cos
E Schneider er 01. /
‘19
DIM porentiul energy surfaces.of ~Bllz) +
DIM calculations were performed using spline fits to the angular functions of LY,__-.o~~.n;:.:cul,. but one could also use analytical fits to. the angles themselves which_wve give in table 2 together with the other fragment information on the DIM caiculations. The extended Morse function [lo] used has the analytical form
X=expi-j3(r-r,)].
V(r)=D,X(X+2p).
I
0
1
2
3
4-S
6
7
8
9
r/o”.
P=A+f?(r-r,)+C(r-rr,.‘,
p=
+l.
(3)
The same form was applied to fit the orthogonalized mixing angles ar,. The PEC fits are not in all cases the best
possible ones with respect to the least mean-square
Fig. 1. hlixing coefticisnts according to eqs. (1) and (2) from AIR1 (O&l) c.tIculations on BH’ with zt basis of 2 and 3 CFS rcspsctivsly. (a) “ff states; (b) ‘Xc sta:es. The dashed curves ore the symmetrically orthogonalized results.
Table 2 Parameters a’ of the fits to the &atomic
interaction
Fragment
Ref.
Type h’
P
H;(lsa,) H; (‘pm,) H,(X’r;) H,(n’X; ) BH +(A’II) BH’(2’TI) BH*(a+l-I) BH+(X ‘\-+) BH ‘(B’S+) BH’(3’1’) BH+(b%+) BH(c’Z’) BH(a%) BH’(‘fI) BH+(‘S+) BH’(‘X+) BH+(‘Z+)
Ital
PUW
-1
1101 DOI WI [Il.131 1111 [1’1 -
pttrc pure pure purtt miXed ptlrt? pure
(12.13,
-
energies and to thr mixing nttgks. DC 2.7931
1 -1 1 -1 1 -1 -1
pure
-1
mixed pure mixed
-1 1 1
pure
-1
a1 Cl QLc’ cc, C’ a, .=’
-1 -1 -1 -1
deviations, because it had to be ensured that the lowest diabatic PEC did not cross the lowest adiabatic PEC under the influence of the mixing. In the light of the errors probably involved in the model (the truncated basis set and the crude diatomic data) we do not consider this a serious deficiency_ -The determination of missing data on diatomic fragments by means of the AIM (OM) method followed the same lines as described in our earlier papers [ 181.
a) D is in eV respectively in rttd, the other parameters ‘) l&r: state. mixed state or mixing angle. Cl Mixing angle. see eqs. (1) and (2).
3.0179 4.75 14 I.9559 3.3X 2.084 0.109 2.183 1.347 0.103 2.715 2.190 2.188 0.6063 - 1.2420 0.5169 0.4533
SW rq.
(3)
r,
A
B
C
2.0032
0.7SjSO
- 1.9686 - 2
1.9994 I .a07 1.4007 2.375 2.275 4.522 2.277 3.662 9.058 2.560 2.611 2.269 3.72s 0.015 2.s73 5.220
0.73394 1.oss47
5.2403 - 3 -4.3713-2
6.4829 - 3 2.4220 - 3 2.5307 - 2
are in atomic units.
0.986SS
O.S299 0.6&U 1.067 1 1.2464 0.6589 0.4312 0.9982 0.7954 1.1935 0.3105 0.0759 0.3947 0.4590
2.0922 - 3
9.768 - 1.767l.SlSS-OS3 1.3654.686 9X01 1.5343.635 4.414-2 5.918-2 6.690-2 6.625 -
3 I
I 2 1 2 2 1 1
2
2.8896 - 2
2.339 4.629 3.250 1.457-2 4X18-2 5.os9 1.001-2 2.710-2 l-1422.092 1.539-2 3.520-3 3_1ss-3
4 2 2
3
1 3
3
1 2 i Of-1 ! -2
-
-3
-
-L
-
-5
-
I
-6
;
b
012345 10 v/&J 9 8
P I
7
6
ab imtio ---__OM
\a
-AIM
1
6
‘,
5
alu
‘I :
EIH’ (‘IT1 16 CF
L 3 BHIc3E*) 17 CF
2 1 0 -1 -2,
1
01~345s
7 rlau
r t
Fr_r. 2. Alhl (0X1) rcAts for BH and BH + bt;ltes compued \\ith nh initio r~su1r.r. (3) BH(\“) states. ab initio points (0. ref. [ISI. and O. ref. [12]). MM points (x). (h) BH+(I’+) ~tatr‘s. ab initio points (0. ref. ill]). (c) BH+(I7) sratcs. ab imrio points (0. ref. [ 11 I).
sists of Is, 2s and 2p atomic orbit& in the form of co&acted gaussian functions. The exponents‘and expansion coefficients for hydrogen [(4slp) primitive gaussians] and boroil [(7s3p) prim&e gaussians] originate from optimizations.by Balint-Kurti and Karplu~ [17] and Whitman hnd Hornback [19], respecti+ely. The AO-representation of the approximate eigenfunctions together with the calculated -and_ eiperime&l energies corresponding to atomic states used in th‘e AIM treatment are given in table 3. Our AIM calculations including the maximum number of diatomic structures are based on 20. 16 and 17 composite function (CF) basis sets describing BH’(S). BH’( H) and BH(Z) states. respectively. The 20 CF basis set involves structures H[(ls), (2s). p] + B*( IS,.). H[(ls). (2s). p] + B’(3P,,). H(k) + B+[(‘P,). (‘I?,>. (‘D,.] and H ‘f B[(‘P,). (“P,). (‘D,)] giving rise to 11 states of’x+ type and 4 states of ‘3’ type. The 16 CF basis set includes structures H[(ls). (2s). p] + B+(‘P,,). H(p)+ B+(‘S,). H(k)+ B+[(‘P,). (“P,). ( ID,)] and H++ B[( ‘P,,). (“P,). (‘D,)] spanning 10 states of :II type and 6 states of ‘II typeFinally the 17 CF basis set is built up from structures H[(ls), (2s). p] + B( ‘P,,). H(p) + B( “Pg). H( Is) + B( ’ Dp), H-( ‘!$) + B *( ‘Sg) to yield 6 states of ‘S ’ type and 6 states of ‘Z+ type. Some of these states relevant to the DIM treatment are plotted in fig. 2 and compared with the results of more accurate calculations.
3. Results of the DIM treatment The calculated PESs are presented in figs. 3-7. The PESs for G_, and C,, symmetries (HBH and BHH configurations) are shown as 2D plots of the lowest two 3A’ and the lowest two ‘A” states. For the coordinate system -chosen (_r- plane) we have the following correlations: In C,,. configurations. the ‘A’ term correlates with stat& of 31Z* and 3KI types, the 3A” term withs311 states; in CZ,.mconfigurations. the 3A’ term correlates with states of 3A, and 3B, types. the ‘A” term with ‘AA,_and 3Bz states_ Crossings of states of -different symmetries in C,, or C,;. geometrkis (dash-dotted lines in figs. 3-6) become avoided for deviations from these geometries and indicate non-adiabatic regions.
b
‘HH
6 5 6
3 2 1
L.
1
2
3
L
5
6
72
3
L
5~6
tJ 7r,
Fig. 3. ‘A” PESs of (BH,)* for C,,(BHH) and Czr_ The energies are in +V. the das h-dotted lines zwe crosGngs of aezs o: different symmslries. (a) I’A”. (h) Z’A”.
Non-adiabatic behnviour of the system can also be expected to occur in the entrance channel for large rDH, where the states 1 -‘A’ and 2 3A’ are quasidegenerate. All energies are given in eV with respect to the separated ground-state atoms B+( ‘S) + 2H( 1s); consequently, -the total energy of the B’(“P) + H,(X ‘Z,‘) entrance channel minimum is obtained as -0.124 eV_ All distances are measured in au. We will briefly discuss the possible processes for total energies up to 2.5 eV_ 3. I. Tile ‘A” smes In fig. 3a the lowest 31T PES is shown; we notice that it is typical of simple adiabatic ion-molecule processes. The minimum allows for complex formation. no saddie point occurs_ The minimum total energy -to form the excited BH*(_4’lI) product molecule is = 1.3 eV; An approach of steeper descent than on 1 ‘IT is possible on the lowest 3B, PES. If the total energy is 2 1.8 eV, the saddle point on the crossing with
3
2
c,,
’ i-
2
3
4
5
.!.
5
6
72
3
L
5
6
c
B-H-HI
6,;
1 ‘A. can bc reached. In this case the reactive pro& proceeds non-adiabatic~tly_ because in the region of the saddle point unstable C,, internicdiates cm the excited 1’*4” PES can be formed (fig. 3b). Since the separated products cannot esist in C,, configurations_ the exit channel ~~~ould be reached in C, or C ~, gcnmrtries. possibly through 311 unet:lblt? c~ruples :it the local D,,,;ninimum (fig. 4. 1‘II). In fig. 7 (table 4) the MEPs are characterized by somt’ stationary points (St’s). in the case of ‘-4” the only SP we found is the C-.. minimum.
for C ~, geometry degenerate \vith the lowest ‘A” PES. The most attractive ground-state geometry corresponds to C,, symmetry. On the 1 jB, PES
(fig. 5a) the MEP goes first through a shallow minimum and then over a very flat saddie point. It is this region, up to which the 1 ‘A’ and 1 -‘i\” PESs are nearly degenerate. From here on the endoegic formation of BH’(A’n) proceeds via the ‘A” PES. while the strongly exoergic processes forming BH+(S
The lowest ‘A’ states (fig. 51. fig. 6) for C,, geometries consist of two regions with ‘II and ‘\‘+ s~mmrtq. respectively. The entrance channel reg10n is for C,, geometq degenerate with the lowest ‘A” state (fig_ 3a. 1 ‘n). while the exit channel describes the ground-state product formation. i.e. BH ‘(X ‘Z+) + H(ls). The total energy of these products is - 2.1s eV_ The entrance channel is attractive. while the excited 1% state entrance channel (fig. 5b). being at infinite rBfI distances degenerate with the ground state. is repulsive_ This upper state leads to the 1 ‘II exit channel which is
‘X+)
can only proceed
on the 1 ‘A’ PES. A
second possibility of forming BH’(A’II) is on the exited 1-‘.4” PES. This state has for large rUH distances a low saddle point and a shallow minimum in C ?,, geometries. while the next SPs on the MEP are a saddle point and a minimum at C,, symmetry_ The latter appears on the crossing seam of the ‘2’
and ‘lI
parts of the lowest 1 3A’ surface.
The most probable processes in collisions of B-(‘P) with H,(X ‘Y’;) on the 3A’ PESs are (i) adiabatic along the 13A’ MEP and (ii) non-adiabatic along the 2 ‘A’ MEP up to the C,,. minimum (fig. 7. table 4) and further in C,,. configurations
Table
4
Stationary points (BH,)*
on potential-energy
SP J’ Symmetry
the minimum-energy surfxes
paths
triplet
‘tw
rtut
Energy
Type
1.40
00
-0.124
rextttnts
2
1.51
3.11
minimum
on 1 ‘W
~3 4
1.60
2.96
- 1.105 - 1.098
minimum
on 1 >A*
5 6 7
I.96 3-77 1.40 1.41
2.94 2.62 6.20 5.19
- 2.360 - 0.086 -0.104
s
1.55
3.51
9
1.95
2.53
2 O.-l05
minimum
oc
3.28 2.3s
-2.153 I.789
ground-state products excited products
C
1
ocl
- 1.018
0.245
s.tddlc point on 1 ‘t\’ minimum 0”~ 1 -‘i\’ saddie point on 2’~~ minimum on 2’~\’ saddle
@int
dcgcnerxy
Fig. 6. ‘A’ PESs of (EH,) + for C,,(HBH). L-V. the d-h-dotted lines .~rr crossings
of
on 2 -‘i\’
on 2 3X and with
1 ‘t\*
The enrr+s :trc in of st;~tes of different
sjmmetnes.
on the 1’A’ PES. obtained. Another
In both cases BH+(X ‘I+) possibility of rearrangement
is is
to pass to the excited BH+(A’II) products from the l-‘A’ PES (via a non-adiabatic transition near the C,, crossing) or the 2’A’ PES if the necessary product energy is available.
either
1
0
-1
The semiquantitative correlation diagram of fig. 7 with the SPs explained in table 4 shows the most pronounced features of the three PESs for processes B+( “P) + H,(X IS;): the degeneracy of the three PESs (1 3A”. 1 ‘A’ and 2’A’) for the isolated reactants, of 1 ‘A’ and 1 ‘A” from (2) the_ near-degeneracy the reactants to the first minimum. and dependmcs of the 3A’ (3) a strong orientation PESs as shown by the MEPs on 1 ‘A’ and 2 -‘A’ at different BHH angles 9. So far the results described in this paper concern only the symmetrically orthogonalized DIhf version. The M EPs at a set of restricted grometriss (with fixed BHH angle) have been recalculated using the non-hermitean DIM version (non-orthogonal mixing). The differences in the resulting paths and energies were negligible (at most 0.05 eV for the ground states. 0.1 eV for 23A’) in the light of the other probable error sources.
(1)
-2
t,:
. -20
:
0
Fig. 7. Energy profiles PESs. The BHH angle denote
SPs (see
.
: 20
:
: 40
!
I !
60
:
:
p--
.R-l
at approximnrr MEPs on fixed-angle 6 is given in degrees. The crosses (f)
table 4). p is a progress
variabls.
4. Conclusions As already derived from preliminary caiculations [l]. it is evident that the observed excited-state products
are probably
formed
predominantly
on
16 May 1953: in final form 2S Srptcmhcr
Collisions
interpretation
19S3
B+(3P) with Hi(X “p’ ) have hrcn studied rcptlatedly uing molecular-hram of the results suffered from missing inform.ttion about the potentini-energy surfxes
of
reports on_ dinromics-in-molcules cnlcultttions for Q wids rttngc of minimum-mergy paths xc determined. Symmetrically orrhogotxdizsd differ only slightly nt the minimum-energy
path. The potmtinl-cnsrgy
surfaces or the 1 ‘A’ and ?‘A’
with the BHH angle. leading possibly to ndinbntic as well as non-adiabatic rlcmcntxy states are nexly degenerate for geometries ranging from the entmnce chxmel to the interxtion surfwxs arc those with_C,,
versions
states show dramatical
proccssrs. The 1 ‘A” and 1 3.4’
r&on.
The most f.tvourabIe
symmetry.
ties [4,6]. In the present paper, we recalculate
1. Introduction
ergy path WEp)
and fragment
information
To describe the DIM calculation, following three basis structures:
-~BH+(X.~Zf,A’n,B’Z+)+H
(1)
B+(‘S)
+ 2ti(ls),
(2)~ B*(3P)
+ 2H(ls),
: (3)
,
B(‘P)+H@s)+Ij+,~
em
1v-edefine the
__
from which the possible:symmetry-adapted 3A’ and 3Ay basis functions (SBFs) were constructed. These SBFs are characterized in table 1: _ The energy Jevels of the atomic species~ were
0301-0104/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland PhysicsPublishing Division) 1
~.
[Sl-
2. DIM calculation
+ H2(X’Zp’)
and its isotopic anhlogue with D, to occur prevailingly through a long-lived complex. The reader is referred to the literature for more detailed information on cross- sections [3], scattering -diagrams [4-61,. translational energy and angular distribu_tions of the products [5]. product internal -state distributions [7] as -well was translational exoergici_
the
PESs using more reliable input data, and determine the stationary points on the minimum-en-
In an earlier paper [l], we presented an approximation to the_lowest (BH,)’ potential-energy surfaces (PESs) within the diatomics-in-molecules (DIM) framework [2] in order to interprete recent molecular-beam data [3]. These measurements give evidence for the reaction B’(3P)
The rhrorericxl for this system. This paper kttiokq points one the
nuclenr geomelries. The and non-hcrmitcan diatomics-in-molecules
chnngs
configur.ttions of approach on thssr potcnkcnttrgy
tcch~niqurs.
-.
~.
-~
‘IS
E Schneider cl af. /
DIM
porenriaf enersr sur-aces
taken from ref. [9]_ The diatomic H,‘and H, inter:1L’t1Wl energies \vrre represented by extended Rfc>rsc curve fits [lo]. The same analytical form ha\ bscn uwi to drscribr the BH and BH‘ inter:tctwns. The BH -(S ‘1: -_ B ‘\“. A’n) potential~ncrgy curves (PECe) are fits to the results of XtRD Cl calculations [I I]. while the BH(a-‘IT) PE<‘ is a fit to GL’B results [12]. Whcrs availabis. the q-wnmcnt:~I valurs of r_ [13] have been used In the fits. The aho\-cmcntionrd diatornic states xs \LJI IS two other BH’ states (aJII. bJ\‘+) have hwn a~~umsd tO he “pure” states. u bile three further cxcitcd states BH *(7 ‘II. 3 ‘X-) and BH(c ‘I- ) have been trcittcd iiS -‘rnised exited >tatr’>” 1141. This concept nwans. that \vc did not ube the bcbt :~v:tilablr PEC inform:ttion [ 1 l-161 but rather interpolated curves brtk\vren several different excited states. The interpolated “miscd” CLI rv’c’s arc more appropriate for our restricted DI Xl bak The simplest straightforward clay to obtain such asmixed” PECs as \\~ll as mising coefficients of Jistomic states of the same symnh2try. c-e_ 131-I-( ‘I-: ) or BH ‘( -wv’). is to perform a VB typr calculation for the diatomic with a basis set reztrictsd CO the character of the Dlhl basis structurt’s (bv wmoving the third atom). For thrsc and ictrth sqL,IIr~L't st.ktrs 0f BH + we uad the AI,\1
off BH,)_
the. (OM). method [17.18] and obtained BH’(Z’IX a’II. 3’S’, b”Z’) and BH(c”S+) PECs and the mixing coefficients of BH’(‘LI) and BH’( ‘I’). The diatomic configuration mixing for the ‘II case has been formulated according to
(;r)=(::-:i)(;$
(1)
where 9, and +2 are the basis functions dissociating into B+(“P) + H(ls) and B(‘P) + H+. rcspectivcly. For the ‘Xc case. we put
A, is the B -( ‘S) + H( 1s) basis function. and the 9-1~. 9$ ( c, = cos
E Schneider er 01. /
‘19
DIM porentiul energy surfaces.of ~Bllz) +
DIM calculations were performed using spline fits to the angular functions of LY,__-.o~~.n;:.:cul,. but one could also use analytical fits to. the angles themselves which_wve give in table 2 together with the other fragment information on the DIM caiculations. The extended Morse function [lo] used has the analytical form
X=expi-j3(r-r,)].
V(r)=D,X(X+2p).
I
0
1
2
3
4-S
6
7
8
9
r/o”.
P=A+f?(r-r,)+C(r-rr,.‘,
p=
+l.
(3)
The same form was applied to fit the orthogonalized mixing angles ar,. The PEC fits are not in all cases the best
possible ones with respect to the least mean-square
Fig. 1. hlixing coefticisnts according to eqs. (1) and (2) from AIR1 (O&l) c.tIculations on BH’ with zt basis of 2 and 3 CFS rcspsctivsly. (a) “ff states; (b) ‘Xc sta:es. The dashed curves ore the symmetrically orthogonalized results.
Table 2 Parameters a’ of the fits to the &atomic
interaction
Fragment
Ref.
Type h’
P
H;(lsa,) H; (‘pm,) H,(X’r;) H,(n’X; ) BH +(A’II) BH’(2’TI) BH*(a+l-I) BH+(X ‘\-+) BH ‘(B’S+) BH’(3’1’) BH+(b%+) BH(c’Z’) BH(a%) BH’(‘fI) BH+(‘S+) BH’(‘X+) BH+(‘Z+)
Ital
PUW
-1
1101 DOI WI [Il.131 1111 [1’1 -
pttrc pure pure purtt miXed ptlrt? pure
(12.13,
-
energies and to thr mixing nttgks. DC 2.7931
1 -1 1 -1 1 -1 -1
pure
-1
mixed pure mixed
-1 1 1
pure
-1
a1 Cl QLc’ cc, C’ a, .=’
-1 -1 -1 -1
deviations, because it had to be ensured that the lowest diabatic PEC did not cross the lowest adiabatic PEC under the influence of the mixing. In the light of the errors probably involved in the model (the truncated basis set and the crude diatomic data) we do not consider this a serious deficiency_ -The determination of missing data on diatomic fragments by means of the AIM (OM) method followed the same lines as described in our earlier papers [ 181.
a) D is in eV respectively in rttd, the other parameters ‘) l&r: state. mixed state or mixing angle. Cl Mixing angle. see eqs. (1) and (2).
3.0179 4.75 14 I.9559 3.3X 2.084 0.109 2.183 1.347 0.103 2.715 2.190 2.188 0.6063 - 1.2420 0.5169 0.4533
SW rq.
(3)
r,
A
B
C
2.0032
0.7SjSO
- 1.9686 - 2
1.9994 I .a07 1.4007 2.375 2.275 4.522 2.277 3.662 9.058 2.560 2.611 2.269 3.72s 0.015 2.s73 5.220
0.73394 1.oss47
5.2403 - 3 -4.3713-2
6.4829 - 3 2.4220 - 3 2.5307 - 2
are in atomic units.
0.986SS
O.S299 0.6&U 1.067 1 1.2464 0.6589 0.4312 0.9982 0.7954 1.1935 0.3105 0.0759 0.3947 0.4590
2.0922 - 3
9.768 - 1.767l.SlSS-OS3 1.3654.686 9X01 1.5343.635 4.414-2 5.918-2 6.690-2 6.625 -
3 I
I 2 1 2 2 1 1
2
2.8896 - 2
2.339 4.629 3.250 1.457-2 4X18-2 5.os9 1.001-2 2.710-2 l-1422.092 1.539-2 3.520-3 3_1ss-3
4 2 2
3
1 3
3
1 2 i Of-1 ! -2
-
-3
-
-L
-
-5
-
I
-6
;
b
012345 10 v/&J 9 8
P I
7
6
ab imtio ---__OM
\a
-AIM
1
6
‘,
5
alu
‘I :
EIH’ (‘IT1 16 CF
L 3 BHIc3E*) 17 CF
2 1 0 -1 -2,
1
01~345s
7 rlau
r t
Fr_r. 2. Alhl (0X1) rcAts for BH and BH + bt;ltes compued \\ith nh initio r~su1r.r. (3) BH(\“) states. ab initio points (0. ref. [ISI. and O. ref. [12]). MM points (x). (h) BH+(I’+) ~tatr‘s. ab initio points (0. ref. ill]). (c) BH+(I7) sratcs. ab imrio points (0. ref. [ 11 I).
sists of Is, 2s and 2p atomic orbit& in the form of co&acted gaussian functions. The exponents‘and expansion coefficients for hydrogen [(4slp) primitive gaussians] and boroil [(7s3p) prim&e gaussians] originate from optimizations.by Balint-Kurti and Karplu~ [17] and Whitman hnd Hornback [19], respecti+ely. The AO-representation of the approximate eigenfunctions together with the calculated -and_ eiperime&l energies corresponding to atomic states used in th‘e AIM treatment are given in table 3. Our AIM calculations including the maximum number of diatomic structures are based on 20. 16 and 17 composite function (CF) basis sets describing BH’(S). BH’( H) and BH(Z) states. respectively. The 20 CF basis set involves structures H[(ls), (2s). p] + B*( IS,.). H[(ls). (2s). p] + B’(3P,,). H(k) + B+[(‘P,). (‘I?,>. (‘D,.] and H ‘f B[(‘P,). (“P,). (‘D,)] giving rise to 11 states of’x+ type and 4 states of ‘3’ type. The 16 CF basis set includes structures H[(ls). (2s). p] + B+(‘P,,). H(p)+ B+(‘S,). H(k)+ B+[(‘P,). (“P,). ( ID,)] and H++ B[( ‘P,,). (“P,). (‘D,)] spanning 10 states of :II type and 6 states of ‘II typeFinally the 17 CF basis set is built up from structures H[(ls), (2s). p] + B( ‘P,,). H(p) + B( “Pg). H( Is) + B( ’ Dp), H-( ‘!$) + B *( ‘Sg) to yield 6 states of ‘S ’ type and 6 states of ‘Z+ type. Some of these states relevant to the DIM treatment are plotted in fig. 2 and compared with the results of more accurate calculations.
3. Results of the DIM treatment The calculated PESs are presented in figs. 3-7. The PESs for G_, and C,, symmetries (HBH and BHH configurations) are shown as 2D plots of the lowest two 3A’ and the lowest two ‘A” states. For the coordinate system -chosen (_r- plane) we have the following correlations: In C,,. configurations. the ‘A’ term correlates with stat& of 31Z* and 3KI types, the 3A” term withs311 states; in CZ,.mconfigurations. the 3A’ term correlates with states of 3A, and 3B, types. the ‘A” term with ‘AA,_and 3Bz states_ Crossings of states of -different symmetries in C,, or C,;. geometrkis (dash-dotted lines in figs. 3-6) become avoided for deviations from these geometries and indicate non-adiabatic regions.
b
‘HH
6 5 6
3 2 1
L.
1
2
3
L
5
6
72
3
L
5~6
tJ 7r,
Fig. 3. ‘A” PESs of (BH,)* for C,,(BHH) and Czr_ The energies are in +V. the das h-dotted lines zwe crosGngs of aezs o: different symmslries. (a) I’A”. (h) Z’A”.
Non-adiabatic behnviour of the system can also be expected to occur in the entrance channel for large rDH, where the states 1 -‘A’ and 2 3A’ are quasidegenerate. All energies are given in eV with respect to the separated ground-state atoms B+( ‘S) + 2H( 1s); consequently, -the total energy of the B’(“P) + H,(X ‘Z,‘) entrance channel minimum is obtained as -0.124 eV_ All distances are measured in au. We will briefly discuss the possible processes for total energies up to 2.5 eV_ 3. I. Tile ‘A” smes In fig. 3a the lowest 31T PES is shown; we notice that it is typical of simple adiabatic ion-molecule processes. The minimum allows for complex formation. no saddie point occurs_ The minimum total energy -to form the excited BH*(_4’lI) product molecule is = 1.3 eV; An approach of steeper descent than on 1 ‘IT is possible on the lowest 3B, PES. If the total energy is 2 1.8 eV, the saddle point on the crossing with
3
2
c,,
’ i-
2
3
4
5
.!.
5
6
72
3
L
5
6
c
B-H-HI
6,;
1 ‘A. can bc reached. In this case the reactive pro& proceeds non-adiabatic~tly_ because in the region of the saddle point unstable C,, internicdiates cm the excited 1’*4” PES can be formed (fig. 3b). Since the separated products cannot esist in C,, configurations_ the exit channel ~~~ould be reached in C, or C ~, gcnmrtries. possibly through 311 unet:lblt? c~ruples :it the local D,,,;ninimum (fig. 4. 1‘II). In fig. 7 (table 4) the MEPs are characterized by somt’ stationary points (St’s). in the case of ‘-4” the only SP we found is the C-.. minimum.
for C ~, geometry degenerate \vith the lowest ‘A” PES. The most attractive ground-state geometry corresponds to C,, symmetry. On the 1 jB, PES
(fig. 5a) the MEP goes first through a shallow minimum and then over a very flat saddie point. It is this region, up to which the 1 ‘A’ and 1 -‘i\” PESs are nearly degenerate. From here on the endoegic formation of BH’(A’n) proceeds via the ‘A” PES. while the strongly exoergic processes forming BH+(S
The lowest ‘A’ states (fig. 51. fig. 6) for C,, geometries consist of two regions with ‘II and ‘\‘+ s~mmrtq. respectively. The entrance channel reg10n is for C,, geometq degenerate with the lowest ‘A” state (fig_ 3a. 1 ‘n). while the exit channel describes the ground-state product formation. i.e. BH ‘(X ‘Z+) + H(ls). The total energy of these products is - 2.1s eV_ The entrance channel is attractive. while the excited 1% state entrance channel (fig. 5b). being at infinite rBfI distances degenerate with the ground state. is repulsive_ This upper state leads to the 1 ‘II exit channel which is
‘X+)
can only proceed
on the 1 ‘A’ PES. A
second possibility of forming BH’(A’II) is on the exited 1-‘.4” PES. This state has for large rUH distances a low saddle point and a shallow minimum in C ?,, geometries. while the next SPs on the MEP are a saddle point and a minimum at C,, symmetry_ The latter appears on the crossing seam of the ‘2’
and ‘lI
parts of the lowest 1 3A’ surface.
The most probable processes in collisions of B-(‘P) with H,(X ‘Y’;) on the 3A’ PESs are (i) adiabatic along the 13A’ MEP and (ii) non-adiabatic along the 2 ‘A’ MEP up to the C,,. minimum (fig. 7. table 4) and further in C,,. configurations
Table
4
Stationary points (BH,)*
on potential-energy
SP J’ Symmetry
the minimum-energy surfxes
paths
triplet
‘tw
rtut
Energy
Type
1.40
00
-0.124
rextttnts
2
1.51
3.11
minimum
on 1 ‘W
~3 4
1.60
2.96
- 1.105 - 1.098
minimum
on 1 >A*
5 6 7
I.96 3-77 1.40 1.41
2.94 2.62 6.20 5.19
- 2.360 - 0.086 -0.104
s
1.55
3.51
9
1.95
2.53
2 O.-l05
minimum
oc
3.28 2.3s
-2.153 I.789
ground-state products excited products
C
1
ocl
- 1.018
0.245
s.tddlc point on 1 ‘t\’ minimum 0”~ 1 -‘i\’ saddie point on 2’~~ minimum on 2’~\’ saddle
@int
dcgcnerxy
Fig. 6. ‘A’ PESs of (EH,) + for C,,(HBH). L-V. the d-h-dotted lines .~rr crossings
of
on 2 -‘i\’
on 2 3X and with
1 ‘t\*
The enrr+s :trc in of st;~tes of different
sjmmetnes.
on the 1’A’ PES. obtained. Another
In both cases BH+(X ‘I+) possibility of rearrangement
is is
to pass to the excited BH+(A’II) products from the l-‘A’ PES (via a non-adiabatic transition near the C,, crossing) or the 2’A’ PES if the necessary product energy is available.
either
1
0
-1
The semiquantitative correlation diagram of fig. 7 with the SPs explained in table 4 shows the most pronounced features of the three PESs for processes B+( “P) + H,(X IS;): the degeneracy of the three PESs (1 3A”. 1 ‘A’ and 2’A’) for the isolated reactants, of 1 ‘A’ and 1 ‘A” from (2) the_ near-degeneracy the reactants to the first minimum. and dependmcs of the 3A’ (3) a strong orientation PESs as shown by the MEPs on 1 ‘A’ and 2 -‘A’ at different BHH angles 9. So far the results described in this paper concern only the symmetrically orthogonalized DIhf version. The M EPs at a set of restricted grometriss (with fixed BHH angle) have been recalculated using the non-hermitean DIM version (non-orthogonal mixing). The differences in the resulting paths and energies were negligible (at most 0.05 eV for the ground states. 0.1 eV for 23A’) in the light of the other probable error sources.
(1)
-2
t,:
. -20
:
0
Fig. 7. Energy profiles PESs. The BHH angle denote
SPs (see
.
: 20
:
: 40
!
I !
60
:
:
p--
.R-l
at approximnrr MEPs on fixed-angle 6 is given in degrees. The crosses (f)
table 4). p is a progress
variabls.
4. Conclusions As already derived from preliminary caiculations [l]. it is evident that the observed excited-state products
are probably
formed
predominantly
on