The 2S(+) - 2P separation in KO is investigated using large basis sets and high levels of correlation treatment. Relativistic effects are included at the Dirac-Fock level and reduce the separation only slightly. The basis set superposition error is considered in detail. On the basis of these calculations, our best estimate places the 2p sub 3/2 state about 200 cm(exp -1) above the ground 2 sigma(+) state in agreement with our previous estimate

Bauschlicher, Charles W., Jr.

Dyall, Kenneth G.

Partridge, Harry

English

NASA Technical Reports Server

r •
The 2E+ - 2K separation in KO
Charles W. Bauschlicher Jr. and Harry Partridge
NASA Ames Research Center
Moffett Field, CA 94035
Kenneth G. Dyall
ELORET Instituter
Palo Alto, CA 94303
Abstract
The "-E + - 'K separation in KO is investigated using large basis sets and high
levels of correlation treatment. Relativistic effects are included at the Dirac-Fock
level and reduce the separation only slightly. The basis set superposition error is
considered in detail. On the basis of these calculations, our best estimate places
the 'Ha/.. state about 200 cm -_ above the ground 2E: state in agreement with our
previous estimate.
I. Introduction
In 1986 we computed the .._+ - 212 separation in KO to be 238 cm -1 wqth
the ..E + state being the lower of the two [1]. This separation was computed at
the singles and doubles configuration interaction (SDCI) levet using a large Slater
basis set. While not definitive, the separation was thought to be accurate because
of the small difference between the SDCI and self-consistent-field (SCF) values.
However, when 15 electrons are correlated, an SDCI treatment can underestimate
the differential correlation effects. Approaches such as the modified coupled-pair
functional (MCPF) method [2], or the coupled cluster singles and doubles method
with a perturbational estimate of the triple excitations [3] [CCSD(T)], account for
the effect of higher than double excitations and can therefore yield superior results
to the SDCI approach.
Experimentally, the ground state has not been determined and there is conflict-
ing evidence. The failure to observe an electron spin resonance (ESR) spectrum [4]
is consistent with a 2II ground state, while the magnetic deflection experiments [8]
suggest a 2X+ ground state. Photoelectron detachment experiments [61 on KO-
t Mailing address: NASA Ames Research Center. Moffett Field, CA 94035-1000
('4,_A-_I-I,,;?,o!',:_} li4b _";(+) - 2; _
b_/72 CI ?11.3¢_
https://ntrs.nasa.gov/search.jsp?R=19930003712 2020-03-17T10:33:39+00:00Z
might offer a mechanism to directly observe both states, and hence determine the
ground state and the separation; such experiments [6] have recently been performed
for NaO- and preliminary results suggest that they are possible for all of the alkali
oxides systems. In addition, microwave experiments I7] have recently been per-
formed on NaO and, with a pure-precession hypothesis, an estimate of the 2 X + - 2 K
separation was obtained. An analogous experiment should be possible for KO.
Given the recent experimental activity on the alkMi oxides, it seems timely to
reinvestigate the _E + - -_II separation in KO at higher levels of theory. We consider
the effect of one-particle basis set and basis set superposition error (BSSE) in more
detail than in our previous work. In addition, the separation between the _+ and
2II states is small enough that relativistic effects could affect the ordering of the
states. These were not included in the previous work and are addressed here.
II. Methods
Two basis sets are used in this work. The small oxygen basis set is the
(13s 9p 6d 4f)/[5s 5t) (2 + 1)d lf] atomic natural orbital [8] (ANO) set {9] de-
termined from the average natural orbitals of O and O-. (The notation n + m in-
dicates n ANO orbitals are employed and rr_ primitive functions are uncontracted).
In the large oxygen basis set only two s and one p ANOs are used. The outer
five s and five p primitives and the d and f polarization functions are uncon-
tracted. This is augmented with two uncontracted 9 functions and a diffuse s
function with an orbital exponent of 0.076666. Thus the final basis set is of the
form (14s 9p 6d 4f 2g)/[(2 + 6)s (1 + 5)p 6d 4f 29].
The small K basis is derived from the (24s 15p) basis [10] augmented with an
s function optimized for K- and three p functions optimized for the 2p state of K.
The s and p basis sets are contracted to (3+6) and (2+7), respectively, where the
three s and two p contraction coefficients are taken from the SCF wave function.
The basis is further augmented with six even-tempered (a,_=2.5'_a0 for r_=0,k) d
functions with a0=0.0455 and four even-tempered f functions with a0=0.12949.
The small K basis set is of the form (25s 18p 6d 4f)/[(3 + 6)s (2 + 7)p 6d 4/]. In
the large K basis set, the s and p functions are contracted (2+12) and (2+9) and
two 9 functions (a=0.768 and 0.307) are added, thus yielding a basis set of the form
(25s 18p 6d 4f 29)/[(2 + 12)s (2 + 9)p 6d 4f 29]. Only the pure spherical harmonic
components of the basis functions are used.
2
The orbitals are optimized using the SCF approach. We have treated the 2i-i
_1.5 _t .5
state using symmetry and equivalence restrictions (i.e., a ,,_ ,,_ occupation ) or
by using a symmetry broken solution (i.e., a Tr_¢_ occupation). Electron correlation
is added using the MCPF or CCSD(T) approaches. Fifteen electrons are correlated,
corresponding to the O 2s and 2p and the K 3s, 3p, and 4s electrons.
Relativistic effects are estimated as the difference between the SCF and Dirac-
Fock (DF) results. Because correlation was not included, it was possible to reduce
the basis set size without affecting the accuracy of the results. The full s and 1o
primitive basis sets for K and O were contracted to [(3 4- 6)s (2 4- 7)p] and [(2 4-
3)s (1 ÷ 4)p] using the orbitals from the SCF wave functions for K + and O-. For
polarization the 6d set and the outer three of the 4f functions on K were used, and
on O the outer 3 primitive d functions and the f function with the largest coefficient
from the ANO polarization set were used. The SCF zE+ - zII separation in this
basis set was identical to that found using the small ANO set.
The SCF/MCPF calculations were performed using the SEWARD Ill]-
SWEDEN [12] program system. The CCSD(T) calculations were performed using
the program developed by Scuseria [13]. The atomic DF calculations were performed
using GRASP [14] while the molecular calculations were performed using the code
developed by Dyall [15]. All calculation were performed on the NASA Ames Central
Computer Facility CRAY Y-MP or Computational Chemistry Branch IBM RISC
System/6000 computers.
III. Results and Discussion
The separation at the SCF level is only slightly larger than in our previous
work [1], with the big basis set result essentially reaching our previous estimate of
250 cm -1 for the numerical Hartree-Foek separation. The SDCI separation in the
small basis set is only 6 cm -1 smaller than that reported in our previous study.
With a symmetry broken SCF solution, the _ll state is predicted to be below the
°'E+ state. When correlation is added at the SDCI level, the 2E+ state is predicted
to be lower. However, the SDCI based on the symmetry broken SCF orbitals yields
a significantly smaller separation. This suggests that the SDCI approach is unable
to overcome the bias in the SCF wave function. At the MCPF level, the effect of
symmetry breaking is smaller, as expected, since the MCPF approach includes the
effect of higher excitations. At this level, the symmetry broken solution actually
3
leads to a larger separation than using the SCF with symmetry and equivalence
restrictions. Both MCPF separations are about 100 cm -1 smMler than the SDCI
result with symmetry and equivalence restrictions. The CCSD separation is the
same as the MCPF. The effect of triples is to further increase the separation by
47 cm -1, which is almost an order of magnitude smaller than the difference be-
tween the SCF and CCSD (368 cm-1). This strongly suggests that even higher
levels of theory will not significantly increase the correlation contribution to the
separation. Expanding the basis set results in a small increase in both SCF and
MCPF separations.
In Table II we report the BSSE at the MCPF level. We compute the BSSE for
K + with the O basis set, K+(O), and O- with the K basis set, because both states
of the molecule at re are best described as K + O-. K + is a closed shell; therefore the
calculation of the BSSE is straightforward, and we consider K+(O) at the two rele-
vant internuclear separations. The 2p s occupation of O- is oriented 2p_r22p_ a and
2po_2p_ 4 for the 2II and 2E+ states, respectively. As shown in previous work [16},
the BSSE can differ significantly for the two occupations. Therefore we use the
BSSE for the 2po'22pw 3 occupation to correct the 2II state and the BSSE for the
2po'12pTr 4 occupation to correct the =E + state.
For K + the BSSE is small for both basis sets. It is slightly larger for the _'_+
state than the -_II state because of the shorter bond length. In contrast, the O-
BSSE is much larger for the smaller basis set. In spite of the longer bond length,
the O-(K) BSSE is larger for the =1-[ state, because a pair of oxygen 2po" electrons
points at the ghost basis set compared with only one electron in the =_+ state.
For both basis sets the total BSSE is very similar for the 'E + and _-II states and
therefore does not have an important differential effect on the separation. Given
the small total BSSE for the big basis set, this conclusion seems definitive in spite
of any uncertainties in how to best compute the BSSE.
One effect not considered to this point is relativity. The spin-orbit splitting in
the O- ion was calculated to be 193 cm -1 at the Dirac-Coulomb level. Inclusion
of the Breit interaction decreased the splitting to 170 cm -1. This value is expected
to be accurate as an analogous treatment of O agrees with experiment to within
2 cm -1. Because the bonding in KO is best described as K+O -, this splitting in O-
can be used in a simple first-order model [17] to estimate the splitting in KO. On
this basis the = +
, 211/, state is unshifted from its nonrelativistic position, the _II1/=
4
state is shifted up by 57 cm -1 and the 2II3/2 state is shifted down by 57 cm -1.
Mixing of K 4s character Dora covalent contributions to the wave functions
and spin-orbit mixing of the 2Iix/2 and 2_1+/2 states could invalidate the first-order
model. Therefore we study the 2IIa/2 and 2_-/2 states at the Dirac-Fock level.
On the basis of the nonrelativistic calculations we use a bond length of 4.4 a0 for
2 + 3/. statethe 2II3/2 state and 4.13 a0 for the Xl/2 state. At this level, the 2II
is lowered by 36 cm -1 and the 2_,+ state is lowered by 24 cm -1, relative to the
"-'1/2
nonrelativistic states. Thus the differential effect of relativity on the state separation
is only 12 cm -1, or about 1/5 of the estimate derived from O-. Clearly, however,
the differential effect of relativity is sufficiently small that it will not reverse the
order of the states computed at the nonrelativistic level.
Our best separation is obtained by correcting the CCSD(T) separation for: 1)
MCPF basis set improvement (+36 cm-1), 2) BSSE (+8 cm -1) and 3) relativistic
effects (-12 cm-1). This yields a separation of 214 cm -1, with the 228+ state
being tower. This is very similar to our previous result [1]. While it is difficult
to be definitive for a separation this small, the calculations strongly suggest that
the ground state is 2p+. Because improving the basis set increases the separation,
as does including higher levels of correlation treatment, and relativistic effects are
very small, it is difl3.cult to imagine what effect wou_ld reverse the order of these two
states.
IV. Conclusions
The separation at our highest level of theory, the CCSD(T) approach, is
182 cm -1. Including the correction for basis set incompleteness from the MCPF
level increases the separation to 218 cm -1, which is very similar to our previous
result [1]. The differential effect of BSSE is 8 cm -1, increasing the separation. Rel-
ativistic effects reduce the separation by only 12 cm -1. Thus we conclude that the
ground state is 2_+.
5
References
1. S. R. Langhoff, C. W. Bauschlicher, and H. Partridge, J. Chem. Phys. 84
(1986)4474. S. 1=(.Langhoff, C. W. Bauschlicher, and H. Partridge, in "Com-
parison of Ab Initio Quantum Chemistry with Experiment" 1=(.J. Bartlett,
ed., D. Reidel Publishing Co. Boston (1985).
2. D. P. Chong and S. 1=(.Langhoff, J. Chem. Phys. 84 (1986) 5606. See also
!=(. Ahlrichs, P. Scharf, and C. Ehrhardt, J. Chem. Phys. 82 (1985) 890.
3. 1=(. J. Bartlett, Annu. Rev. Phys. Chem. 32 (1981) 359; K. Raghavachari,
G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem. Phys. Lett. 157
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4. D. M. Lindsay, D. 1=(. Herschbach, and A. L. Kw]ram, J. Chem. Phys. 60
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8. J. AlmlSf and P. 1=(. Taylor, J. Chem. Phys. 86 (1987) 4070.
9. C. W. Bauschlicher, H. Partridge, and S. 1=(. Langhoff, Chem. Phys. 148
(1990) 57.
H. Partridge, J. Chem. Phys. 90 (1989) 1043.
1=(. Lindh, U. Ryu, and B. Liu, J. Chem. Phys. 95 (1991) 5889.
SWEDEN is an electronic structure program written by J. Alml6f, C. W.
Bausch]_icher, M. 1=(. A. Blomberg, D. P. Chong, A. Heiberg, S. 1=(. Langhoff,
P.-i. Malmqvist, A. P. Rendell, B. O. Ross, P. E. M. Siegbahn, and P. 1=(.
Taylor.
G. E. Scuseria, Chem. Phys. Lett. 176 (1991) 27.
K. G. Dyall, I.P. Grant, C. T. Johnson, F. A. Parpia, and E. P. Plummer,
Computer Phys. Cornmun. 55 (1989) 425.
Open-shell DF code: K. G. Dyall, to be published, follows same methods as
Closed-shellcode, K. G. Dyall, K. F_egri,Jr.,P. 1=(.Taylor, and If.Partridge,
J. Chem. Phys. 95 (1991) 2583.
16. If.Partridge, C. W. Bauschlicher, and S. R. Langhoff, Theor. Chim. Acta.
77 (1990) 323.
17. Lefebvre-Brion, H.; Field, 1=(.W., Perturbation_ in the Spectra of Diatomic
10.
11.
12.
15.
6
Molecules (Academic Press, Inc.; Orlando; 1986.)
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Table If. Summary of the BSSE at the MCPF level.
Small basis set
2E+
K+(O) at r=4.13
O-(K) at r=4.13
Total
K+(O) at r=4.40
O-(K) at r=4.40
Total
Big basis set
K+(O) at r=4.13
O-(K) at r=4.13
Total
K+(O) at r=4.40
O-(K) at r=4.40
Total
BSSE(cm -1)
32.1
348.4
380.5
20.9
364.5
385.4
32.5
88.5
121.0
25.8
103.4
129.2
9


The 2S(+) - 2P separation in KO

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