High quality ab initio electonic structure calculations were performed on the 2D Rydberg series in Al I. The configuration 3s3p2(2D) is shown to contribute substantially to the lowest four 2D Rydberg states. The same configuration also contributes substantially to a 2D state embedded in the ionization continuum. Computed oscillator strengths for the first six members of the 2D Rydberg transitions are given: these should be of substantially high accuracy than currently available values

Bauschlicher, Charles W., Jr.

Langhoff, Stephen R.

Taylor, Peter R.

English

NASA Technical Reports Server

//C.C, 2-
The 2±> Rydberg series in Al I /^
/cr-/<!>
Peter R. Taylor 'Q
ELORET Institutef \ (
Sunnyvale, CA 94087
and
Charles W. Bauschlicher Jr. and Stephen R. Langhoff
NASA Ames Research Center
Moffett Field, CA 94035
Abstract
High-quality ab initio electronic structure calculations have been performed
on the 2D Rydberg series in Al I. The configuration 3s3p2(2.D) is shown to con-
tribute substantially to the lowest four 2D Rydberg states. The same configuration
also contributes substantially to a 2Z> state embedded in the ionization continuum.
Computed oscillator strengths for the first six members of the 2Z> Rydberg tran-
sitions are given: these should be of substantially higher accuracy than currently
available values.
' I USA-IB-101189) THE 2D BYBEIBG SERIES IB
Al I (KASfl) 8 F cscl "
Unclas
G3/72 0158954
f Mailing address: NASA Ames Research Center, Moffett Field, CA 94035
1
https://ntrs.nasa.gov/search.jsp?R=19880019356 2020-03-20T05:37:57+00:00Z
Some controversy exists concerning the assignment of the 3s2nd(2D) Rydberg
series in Al I. It was pointed out some time ago (see, for example, Moore (1949) and
refs. therein) that one of the lowest terms in the 2D sequence might correspond to
the configuration 3s3p2, and that the assigned term numbering might therefore have
to be revised. Based on an analysis of the intensity of the lowest 2P — 2D transition,
Budick (1966) concluded that the lowest 2D state should indeed be identified with
the configuration 3s3p2. However, experimental results reported by Carton (1962)
(see also Eriksson and Isberg (1963)) support the assignment of all observed terms
in the series as 3-s2nd. This latter identification is the generally accepted one,
as it is also consistent with theoretical studies by Weiss (1973). Although those
theoretical studies clearly demonstrate considerable configuration mixing between
the 3s3p2 and 3s23d terms, there have been no investigations considering possible
mixing between 3.s3p2 and higher nd terms. It is therefore still unclear whether
the 3s3p2 configuration is simply distributed among the various terms of the 2Z?
Rydberg series or whether there is some other state that is substantially derived
from 3s3p2. Experimental observations by Carton (1962) suggest that a state lying
beyond the ionization limit of the 2D series is derived principally from the 3s3p2
configuration.
In the present work, we report the results of very accurate ab initio calculations
on the 2D series in Al I. The configuration 3s3p2(2jD) is found to contribute sub-
stantially (more than 5%) to the lowest four members of the series; the remainder
of the configuration lies some 1000 cm"1 beyond the ionization limit. In addition,
we have computed oscillator strengths for a number of terms in the series. The
results are expected to be much more accurate than the rather discordant values
presently available in compilations. The oscillator strengths for the lowest states
show substantial perturbation by the 3s3p2 configuration, but the configuration
mixing causes little deviation from the Rydberg formula for the excitation energies.
The results reported here are obtained with full CI calculations in which only
the three Al valence electrons are correlated. The Is, 2s and 2p core orbitals are
held fully occupied in the form obtained from an atomic SCF calculation on Al
3s23p(2P), and the full CI configuration space results from allocating the three
valence electrons in all possible ways (consistent with the desired spin and spatial
symmetry) among the remaining orbitals. The orbitals are expanded in a basis set of
contracted Gaussian functions: this basis is derived from a (20s 13p) primitive set,
obtained using the even-tempered parameters of Schmidt and Ruedenberg (1979),
augmented initially with a (6d 4/) polarization set and then with additional diffuse d
sets, as discussed below. The initial Qd set is an even-tempered sequence of the form
a(3k, 0 < k < 5 with a = 0.03 and (3 = 2.5. The 4/ set is an even-tempered sequence
with a = 0.10 and (3 = 2.5. This (20-s 13p Qd 4/) primitive set is contracted using
atomic natural orbitals (ANOs) (Almlof and Taylor 1987) from a single reference
single and double excitation CI calculation on the Al ground state. The contracted
functions comprise the first five s, four p, two d and two / ANOs, plus the outermost
two s, two p, two. d and / primitives, which are left uncontracted to improve the
flexibility of the description of the outer regions of the charge density. The resulting
basis can be denoted [75 6p 4d 3/]. Various sets of additional diffuse d functions
are added to the basis to describe the d Rydberg states: these sets comprise an
even-tempered sequence added to the above d set, with /? = 2.5. These added sets
are denoted -f (3d), +(5d) and -j-(7d).
The full CI calculations are performed in an orbital basis denned by SCF
calculations on the Al and Al+ ground states. Full atomic symmetry and equivalence
restrictions are imposed. SCF orbitals for Al 3s23p(2P) are used for the s, p and
/ symmetries, while the orbitals for the d symmetry are obtained from an SCF
calculation on Al+ 3s2(l5). The full CI energies and total wave functions are, of
course, invariant to any unitary transformation on the orbitals included in the full
CI wave function: the advantage of using d orbitals from the positive ion is that
each ^ D Rydberg state is dominated by a single d orbital in the configuration 3s2nd.
This makes it easier to analyze the wave functions of the various terms.
The 2Z? excitation energies, relative to ground-state Al, are given in Table 1
for various diffuse d sets. Also included are the computed ionization limit, the
3.s3p2(2P) excited state excitation energies, the corresponding experimental results
(Moore 1949) and the fraction of each 2D Rydberg state derived from the term
3,s3p2(2.D). The lowest 2D state excitation energies are relatively unaffected by
extension of the d space beyond the addition of the (Zd] diffuse set, while each ad-
ditional d function added allows one more Rydberg state to be properly described.
The agreement between the computed and experimental results is excellent: the
lowest excitation energy is underestimated by less than 250 cm"1, while the exci-
tation energy for the highest state considered (3s2 Wd) is overestimated by only a
little over 300 cm"1. The most likely source for these discrepancies, at least for the
lower members of the series, is the omission of core-valence correlation effects. The
computed ionization potential is only 100 cm"1 less than the experimental value,
while the error in the 3.s3p2(2P) excitation energy is slightly larger than for the
3s2nd series. This again is likely to be due to the differential effects of core-valence
correlation.
It can be seen from Table 1 that the configuration 3s3p2(2D) makes a sub-
stantial contribution to the lowest few 2D states. This contribution is obtained as
the square of the coefficient of this configuration in the various normalized full CI
wave functions, expressed as a percentage. The computed contributions converge
well with the expansion of the d basis, as do the excitation energies. The 3.s3p2(2.D)
term contributes essentially nothing to the n = 8 and higher Rydberg states. The
contribution to the lowest Rydberg state is similar to the value of 21% obtained
by Weiss (1973), although no excitation energy is given in his review. Matos et
al. (1987) obtain a larger percentage, but, as these authors point out, their d basis
(which was developed for A1H) is not sufficiently diffuse to describe the 3s~3d term
accurately.
As Weiss (1973) hypothesized, a major part of the 3s3p2(2.D) configuration
is thus "smeared out" over the 2D Rydberg series, although the larger number of
Rydberg states computed in the present work indicates that this smearing is con-
fined to the lowest few states. However, the present work also shows an additional
2£) state, labelled A in Table 1, at about 1000 cm"1 beyond the ionization limit,
which has a substantial contribution from 3.s3p2. This seems to agree very well
with the assertion of Carton (1962) that a diffuse doublet, which occurs "a short
way beyond" the ionization limit, is in fact the 3s3p2(2D) term. (Unfortunately,
Carton's review contains no quantitative information on the location of this dou-
blet.). Such a state is expected to be diffuse, as it will couple to ionizing states in
the continuum of Al II 3s2, but as the 3s3p2 term itself cannot autoionize to this
limit in a one-electron process, the observed doublet will show a band-like, rather
than continuum-like, structure.
We also list in Table 1 oscillator strengths for a number of transitions of the
form 2P —*• 2£). Transition moments are computed in the dipole length formula-
tion. Apart from the perturbation in the lowest few values caused by the 3s3p2
configuration, the results follow the expected trend. The term arising from the
remainder of the 3.s3p2 configuration carries considerable intensity, as expected for
a dipole transition with no change in principal quantum number. Of course, a full
treatment of the intensity of transitions to this state would involve coupling to the
continuum, which is beyond the scope of this work. It is interesting that the per-
turbing effects of the 3s3p2 configuration are confined to intensities — the excitation
energies for the entire Rydberg series fit extremely well (both for the computed and
experimental values) to the conventional empirical Rydberg formula. The oscillator
strength for the lowest transition is in excellent agreement with the level-crossing
spectroscopy result of Budick (1966). However, his contention that this supports
a 3.s3p2 configuration for the lowest 2D state must be rejected: inadequacies in
the Coulomb model used in analyzing the lifetimes are probably responsible for the
error. Given that core relaxation and correlation effects do not affect the lifetimes
(which is supported by other calculations on Al (Weiss 1973)) wave functions of the
quality used in this work would be expected to yield lifetimes accurate to better
than 10%, consistent with the agreement between this work and Budick's measure-
ments. However, while the overall trend in our computed oscillator strengths across
the series agrees qualitatively with that of the experimental results given by Penkin
and Shabanova (1963,1965), the values themselves agree very poorly. Penkin and
Shabanova overestimate considerably the oscillator strength for the lowest transi-
tion, so in the tables of Wiese et al. (1969) their results have been rescaled to agree
with Budick's value for the lowest transition. Even with such rescaling the results
do not agree with our computed values to within Wiese's suggested error bars of
±25%. It seems very unlikely that our results would show random deviations from
the true values, and no systematic error (which in view of the quality of the re-
sults is unlikely anyway) in the computed results can explain the discrepancy. It
seems probable that the Penkin and Shabanova results are not as reliable as the
uncertainty estimate of Wiese et al. suggests.
The 3s3p2(2.D) term has been shown to contribute significantly to the lowest
few 2.D Rydberg states of Al I; the residuum from these contributions appears about
1000 cm"1 beyond the ionization limit that gives ground-state Al II. The oscilla-
tor strengths for the lowest few transitions in the 2D series are strongly perturbed
by the 3.s3p2 configuration, in general agreement with the available experimental
results, but quantitative agreement between the computed and experimental oscil-
lator strengths is obtained only for Budick's measurement of the lowest transition.
In view of the quality of the present calculations we suggest that the oscillator
strengths of Penkin and Shabanova are not reliable.
References
Almlof J and Taylor P R 1987 J. Chem. Phys. 86 4070
Budick B 1966 Bull. Am. Phys. Soc. 11 456
Eriksson K B S and Isberg I B S 1963 Arkiv Fysik 23 527
Carton W R S 1962 in "Proceedings of the Fifth Conference on lonization Phenom-
ena in Gases, 1961" (Amsterdam: North-Holland)
Matos J M 0, Malmqvist P-A and Roos B 1987 J. Chem. Phys. 86 5032
Moore C E 1949 "Atomic Energy Levels, Vol I" (Washington: National Bureau of
Standards)
Penkin N P and Shabanova L N 1963 Opt. Spectry. 14 5
Penkin N P and Shabanova L N 1965 Opt. Spectry. 18 504
Schmidt M W and Ruedenberg K 1979 J. Chem. Phys. 71 3951
Weiss A W 1973 Adv. At. Mol. Phys. 9 1
Wiese W L, Smith M W and Miles B M 1969 "Atomic Transition Probabilities,
Vol II" (Washington: National Bureau of Standards)
Table 1. Full CI excitation energies" (cm ]) and oscillator strengths for states of Al I.
AE 3s3p2(2D)6
Configuration
3s23d
3s2 4d
3s25d
3s26d
3s27d
3s28d
3s2Qd
3s2Wd
l.P.
A 3s3P2(2D)f
\ C X TI ( r^ 1OoO// I J I
+(3rf)c
32189
38664
42083
44099
48840
56237
+(5d)
32189
38664
42142
44063
45262
46131
49189
56237
+(7cf)
32189
38664
42079
44071
45262
46110
46785
47290
48179
49225
56237
Exptd
32436
38931
42236
44168
45345
46094
46594
46942
48279
56699
+(3d) +(5d)
23.9 23.9
22.7 22.7
12.6 12.5
7.2 6.1
2.5
1.7
19.1 17.4
+(7<f)
23.9
22.7
12.5
6.1
2.5
1.9
< 1
< 1
17.2
fik(2P -> 2D)
+(5d)
0.166
0.077
0.150
0.110
0.055
0.014
1.270
Expte
0.230(0.175)
0.057
0.157
0.127
0.085
0.056
a
 Relative to 3s23p(2P) total energy of -241.934137^-
6
 Percentage of normalized CI wave function.
0
 Denotes number of diffuse d functions added to [7-s 6p 4rf 3/] basis.
d
 Moore (1949), Wiese et al. (1969).
6
 Penkin and Shabanova (1963,1965), result in parentheses from Budick (1966).
* See text.


The 2D Rydberg series in Al I

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