Metastability calculations of energy states of nitrogen negative io

Harris, F. E.

Schaefer, H. F., III

English

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Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19690001379 2020-03-12T06:14:15+00:00Z
NASA CR 'I 3 A I P
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FINAL REPORT- NEGATIVE ION STABILITY CALCULATIONS
by Henry F. Schaefer 111 and Frank E. Harris
September 15, 1968
Distribution of this report is provided in the interest
of information exchange. Responsibility for the c,.--ntents
resides in the author or organization that prepared it.
Prepared under Contract No. NAS2-4882 by
Stanford University
Department of Chemistry
Frank E. Harris, principal Investigator
^t
for
AMES RESEARCH CENTER
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
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trim	 "g,
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1, General
Calculations have been performed as s pecified in the
contract to determine the energies of PJ ( 1D) relative to
N C D) , of N- ( 3 P) relative to N ( 4S) , of 0 ( 2 P) relative to
0 t 3 P), and, in addition, of F ( 1 S) relative to F ( 2 P) and of
C ( 4S) relative: to C ( 3 P). These calculations clearly indicate
that N C 1D) is metastable, lying below N C 2D), that N ( 3 P) is
unstable relative to N ( 4S), and that the methods of calculation
are reliable. This work is described in detail in an appendix
to this report entf tied "Me:astabi i i ty of the I D state of the
Nitrogen Negative ion." It is planned to submit this material
for publication in Physical Review Letters or in some other
appropriate ,journal.
One copy of certain material produced in the calculations
is simultaneously with the submission of this report being
transmitted to the Technical Monitor. This material, though not
essential to the report, may be of use if Ames Research Center
desires to make studies of additional properties of the atoms and
ions here investigated. In particular, the material includes
previously produced descriptions of the detailed methods of
calculation and explicit wavefunctions for certain of the stable
and metastable species investigated.
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il. Certification
On behalf of the Contractor, it is hereby certified t.,at
the level of effort specified in .article I of the contract was
used in its performance.
Signed,
P. M. West
Administrative Officer
Chemistry Department
Stanford university
1190 11	 ,1
APPENDIX
Metastability of the 1D State of the Nitrogen Negative Ion*
Henry F. Schaefer, i I It
Dept. of Chemistry, Stanford University, Stanford, California
and
Frank E. Harris
Dept. of Physics, University of Utah, Salt Lake City, Utah
Abstract
Ener g ies of the 3 P and 1 D states of N have been ca lculated
using a f i rst -order wavefunct i on designed to Include  the strong-
ly structure-dependent part of the correlation energy. Compar-
ing the N calculations to those of other a pp ro p riate sys;ems,
the remaining correlation energy is reliably estimated and the
-
D N state is predicted to be metastable, lying 0.844 eV below
the D state of N. instability of the 3 P N state is predic ad.
*
Supported by the National Aeronautics and S pace administration,
Ames Research Center, under Contract No, NAS 2-4882.
Ot National Defense Education Act Title IV Predsctoral Fellow.
1 -
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- 2 -
Severml experiments I
 have indicated the existence of one or
more states of the ion N	 However, as the lowest state of
atomic nitrogen lies below most estimates of the energy of a
hypothetical 3 P around state of N% the indicated r! state(s) May
be metastable with respect to electron detachment, 2 A 3 P state
of N could be expected to decay rapidly into a free electron
plus the ground 4S state of N. Bates and Moiseiwitsch 3 nave sug-
1	 -
gested that a D state of N might be stable relative to all
excited states of N. and would have a long lifetime because the
process
N ( D) NmO N ( 4S) + e
is forbidden. This letter reports calculations comparing the
ies	 _
energA of 1D N and the first  excited state ( 2 D) of atomic
nitrogen.
Our calculations are based on wavefunctions designed to
include in a nonrelativistic formulation the Hartree-Fock energy
plus that part of the correlation energy which depends strongly
upon the symmetry and shell structure of the electronic config-
uration. Such wavefunctions will then be subject to errors
resulting from the omission of the remainder of the correlation
•	 energy and from relativistic effects. These residual errors,
which vary smoothly with respect to the nuclear charge and number
of electrons in an atomic system, can be closely estimated by
Interpolative methods. 4 This type of partitioning of the corre-
lation energy was suggested by Sil ,^irstone and Sinano2lu5,
and we call the structure-sensitive part of the correlation
energy the orbit L correlation energy.
To calculate the orbital correlation energy we use what
a e call the first-order wavefunction, defined to be a configura-
tion interaction L-S eigenfunction including all orbital
occupancies in which at most one electron is assigned to an
r rb i to 1 beyond the valence shell, For first-row  a torns, this
weans configurations in which a11, or all but one, of the
Electrons are assigned to Hartree-Fock 1s, 2s, or 2p orbitals.
The orbital correlation energy is the difference between the
energy of the first-order wavefunction and the Hartree-Fuck
energy.
Our first-order  wavefunction includes configurations of the
types suggested for the same purpose by Silverstone and Sinan-
oglu, with the difference that their configurations refer to
Slater-determinants while ours refer to L-S eigenfunctions.
Our first-order wavefunction includes determinants which are
not includes in the Silverstone-Sinanogiu enumeration, but
v.hose existence depends upon the electronic shell structure.
The significance of this difference is indicated by recent work
to
of Sinanoglu and Oksuz 6, who find a structure dependent
2
correlation energy of -1.31 eV for 0 N while our first-order
vavefunction yields an orbital correlation energy of -1.61 eV.
- 3 -
x
Using first-order wavefuncticns with basis sets suffici-
ently large to give convergence in energy to within 0.0001 har-
tree, we have calculated the energies of the lowest 2D state of
N and the lowest  D state of N.-
 To aid in estimation of the
residual errors, we also carried out corresponding calculations
on 0 +
 ( D) and 0 ( 1D), and on the ground states of C. C- , Nt,
N, h , 0♦ 0 0 0 0 , F # , F, F% and Ne i .	 Some of these calcula-
tions are described in Table 10
The calculated energies were processed'by taking difference3
corresponding to electron affinities of the neutral atoms and
positive ions. Following this, the computed electron affinities
of positive ions were compared with the experimental ionization
7potentials,	 it was found that the residual error in the
electron affinities indeed varied regularly, de pendinb mainly on
the number of electrons, and that a rather good estimate of the
electron affinity of a neutral atom could be obtained by
same
assuming the calculated value to have theAresidual error as was
found for the electron affinity of the isoelectronic positive
Ion. Affinities estimated on the basis of this simple
assumption are shown in Table 11,
Better estimates of the electron affinities of neutral atoms
can be produced by noting that the results just cited eaviate.
from experimental values by amounts approximately proportional
to the number of Zp electrons in the neutral atom. There is some
theoretical ,justification for such behavior, as more extensive
i
• 4
eA_h 1,i,i calculations B an B and 6 have shown that higher
order correlations within the is 2 2s 2 core contribute relatively
little  to the electron affinity of boron. Assuming, then, an
additional residual error of 0.065 eV per 2p electron, we obtain
the final estimates listed in Table ii.
affinities
For all three atoms whose electron,A are known, these final
estimates agree with the experimental data to within the claimed
accuracy of measurement, and we are led to conclude that the
estimates for the unmeasured affinities of N t 4S) and N ( 2D) are
cf comparable reliability. We therefore predict the instability
cf the hypothetical 3 P state of N" , and the existence of
metastable 1D state of N lying 1.539 eV above the S ground
state of N. and 0.844 eV below the 20 N excited state.
Y
5
ti
k
I* G. Boldt, Z. Physik jjj, 330 (1959); Ya. M, FoZel, V, F.
Kozlov, and A. A. Kalm ykov, Soviet Phys. • JETP J., 963 (1959);
R. A. Allen and A. Textor l s, J. Cher. Phys. ,U, 3445 (1964);
D. M. Cooper, unpublished work at Ames Research Center,
2. B, L. Moiseiwitsch, AdvAneRs in Atornic Anft 6yig lecti la.r Physics
(Academic Press Inc., New York, 1965), Vol, 1 0 p, GI,
3 9 D. R. Bates and B. L. Moiseiwitsch, Proc, Phys. Soc,
(London) AU, $40 (1955).
49 E. Clementi, J. Chem. Phys. JUo 2248 (1963); d,, 175 (1963);
2783 (1965); E. Clementi and A. Veil lard, J. Chem. Phys.
3050 (1966); H. Hartman and E. Clementi, Phys, Rev. ,,
Al295 (1964).
5. H. J Silverstone and G. Sinanoglu, J. Chem, Phys, U, 1899
(1966);, 3608 (1966).
6. 0, S i nanoSl u and 1. Oksuz, Phys, Rev. Letters, 11, $07
(1968).
7. B. Edlen, J. Chem, Phys, JZ 98 (1960).
44
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