Ab initio Yb·Ne potentials: Supplementary material to Electronic
Spectroscopy of Ytterbium in a Neon Matrix
A. A. Buchachenko,1, a) R. Lambo,2 L. Wu,2 Y. Tan,2 J. Wang,2 Y. R. Sun,2 A.-W. Liu,2 and S.-M. Hu2
1)
Department of Chemistry, M. V. Lomonosov Moscow State University, Moscow 119991,
Russia
2)
Hefei National Laboratory for Physical Science at the Microscale, University of Science and Technology of China,
Hefei, Anhui 230026, China
(Dated: 8 January 2013)
Assuming weak perturbations of the Yb electronic
structure by Ne, it is straightforward to establish the
correlation between the states of atomic Yb and Yb·Ne
dimer. In the non-relativistic and scalar relativistic
(SR) approximations, the former are classified as 2S+1 L,
whereas for the latter, Hund’s case (a) is appropriate,
2S+1 σ
Λ , where S is the electronic spin angular momentum, L and Λ are the electronic orbital angular momentum and its projection onto the molecular axis R, respectively, and σ = ± specifies the reflection symmetry for
the Λ = 0 states. When the vectorial SO coupling is included, the total electronic angular momentum J appears
in the atomic term specification 2S+1 LJ and molecular
states are classified within the Hund’s case (c), Ωσ , with
Ω being the projection of J onto R The symmetries of
states considered here are specified in the Table I.
TABLE I. Correlation of the atomic SR 2S+1 L and SOcoupled 2S+1 LJ terms with the molecular Hund case (a)
2S+1 σ
Λ and Hund case (c) Ωσ states for Yb and Yb·Ne.
Yb
2S+1
1
3
L
1
S
◦
P
3
Yb–Ne
2S+1
D
P◦
1
D
1
S0
P◦0
3 ◦
P1
3 ◦
P2
3
D1
3
3
1
2S+1
LJ
3
Λσ
Ωσ
Σ+
0+
+
0−
3
Σ , Π
0+ , 1
−
0 , 1, 2
3
+
3
3
Σ , Π, ∆
0− , 1
+
D2
0 , 1, 2
3
D3
−
1
P◦1
1
D2
0 , 1, 2, 3
1
1
Σ+ , 1 Π
+
1
1
Σ , Π, ∆
0+ , 1
+
0 , 1, 2
All ab initio calculations presented here were performed using the MOLPRO program package1 within the
C2v symmetry group.
For the ground X 1 Σ+ state of the Yb·Ne dimer, the
single-reference coupled cluster method with singles, doubles and non-iterative correction to triples, CCSD(T)2 ,
was employed. It was used with the small-core effective
a) Electronic
mail:
core potential ECP28MDF, parameterized in the DiracFock relativistic calculations3 for the Yb atom with the
supplementary contracted [12s11p9d8f4g] basis set further expanded by adding the set of spdfg primitives continuing the smallest exponents in each symmetry type
as an even-tempered sequence. This augmentation is
important for convergence of the Yb polarizabilities4,5 .
All-electron augmented correlation consistent polarized
quadruple-zeta aug-cc-pVQZ basis set6 was employed for
the Ne atom. To further saturate dispersion interaction, the 3s3p2d2f1g bond function set7 was added in
the middle of the Yb·Ne distance. The Yb(4s2 4p6 4d10 )
and Ne(1s2 ) shells were kept in the core.
The calculations of the dimer states that correlate to
the 6s2 1 S, 6s6p 1,2 P and 5d6s 1,3 D terms of Yb atom were
performed within the multireference approaches. Since
the spin-orbit part of the ECP28MDF pseudopotential
was not available, the slightly less accurate ECP28MWB
(Wood-Boring)8 one was used for the Yb atom with the
segmented (14s13p10d8f6g/10s8p5d4f3g] basis set9 augmented by the s2pdfg set of diffuse primitives recommended in Ref.10 . The Ne atom was described as has
been given above. The reference orbitals were obtained
using the complete active space multiconfigurational selfconsistent field (CASSCF) method11 with 5d, 6s and 6p
Yb orbitals included in the active space. Equal-weight
averaging was made over all the components of interest.
Special care was taken to guarantee the proper value of
the projection Λ, calculated through the hL2z i expectation value. The internally contracted multireference single and double configuration interaction (MRCI)12 calculations with the Davidson correction13 were then carried
out for all the components in each representation of the
C2v group. The same orbitals were assigned as active,
whereas the 4f shell of Yb was correlated as doubly occupied, so that the states of atomic Yb associated with
the excitations of 4f electrons do not appear in our treatment. Attempts to include the 4f orbitals in the active
space made the calculations extremely demanding and
applicable, at best, to the states of the lowest 1 S and
3
P limits. Previous studies of the atomic polarizabilities
revealed relatively minor effect of these states4,14,15 .
Spin-orbit calculations were performed using the stateinteracting approach16 . All the scalar-relativistic states
were included and SO matrix elements were computed using the full Breit-Pauli operator for the inner parts of the
multiconfigurational expansions (i.e., on the CASSCF
2
wave functions) within the ECP28MWB pseudopotential
including its SO part. It was checked that the additon
of the excitations to the outer part accounted within the
mean-field approximation did not change the SO matrix
elements and splittings significantly.
The final set of the potentials was obtained in the range
of interatomic distances R from 2.3 to 30 Å as follows.
The ground-state CCSD(T) potential was computed with
the counterpoise correction to the basis set superposition
error17 . The MRCI excitation energies, taken as the difference between the excited- and ground-state energies
at each R, were then added to the CCSD(T) potential.
Each potential was then shifted to the corresponding center of the multiplet18 at R = 30 Å. The resulting curves
were used to parameterize the diagonal part of the SO
Hamiltonian matrix whose diagonalization provided the
SO-coupled potentials. The differences between the excitation energies of Yb atom calculated in this way and the
experimental ones18 are, in cm−1 , 65, -35, -84 (3 P0,1,2 );
-11, -1, -21 (3 D1,2,3 ); 154 (1 P1 ); 35 (1 D2 ).
The corresponding potentials are shown in the Figure 1.
1 H.-J.
Werner, P. J. Knowles, G. Knizia et al., MOLPRO, version
2010.1, a package of ab initio programs, Cardiff, UK, 2010.
2 P. J. Knowles, C. Hampel, and H.-J. Werner, J. Chem. Phys. 99,
5219 (1993); ibid. 112, 3106 (2000) (Erratum).
3 Y.
Wang and M. Dolg, Theor. Chem. Acc. 100, 125 (1998).
A. Buchachenko, Eur. J. Phys. D 61, 291 (2011).
5 P. Zhang and A. Dalgarno, J. Phys. Chem. A 111, 12471 (2007).
6 T. H. Dunning, Jr. J. Chem. Phys. 90, 1007 (1989).
7 S. M. Cybulski and R. R. Toczylowski, J. Chem. Phys. 111,
10520 (1999).
8 M. Dolg, H. Stoll, and H. Preuss, J. Chem. Phys. 90, 1730 (1989).
9 X. Cao and M. Dolg, J. Mol. Structure (THEOCHEM) 581, 139
(2002).
10 A. A. Buchachenko, G. Chalasiński, and M. M. Szczȩśniak,
Struct. Chem. 18, 769 (2007).
11 H.-J. Werner and P. J. Knowles, J. Chem. Phys. 82, 5053 (1985);
P. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 115, 259
(1985).
12 H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988);
P. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, 514
(1988).
13 S. R. Langhoff and E. R. Davidson, Int. J. Quant. Chem. 8, 61
(1974).
14 S. G. Porsev, Yu. G. Rakhlina, and M. G. Kozlov, Phys. Rev. A
60, 2781 (1999).
15 V. A. Dzuba and A. Derevianko, J. Phys. B 43, 074011 (2010).
16 A. Berning, M. Schweizer, H.-J. Werner, P. J. Knowles, and P.
Palmieri, Mol. Phys. 98, 1823 (2000).
17 S. F. Boys and F. Bernardi, Mol. Phys. 19, 553 (1970).
18 Yu. Ralchenko, A. E. Kramida, J. Reader, and NIST ASD
Team, NIST Atomic Spectra Database (ver. 4.0.1) (National
Institute of Standards and Technology, 2010). Available online
http://physics.nist.gov/asd.
4 A.
3
30000
1
1
D
D
27500
2
D
P
25000
1
3
)
-1
E (cm
P
3
D
3
D
3
D
22500
1
2
3
P
20000
2
3
P
17500
5000
2500
0
1
3
1
3
4
R
1
3
1
3
1
3
5
(Å)
3
P
1
+
0
0
1
2
1
S
6
3
P
0
1
S
3
3
4
R
5
0
6
(Å)
FIG. 1. Ab initio potentials of the Yb·Ne dimer. Left panel – SR case, right panel – SO-coupled potentials. The 1 P1 (25070
cm−1 ) and 3 D3 (25270 cm−1 ) limits appear as degenerated on this scale. Note the energy axis break from 5000 to 17000 cm−1 .