1. Multireference Spin-Orbit Configuration Interaction with Columbus; Application to the Electronic Spectrum of UO2+
Russell M. Pitzer
The Ohio State University
Winter School Helsinki, 2007

2. MRCI Method Choose Relativistic Effective Core Potentials
(and Spin-Orbit Operators)
AO Basis Sets
Determine MOs (SCF or MCSCF)
Reference electron configurations
Active space (MOs/electrons to be correlated)
No. of roots
Use all single and double excitations

3. MRCI Method Advantages:
Graphical Unitary Group Approach (GUGA) provides efficient formulation of integrals over spin eigenfunctions (configuration state functions, CSFs) rather than Slater determinants.
Easily describes any type of electron coupling
Works effectively in parallel

4. MRCI Method Disadvantages
Doesn’t describe electron correlation as efficiently as CC or DFT
Involves many choices

5. Actinyl Ions Ox. No. V AnO2+ Ox. No. VI AnO22+
Short, strong axial bonds
Long, weak equatorial interactions
An , AOs involved in bonding
An ,  AOs nonbonding
References
R. G. Denning, J. Phys. Chem. A, 2007, 111, 4125
J. C. Eisenstein & M. H. L. Pryce, Proc. Roy. Soc. London 1955, A229.20
S. Matsika et al., J. Phys. Chem. A, 2001, 105, 3825

6. UO2+ Usually disproportionates in solution to U(IV) + U(VI)
2UO2+ + 4H+  UO22+ + U4+ + 2H2O
Spectrum is similar to that of NpO22+
One electron outside of the UO22+ closed shell,
in 5f or 5f (strong spin-orbit mixing)
Ω values 5/2, 3/2, 5/2, 7/2 (S = ½)
Higher states are from ( S = 3/2)
Gas-phase experiments by M. Heaven et al.

7. UO2+ - Choice of RECPs 60, 62, 68, 78 – electron cores available
smaller cores – more electrons adapt to molecular interactions
fewer electrons have scalar relativity included
outer core shells included or not depending on energy and radial extent
we used 68-electron core (P. Christiansen, unpublished)

8. UO2+ - Choice of AO Basis Set
Use set provided with RECP or
Develop your own with atomic SCF program
ATMSCF optimizes orbital exponents, but pairs of exponents tend to coalesce
ATMSCF with Legendre-expansion constraints can be used

9. O RECP cc-pVDZ Basis Set
Exponents
Contraction coefficients
/ !No. primitives, PQN, No. contracted fns (0 s set)
41.04
0.0
7.161
0.9074
1.0
0.2807
/ !No. primitives, PQN, No. contracted fns (0 p set)
17.72
3.857
1.046
0.2752
/ !No. primitives, PQN, No. contracted fns (0 d set)
1.215

10. UO2+ - MOs Determine MOs by SCF u2 u1 2u?
Problem: several u orbitals occupied. How to get best linear combination for excitation?
Do SCF on u1 u2
This has the effect of optimizing the u MO for excitation, but has little effect on the ground state u MOs
Alternative: MCSCF on average of states

11. UO2+ - References
Choose all CSFs arising from u2u1, u2u1, u1u2, u1u1u1, u1u2
Length of expansion is approx. proportional to the number of references, so throw out any that are unimportant.

12. MRCI - algorithms
Graphical Unitary Group Approach (GUGA). Efficient formulation of integrals over spin eigenfunctions (configuration state functions, CSFs) rather than Slater determinants.
Works efficiently in parallel, up to 103 cpu’s tried. Work on petascale computers?

13. UO2+ Results for u States
u1/u1 states (cm-1)
Ω Heaven et al. Infante et al. 5/
3/ or 5/ 7/
u1 states 1/ 3/

14. UO2+ Results for u States (continued)
State: ΔE (cm-1)
u1 u1 u1
Ω=7/2?
u1 u2
Ω=?
Ω=9/2?

15. Mike Mrozik (graduate student) And support from U.S. Dept. of Energy
With thanks to
Mike Mrozik (graduate student)
And support from
U.S. Dept. of Energy
The Ohio State University
And special recognition to
Pekka Pyykkö
For organizing and stimulating so much activity in this field