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

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

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

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

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

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.

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outer core shells included or not depending on energy and radial extent we used 68-electron core (P. Christiansen, unpublished)

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

O RECP cc-pVDZ Basis Set Exponents Contraction coefficients 4 1 3 / !No. primitives, PQN, No. contracted fns (0 s set) 41.04 -0.0095512 0.0 7.161 -0.1334986 0.9074 0.5985186 1.0 0.2807 0.5094281 4 2 2 / !No. primitives, PQN, No. contracted fns (0 p set) 17.72 0.0430232 3.857 0.2287623 1.046 0.5090575 0.2752 0.4604006 1 3 1 / !No. primitives, PQN, No. contracted fns (0 d set) 1.215 1.000000

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

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.

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?

UO2+ Results for u States u1/u1 states (cm-1) Ω Heaven et al. Infante et al. 5/2 0 0 0 3/2 661 2678 or 2545 2736 5/2 5201 - 6567 7/2 5809 - 5751 u1 states 1/2 17751 3/2 20868

UO2+ Results for u States (continued) State: ΔE (cm-1) u1 u1 u1 Ω=7/2? 21534 u1 u2 Ω=? 23130 Ω=9/2? 23892

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