Computational Spectroscopy II. ab initio Methods

1. Computational SpectroscopyII. ab initio Methods Multi-configuration Self-Consistent Field Theory Chemistry 713 Trocia Clasp

2. Outline • What is MCSCF field theory? • How one uses this program ? • How one determine if this method appropriate for his/her specific molecular system?

3. Brief Introduction of Multiconfigurational self consistent field theory (MCSCF) • How does MCSCF theory is applied to computers software programs such as: Molpro, Gaussian • Differences between the two software Gaussian and Molpro

4. Hartree-Fock Calculations Hartree Fock Calculations is solved iteratively through a procedure called Self Consistent Field theory. making an initial guess of the spin orbitals,then it is used to solve the eigenvalue equation. The procedure is repeated until it converged.

5. Slater Determinant • The spin orbitals are arranged in a determinantal wavefunction For ex: The ground state of H2 molecule *u = g

6. How to describe the wavefunction when the hydrogen bonds are broken H2 ? • In Hartree Fock the wavefunction have equal amounts of covalent and ionic terms because it is single determinate Covalent H·H· ionic H+H- However when H2 dissociates the hydrogen atoms are covalent.. This can be corrected by using multiconfiguration theory.

7. Multi-Configuration SCF • In Multi-Configuration Theory the wavefunction is represented by more than one determinant also called configuration state functions (CSFs) x c many other different arrangement of electrons in the Spin orbitals *u + g Using H2 still as an example

8. MCSCF theory is used in systems • Bond breakage/ Bond formation • Radicals • Degenerate configurations of molecules such as ozone,NO2

9. How to determine if you need to run a MCSCF calculation? • Run an optimization calculation of the specific molecule using NBO as keyword, NBO is natural bond orbital Example #P MP2/6-311+G(3df,2p) POP=NBO 0 1 Molecule specification

10. NBO output of Methanol • The section that depict Occupancy No. of 1.99550. • The occupancy number are either 1.99 or 1 or 0 but fractional number that are <1.99 or >0.02 indicates that MCSCF calculations is necessary.

11. Example of output NBO file in Gaussian • ******************************Gaussian NBO Version 3.1****************************** N A T U R A L A T O M I C O R B I T A L A N D N A T U R A L B O N D O R B I T A L A N A L Y S I S ******************************Gaussian NBO Version 3.1****************************** /RESON / : Allow strongly delocalized NBO set Analyzing the SCF density NATURAL POPULATIONS: Natural atomic orbital occupancies 1. (1.99554) BD ( 1) H 1 - O 2 ( 32.83%) .5730* H 1 s( 99.80%)p .00( .20%) .9990 -.0015 .0002 .0176 .0377 .0065 .0139 .0000 .0000 ( 67.17%) .8196* O 2 s( 38.01%)p 1.63( 61.88%)d .00( .11%) f .00( .00%) -.0001 .6162 -.0160 .0133 .0001 -.7171 .0503 -.0051 -.0056 -.3168 .0404 -.0034 -.0005 .0000 .0000 .0000 .0000 .0082 .0052 .0018 .0000 .0000 .0000 .0000 .0000 .0000 .0233 .0090 .0019 -.0184 -.0021 -.0011 .0000 .0035 -.0001 .0000 .0000 .0011 -.0046 2. (1.99799) BD ( 1) O 2 - C 3 ( 67.12%) .8193* O 2 s( 27.74%)p 2.60( 72.18%)d .00( .07%) f .00( .01%) BD*- antibonding orbitals Rydberg- are orbitals at very high principal quantun number LP-lone pairs Occupancy no Bonding orbitals

12. NBO example of Methanol

14. Extended both R-CH and OH bonds of methanol Equilibrium

15. Ozone

16. An example of an input structure in Molpro Geometry specifications Basis set,cc-pvdz Hartree-Fock calculations must precede first before multiconfigurational calculation Multiconfigurational calculation

17. Running the File on Molpro • The file is saved as .int extension (Meth.int) or .com file • Used the command molpro filename & in the unix terminal

18. Output of Multiconfiguration calculations in Molpro CSFs’ space End of file Where the input file is Meth.int and the output is Meth.out

19. Specific example of MCSCF in Molpro Reduce Time and memory

20. The output file of Molpro CSFs

21. Definition of Molpro input structure Wf, 18, 1, 0 represents Wf, nelec, symmetry, spin In the MCSCF calculations Closed,4; occ,11,3; wf, 18,1,0 closed is the number of orbitals that are doubly occupied and does not participate in bond breakage or bond formation usually the core orbitals. Occ are the number of occupied orbitals and virtual orbitals that make up the active space where electrons play a role in bond breakage/bond formation.

22. Need 10 orbitals to obtain Different arrangement of Configurations So you need 14 total orbitals And four of the 14 is the core Core electrons

23. MCSCF Calculation in Gaussian • In Gaussian calculations the following keyword CASSCF (N,M) input is used where N is the number of electrons involved in bond breakage/formation M is the active orbitals the total number of occupied + virtual orbitals

24. Example of Gaussian output Calculations

25. Differences between Gaussian calculation and Molpro • Molpro converges more quickly then Gaussian but takes more time to complete the calculation than Gaussian because of its convergence criteria. • Gaussian calculations need more time spent on finding the right orbitals and it is less robust.. • Molpro has many other multiconfiguration methods such as: MRCI, CASPT2, CASPT3

26. Final Words • Molpro does not have a visualization interface • Download for free Molden http://www.cmbi.kun.nl/molden/molden.html to visualize the geometries and orbitals but in the input file of molpro the following command is saved at the end of file put, molden, filename;