Multi-reference Configuration-Interaction Calculations of the Low-Lying Electronic States of Iron and Vanadium Monohydride, FeH and VH Zhong Wang, Trevor.

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Presentation transcript:

Multi-reference Configuration-Interaction Calculations of the Low-Lying Electronic States of Iron and Vanadium Monohydride, FeH and VH Zhong Wang, Trevor J. Sears and James T. Muckerman Chemistry Department Brookhaven National Laboratory Upton, NY

General stabilization of 3d with respect to 4s with increasing Z Preference for a maximum number of high spin coupled 3d orbitals Bonding with H may involve either the 4s 2 3d n or 4s 1 3d n+1 state For the 4s 2 3d n state, the bonding involves the formation of sp hybrids arising from the promotion to the 4s 1 4p 1 3d n configuration (promotion energy rises monotonically with Z) For the 4s 1 3d n+1 state, the bonding simply involves a M(4s)-H(1s) bond (stronger) Competition: 4s 2 3d n to 4s 1 4p 1 3d n versus 4s 2 3d n to 4s 1 3d n+1 What is interesting about the first-row transition-metal hydrides? J. Chem. Phys. 78, 4597 (1983) 4s 1 3d n+1 – 4s 2 3d n splitting as a function of Z

Previous Theoretical Work on FeH and/or VH Scott & Richards (1974): Predicted the ground state of VH to be 5  Walch & Bauschlicher (1983): Demonstrated the difficulty in obtaining the correct 6  - 4  splitting in FeH; confirmed 5  ground state for VH. Bauschlicher & Langhoff (1988): Confirmed 4  ground state for FeH by adding MCPF correlation of 3s and 3p to their best CASSCF/MRCI+Q valence treatment. Obtained 6  - 4  splitting of 0.10 eV. Langhoff & Bauschlicher (1990): Calculated quartet and sextet states of FeH below 25,000 cm -1 using the state-averaged CASSCF/MRCI method. Reported spectroscopic constants for many states, but do not compare energies of quartet and sextet manifolds. No absolute energies quoted. Tanaka, Sekiya & Yoshimine (1991): Applied multi-reference coupled pair approximation [MRCPA(4)] and MRCI+Q method to calculate the ground and lower excited states of FeH. Obtained good value for 6  - 4  splitting, but selected reference configurations in an unspecified manner. The present work suggests that this biased their results.

Strategy of Present Work Calibrate the details (i.e., basis set, MCSCF active space, state averaging, etc.) of multi-reference configuration interaction (MRCI) calculations on FeH to achieve agreement with experimental results in an unbiased manner. Apply that level of theory to VH, about which very little is known, to make reliable predictions about its electronic states. Carry out all calculations in C 2v symmetry while imposing the full C ∞v symmetry on the orbitals. Choose a very large basis from the start and stick with it. Systematically enlarge the MCSCF active space to do the best possible job on the 6 D- 4 D splitting of FeH in subsequent internally contracted MRCI calculations using the full CASSCF reference function. Treat states of one multiplicity and symmetry (C 2v irreducible representation) at a time, insuring the orbitals are appropriate for excited states of that symmetry by state averaging in the MCSCF calculation (e.g., obtain two 4  states by state averaging 40% 1 4 B 1, 40% 1 4 B 2, 10% 2 4 B 1 and 10% 2 4B 2 ).

Walch & Bauschlicher (1983) Tanaka, Sekiya & Yoshimine (2001) Walch & Bauschlicher (1983) Tanaka, Sekiya & Yoshimine (2001) Basis: Bauschlicher-ANO (V, Fe) – [7s,6p,4d,3f,2g ] / (20s,15p,10d,6f,4g ) Dunning aug-cc-pVTZ (H) – [4s,3p,2d ] / (6s,3p,2d ) What happens to E( 6  ) – E( 4  ) in FeH as the active space is augmented? 44 66

FeH Active Space Natural Orbitals 66 11 77 33 88 44 99 10  11  55

X 4  A 4  B 4   C 4  D 4   E 4  F 4  a 6  b 6  c 6  

a A. E. Stevens, C. S. Feigerle, and W. C. Linderberger, J. Chem. Phys. 78, 5420 (1983) b D. M. Goodridge, D. F. Hullan, and J. M. Brown, J. Chem. Phys. 108, 428 (1998) c J. G. Phillips, S. P. Davis, B. Lindgren, and W. J. Balfour, Astrophys. J., Suppl. Ser. 65, 721 (1987) d K. Tanaka, M. Sekiya and M. Yoshimine, J. Chem. Phys. 115, 4558 (2001) e S. R. Langhoff and C. B. Bauschlicher, Jr., J. Mol. Spectrosc. 141, 243 (1990) f M. Sodupe, J. M. Lluch, A. Oliva, F. Illas, and J. Rubio, J. Chem. Phys. 92, 2478 (1990) g Relative to the total energy of a 6 Δ h C. Wilson, H. M. Cook, and J. M. Brown, J. Chem. Phys. 115, 5943 (2001) i W. J. Balfour, J. M. Brown, and L. Wallace, J. Chem. Phys. 121, 7735 (2004) j Estimated from the results of ref. (i) Comparison of Calculated and Experimental T e Values for FeH

What is wrong with the B 4   and D 4   states? Look at D 4   case at R=1.55 Å… 9264 cm -1

Comparison of Calculated and Experimental R e Values for FeH a W. J. Balfour, B. Lindgren, and S. O’Connor, Phys. Scr. 28, 551 (1983) b A. E. Stevens, C. S. Feigerle, and W. C. Linderberger, J. Chem. Phys. 78, 5420 (1983) c K. Tanaka, M. Sekiya and M. Yoshimine, J. Chem. Phys. 115, 4558 (2001) d S. R. Langhoff and C. B. Bauschlicher, Jr., J. Mol. Spectrosc. 141, 243 (1990) e M. Sodupe, J. M. Lluch, A. Oliva, F. Illas, and J. Rubio, J. Chem. Phys. 92, 2478 (1990) f W. J. Balfour, J. M. Brown, and L. Wallace, J. Chem. Phys. 121, 7735 (2004)

Comparison of Calculated and Experimental  e Values for FeH a J. G. Phillips, S. P. Davis, B. Lindgren, and W. J. Balfour, Astrophys. J., Suppl. Ser. 65, 721 (1987) b K. Tanaka, M. Sekiya and M. Yoshimine, J. Chem. Phys. 115, 4558 (2001) c S. R. Langhoff and C. B. Bauschlicher, Jr., J. Mol. Spectrosc. 141, 243 (1990) d M. Sodupe, J. M. Lluch, A. Oliva, F. Illas, and J. Rubio, J. Chem. Phys. 92, 2478 (1990) e C. Wilson, and J. M. Brown, J. Mol. Spectrosc. 197, 188 (1999) f C. Wilson, and J. M. Brown, Mol. Phys. 99, 1549 (2001)

cm -1

X 5X 5 55 55 55 55 33 33 33 33 Laser-induced excitation fluorescence spectrum

End This work was performed at Brookhaven National Laboratory (BNL) under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy and supported by it Division of Chemical Sciences, Office of Basic Energy Sciences. 44 99

a K. Tanaka, M. Sekiya and M. Yoshimine, J. Chem. Phys. 115, 4558 (2001) b M. Dolg, U. Wedig, H. Stoll, and H. Preuss, J. Chem. Phys. 86, 2123 (1987) c D. P. Chong, S. R. Langhoff, C. W. Bauschlicher, Jr., S. P. Walch, and H. Partridge, J. Chem. Phys. 85, 2850 (1986) d T. C. Steimle et. al J. Chem. Phys. (in press) Comparison of Calculated and Experimental Dipole Moment Values for FeH

a K. Tanaka, M. Sekiya and M. Yoshimine, J. Chem. Phys. 115, 4558 (2001) b M. Dolg, U. Wedig, H. Stoll, and H. Preuss, J. Chem. Phys. 86, 2123 (1987) c D. P. Chong, S. R. Langhoff, C. W. Bauschlicher, Jr., S. P. Walch, and H. Partridge, J. Chem. Phys. 85, 2850 (1986) Comparison of Calculated and Experimental Dipole Derivative Values for FeH

What is wrong with the B 4   and D 4   states? Look at D 4   case at R=1.55 Å… 9264 cm -1