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 DepartmentBrookhaven National Laboratory

Upton, NY 11973-5000

• 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 4s2 3d n or 4s1 3d n+1 state• For the 4s2 3d n state, the bonding involves the formation of sp hybrids arising from the promotion to the 4s1 4p1 3d n configuration (promotion energy rises monotonically with Z)• For the 4s1 3d n+1 state, the bonding simply involves a M(4s)-H(1s) bond (stronger)• Competition: 4s2 3d n to 4s1 4p1 3d n versus 4s2 3d n to 4s1 3d n+1

What is interesting about the first-row transition-metal hydrides?

J. Chem. Phys. 78, 4597 (1983)

4s1 3d n+1 – 4s2 3d n

splitting as a functionof 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 C2v 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 the6D-4D splitting of FeH in subsequent internally contracted MRCI calculations using the full CASSCF reference function.

Treat states of one multiplicity and symmetry (C2v 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 stateaveraging 40% 1 4B1, 40% 1 4B2, 10% 2 4B1 and 10% 2 4B2).

-1263.11787 -1263.12374 Walch & Bauschlicher (1983)-1263.1922 -1263.2015 Tanaka, Sekiya & Yoshimine (2001)

-1263.10769 -1263.12038 Walch & Bauschlicher (1983)-1263.1819 -1263.2048 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?

Active space MRCI energy MRCI+Q energy C(0) Ref. CSFs

Contracted configurations (MRCI) (MRCI+Q)

Quartet Delta state (R=1.55) CAS(9,10) -1263.207664 -1263.220509 0.947 4,872 841,688 -0.202 -0.082 CAS(9,11) -1263.210351 -1263.222678 0.947 14,368 1,828,348 -0.158 -0.046 CAS(9,12) -1263.215878 -1263.228389 0.948 37,448 3,850,832 -0.046 0.089 CAS(9,14) -1263.221600 -1263.230908 0.960 194,710 14,840,046 0.053 0.123 Sextet Delta state (R=1.69) CAS(9,10) -1263.215074 -1263.223539 0.975 1,263 407,033 CAS(9,11) -1263.216168 -1263.224386 0.975 4,158 789,663 CAS(9,12) -1263.217566 -1263.225105 0.977 11,739 1,586,523 CAS(9,14) -1263.219654 -1263.226379 0.978 67,935 6,100,471

4

6

FeH Active Space Natural Orbitals

6 1 7 3

8 4 9

10 11 5

FeH States: MRCI+Q/ANO/AVTZ

States X4Del A4Pi B4Sig- C4Phi D4Sig+ E4Pi F4Del a6Del b6Pi c6Sig+Re (Å) 1.5684 1.5527 1.5685 1.6006 1.5387 1.6553 1.7176 1.6876 1.6819 1.6917Te (eV) 0.0000 0.0942 0.0920 0.4701 0.2276 0.9459 1.0158 0.1107 0.3515 0.4670Te (cm-1) 0 760 742 3791 1836 7630 8193 893 2835 3767Frequency (cm-1) 1744 2043 1796 1393 1971 1548 1431 1634 1570 1539Dipole moment (D) 1.8993 1.9193 3.1047 3.0572 1.1037 1.7508 0.3289 0.8860 1.0328 0.9722Dipole deriv. (D/Å) 0.2554 0.5807 2.4434 2.2330 0.3573 2.5239 2.0794 3.2115 3.0607 2.8568

X 4 A 4 B 4 C 4 D 4 E 4 F 4 a 6 b 6 c 6

Calculated State Te (cm-1)

Observed CASSCFe MRCIe MRCI+Qe MRCPA(4)d +Qd SLOIR

CIPSIf X4Δ 0 0 0 0 0 A4П 760 1140j 1255 1200 2016 726 645 B4Σ- 742 5389 5089 C4Φ 3791 3175h 6416 5078 5969 4759 D4Σ+ 1836 7061 7158 E4Π 7630 7231i 8347 7416 F4Δ 8193 9921c 9856 9463 9437 9437 a6Δ 893 2061a (2270h) (0.0g) (0.0g) (0.0g) 2178 726 2258 b6П 2835 (1831g) (2044g) (1954g) 3307 1936 3388 c6Σ+ 3767 4839b (2355g) (2573g) (2404g) 4597 3226 4597

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 a6Δh 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 Te Values for FeH

4+ CAS(9,14) reference function: 80% 4, 10% 4+, 10% 4 SACAS(9,14) reference function

C(0) = 0.9469 C(0) = 0.9591

C(0) = 0.9785

Reference coefficients greater than 0.10 Reference coefficients greater than 0.10 a1 b1 b2 a2 coef. a1 b1 b2 a2 coef. 4 coef. 4+

Compare with reference function CAS(9,14) CI coefficients

Reference energy Reference energy Correlation energy Correlation energy MRCI STATE ENERGY MRCI STATE ENERGY Cluster corrected energy (Davidson)

Cluster corrected energy (Davidson)

What is wrong with the B 4 and D 4 states? Look at D 4 case at R=1.55 Å…

9264 cm-1

Calculated State Re (Å) Observed MRCPA(4)c +Qc LB d

+Q SPOIRe CIPSI

X4Δ 1.5684 1.589a(1.620f) 1.596 1.582 1.588 1.578 A4П 1.5527 1.529f 1.552 1.552 1.553 1.539 B4Σ- 1.5685 C4Φ 1.6006 1.599 1.611 1.585 D4Σ+ 1.5387 E4Π 1.6553 1.632f F4Δ 1.7176 1.707f 1.720 1.724 1.718 a6Δ 1.6876 1.77±0.06b 1.712 1.693 1.690 1.718 b6П 1.6819 1.697 1.683 1.683 1.717 c6Σ+ 1.6917 1.688 1.694 1.688

Comparison of Calculated and Experimental Re 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)

Calculated State Frequency (cm-1)

Obs. CASSCFc MRCIc MRCI+Qc MRCPA(4)b +Qb LB c

+Q SPOIRd CIPSI

X4Δ 1744 1762a 1643 1672 1735 1778 1643 1701 A4П 2043 1695 1916 1782 1790 1916 1666 B4Σ- 1796 1875 1909 C4Φ 1393 1765f 1836 1853 1690 1628 1853 D4Σ+ 1971 1651 1688 E4Π 1548 1839 1890 F4Δ 1431 1499a 1538 1634 1498 1468 1634 a6Δ 1634 1620e 1482 1634 1629 1571 1638 1629 1564 b6П 1570 1542f 1388 1568 1573 1546 1570 1573 1602 c6Σ+ 1539 1372 1565 1569 1570 1565 1569

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)

7260-7430 cm-1

VH States: MRCI+Q/ANO/AVTZ

States X5Del 5Pi 5Sig+ 5Sig- 5Phi 3Del 3Pi 3Phi 3DelRe (Å) 1.7111 1.7386 1.8029 1.8480 1.8377 1.7319 1.7412 1.7006 1.7002Te (eV) 0.0000 0.2005 0.6246 0.7736 0.8571 0.7135 0.7373 0.7422 1.6804Te (cm-1) 0 1617 5038 6240 6913 5755 5947 5986 13553Frequency (cm-1) 1612 1589 1475 1436 1416 1548 1542 1534 1689Dipole moment (D) 2.5942 2.5168 4.6999 1.3635 1.2632 1.5469 1.3577 1.7512 2.1852Dipole deriv. (D/Å) 2.0403 1.7844 2.2536 3.6959 3.3605 2.0338 1.3051 1.3683 1.8763

X 5 5 5 5 5 3 3 3 3

7260-7430 cm-1

Laser-induced excitationfluorescence 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 9

Calculated State Dipole moment (D) Observed MRCPA(4)a SDCIb MCPFc

X4Δ 1.8993 2.61d 2.59 3.77 2.90 A4П 1.9193 2.82 B4Σ- 3.1047 C4Φ 3.0572 3.63 D4Σ+ 1.1037 E4Π 1.7508 F4Δ 0.3289 1.27d 2.43 a6Δ 0.8860 1.38 0.95 0.900 b6П 1.0328 1.32 c6Σ+ 0.9722 1.74 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

Calculated State Dipole deriv. (D/Å) MRCPA(4)a SDCIb MCPFc

X4Δ 0.2554 1.10 1.66 1.61 A4П 0.5807 1.17 B4Σ- 2.4434 C4Φ 2.2330 1.26 D4Σ+ 0.3573 E4Π 2.5239 F4Δ 2.0794 1.13 a6Δ 3.2115 1.07 1.79 1.67 b6П 3.0607 1.42 c6Σ+ 2.8568 2.10

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

4+ CAS(9,14) reference function: 80% 4, 10% 4+, 10% 4 SACAS(9,14) reference function

C(0) = 0.9469 C(0) = 0.9591

C(0) = 0.9785

Reference coefficients greater than 0.05 Reference coefficients greater than 0.05 a1 b1 b2 a2 coef. a1 b1 b2 a2 coef. 4 coef. 4+

CAS(9,14) CI coeffs.

Reference energy Reference energy Correlation energy Correlation energy MRCI STATE ENERGY MRCI STATE ENERGY Cluster corrected energy (Davidson) Cluster corrected energy (Davidson)

What is wrong with the B 4 and D 4 states? Look at D 4 case at R=1.55 Å…

9264 cm-1