1. Vibronic Perturbations in the Electronic Spectrum of Magnesium Carbide Phalgun Lolur*, Richard Dawes*, Michael Heaven + *Department of Chemistry, Missouri S&T, Rolla, MO. + Department of Chemistry, Emory University, Atlanta, GA.

2. Motivation Magnesium – a high performance material Interest in covalent bonding characteristics of IIA group metals –ns 2 configuration Challenge for ab initio theory models –Multi-configurational, multiple states in the energy range of interest Provide predictions for experimentalists –Comparison with the valence iso- electronic BeC system 2

3. Resonantly enhanced multiphoton ionization (REMPI) spectrum for BeC 3 Barker et al. J. Chem. Phys. 137, 214313 (2012) T: 3 3 Π - X 3 Σ − Q: 1 5 Π - 1 5 Σ −

4. Outline 1.Potential Energy Curves  Molecular states from atomic states 2.Diabatic transformation of adiabats  Vibronic states  Spectroscopic constants and lifetime of states. 3.Results and Conclusions 4

5. Magnesium – Atomic States 5 Source: http://physics.nist.gov/PhysRefData/ASD/levels_form.htmlhttp://physics.nist.gov/PhysRefData/ASD/levels_form.html

6. Carbon – Atomic States 6 Source: http://physics.nist.gov/PhysRefData/ASD/levels_form.htmlhttp://physics.nist.gov/PhysRefData/ASD/levels_form.html

7. Combining Mg ( 1 S, 3 P) + C ( 3 P, 1 D) in C 2V Symmetry MOLPRO was used to calculate the energies of these states Combining the states (with a cut off at 44,000 cm -1 ), – 1 (5A 1 +3B 1 +3B 2 +4A 2 ) – 3 (9A 1 +10B 1 +10B 2 +10A 2 ) – 5 (2A 1 +2B 1 +2B 2 +4A 2 ) 7

8. DW-AE-MRCI/CBS(3,4,5) R (Å) Energy (cm -1 ) Mg ( 1 S) + C ( 3 P) 3Σ-3Σ- 1 3 Π 2 3 Π 5Π5Π 4 3 Π 5Σ-5Σ- 3 3 Π 21867 cm -1 (21890 cm -1 ) 32071 cm -1 (32053 cm -1 ) Experimental atomic gaps from NIST are mentioned in parenthesis. Each state was individually optimized using dynamic weighting schemes. 8

9. Dynamic weighting in BeOBe 9 f(  E)  2/((exp(-  *  E)+ exp(  *  E))^2)

10. PECs of the triplet states 10 Mg ( 1 S) + C ( 3 P) 3Σ-3Σ- 1 3 Π 2 3 Π 3 3 Π 4 3 Π Mg ( 3 P) + C ( 3 P) Mg ( 3 P) + C ( 1 D) Strong coupling between states Diabatization of adiabats R (Å) Energy (cm -1 ) NACME COUPLING GAUSSIAN MODEL COUPLING

11. Electronic states of MgC 11 Mg ( 1 S) + C ( 3 P) 3Σ-3Σ- 1 3 Π 2 3 Π 3 3 Π 4 3 Π Mg ( 3 P) + C ( 3 P) Mg ( 3 P) + C ( 1 D) R (Å) Energy (cm -1 ) R (Å) 3Σ-3Σ- 1 3 Π 2 3 Π 3 3 Π 4 3 Π

12. Comparison of BeC and MgC electronic states 12 BeC MgC

13. Calculating the vibrational levels using the sine-DVR method V + T d T nd 13

14. Calculated vibrational levels on the X 3 Σ - electronic ground state vE(v)E(v)-E(0) (cm -1 ) 0293.140.00 1841.65548.51 21381.171088.03 31911.331618.19 42432.102138.96 52943.412650.26 63444.873151.72 73936.113642.97 84417.134123.99 94887.684594.54 105347.355054.21 115796.005502.86 14

15. Calculating the vibronic states on 4 3 Π states V1V1 V2V2 V3V3 V4V4 V 21 V 32 V 43 V 12 V 23 V 34 T1T1 T1T1 T2T2 T2T2 T3T3 T3T3 T4T4 T4T4 V 21 = V 12 V 32 = V 23 V 43 = V 34 V 31 = V 13 V 42 = V 24 V 1 = V Π1 +V rot – i*U The complex part of the eigenvalues relate to the width of states Franck Condon Factors from the ground state were computed. V 31 V 42 V 13 V 24 CAP 15

16. Favorable states for observation 16 LevelE(n)E(n)-ZPE(GS)1 3 Π %2 3 Π %3 3 Π %4 3 Π % ( )- 1/2 WidthFC (cm -1 ) (Å) (cm -1 ) 43 31153.9530860.810.0000.2180.41899.3641.976421.972725.16E-070.48 48 31757.3831464.240.0001.3521.22697.4212.005691.992531.86E-050.35 55 32402.9532109.810.0051.6311.27097.0942.014491.994002.60E-030.11 R (Å) Energy (cm -1 ) R (Å)

17. InteractionInteraction between states Uncoupled 4 3 Π Diabatic calculation Uncoupled 4 3 Π Adiabatic calculation Coupled four- state 3 Π Diabatic calculation (cm -1 ) 31154.9232187.0131153.95 31758.6133316.7531241.71 32401.3134211.9931339.49 33059.8835055.5731571.19 33695.1135844.5131614.09 34317.6736593.8331757.38 17 R (Å) Energy (cm -1 ) 41 %58 % % 4 3 Π - 99 %

18. Strongly mixed states still favorable for observation 18 LevelE(n)E(n)-ZPE(GS)1 3 Π %2 3 Π %3 3 Π %4 3 Π % ( )- 1/2 WidthFC (cm -1 ) (Å) (cm -1 ) 4431241.7230948.580.02041.21358.0480.7192.51052.4633 1.13E-05 0.152 4731614.3231321.180.26242.74255.9481.0482.56612.4947 2.58E-02 0.087 5332285.4031992.260.32650.86146.7542.0592.61772.5287 1.09E-01 0.097 5632587.0832293.940.02256.91742.3810.6812.66652.5806 7.84E-03 0.112 The above states have a significant level of mixing and narrow widths and Franck-Condon (FC) factors greater than 0.05

19. States with a significant level of mixing and FCFs more than 0.05 19 R (Å) Energy (cm -1 ) R (Å) Energy (cm -1 ) R (Å) Energy (cm -1 ) R (Å) Energy (cm -1 )

20. Spectroscopic constants  Ground state ZPE = 293.14 cm -1, ω e = 558.53 cm -1, ω e χ e = 4.76 cm -1  38 vibrational levels were identified on the ground state  94 vibrational levels were identified on the coupled Π states up to 42000 cm -1 20 StateReRe R0R0 DeDe BD (Å) (cm -1 ) X 3 Σ - 2.0592.06811922.171 1.927 6.00E-06 1 3 Π 2.2732.292 2229.446 1.740 1.03E-05 2 3 Π 1.8591.88016127.862 2.051 6.67E-06 3 3 Π 2.5962.610 6274.866 1.642 1.06E-05 4 3 Π 1.9611.97313149.273 1.897 5.96E-06

21. Conclusions Development of robust schemes to construct global potential energy surfaces –Compute all molecular states from first principles including all energetically relevant atomic states on an equal footing Calculate ro-vibrational states with predictive spectroscopic accuracy –Explain and Predict Spectra 21

22. Acknowledgements Dawes Research group: Richard Dawes Moumita Majumder Steve Ndengue Spencer Norman Andrew Powell Collaborator: Michael Heaven, Emory Department of Chemistry, Missouri S&T 22