Vibrational Stark Effect: Theory and Analysis. NC State University

Transcription

1 Vibrational Stark Effect: Theory and Analysis NC State University

2 Vibrational Stark Effect Surface effect on bound ligands (interfacial) CO on metal surfaces Electrostatic environment in a protein (matrix) e-bound CO, NO, Artificial amino acid CN Applied electric field (capacitor) Nitrile and carbonyl groups in molecules

3 Systematic study of CO and CN vibrations Perform DT calculations of frequencies and potential energy surfaces based on the eigenvector projection of the relevant CO or CN stretching mode. Perform frequency calculations on geometry optimized structures at each electric field value and calculate the frequency. Calculate the anharmonic potential energy surface and anharmonic correction at each projected geometry.

4 Potential energy surface model Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

5 Compare potential surfaces Eliminate higher order terms using the device e b a U = 3 2 ) ( ) ( ) ( ) ( µ e b a U ) ( ) ( ) ( ) ( 3 2 = ) (1 ε = x x b = b 2 1 ) 3 1 ( 2 x a e a b x e a a = 2a e x x = The field-dependent coefficient and geometry changes are Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

6 A quadratic surface becomes non-harmonic in an applied field U ( ) µ ( ) = a ( ) 2 e 2 U ( ) = a ( ) e( ) Eliminate higher order terms using the device x = x(1 ε ) The field-dependent coefficient and geometry changes are a = a 1 x 1 x x = x (1 x) x = e 2a x Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

7 Anharmonic wavefunctions Energy (x1 3 ) (cm -1 ) Normal Coordinate Displacement Use Cooley-Numerov Algorithm to obtain eigenvalues and eigenfunctions for a polynomial model of PES Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

8 Calculation of the Stark tuning rate anharm geom tot µ µ µ = E E E = = µ A M M = ) ( Calculation of the transition polarizability χ χ 1 µ M = α χ χ = η µω α = = M M M M A χ χ χ χ χ χ χ χ Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

9 Correlation of µ Molecule Stark Tuning Rate Calculated A (cm -1 /(MV/cm) Stark Tuning Rate Calculated B (cm -1 /(MV/cm) Stark Tuning Rate A B Stark Tuning Rate Experimental (cm -1 /(MV/cm) C acetone CO D CN HCN E ACN BCN MVK NMP chlorobenzonitrile chlorobenzonitrile chlorobenzonitrile methoxybenzonitrile propionitrile butyronitrile valeronitrile hexanenitrile Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

10 Correlation of µ Experimental µ (cm -1 /MV/cm) Calculated µ (cm -1 /MV/cm) Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

11 Correlation of A A = 1 M1 χ χ1 M1 χ χ1 M1 χ χ1 M1 χ χ1 2 A (x1-4 ) A (x1-4 ) Molecule A (x1-4 ) (D/(MV/cm)) I (D/(MV/cm)) II (literature values) (D/(MV/cm) III acetone CO CN HCN IV ACN BCN MVK NMP chlorobenzonitrile chlorobenzonitrile chlorobenzonitrile methoxybenzonitrile propionitrile butyronitrile valeronitrile hexanenitrile Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

12 Correlation of A Brewer, S. H., ranzen, J. Chem. Phys. 23, 119,

13 DT case study CO in myoglobin Calculate frequencies of CO vibrations in various geometries Compare to experiment and determine calibration of frequency, bond length and Mulliken charge. A states - CO bound states. There are often multiple CO stretching frequencies. These have been attributed to specific interactions with residues such as histidine. B states - Photolyzed CO states. CO is trapped inside the protein and yet its frequency is shifted due to interactions with particular groups.

14 MbCO The peptide backbone is shown as a ribbon that follows the a-helical structure of myoglobin. The structure shown is at equilibrium. Conformational substates are called A states. Teng, Srajer, Moffat Nature Struct. Biol. (1994), 1, 71

15 Mb:CO The photoproduct. Iron moves out of the heme plane when CO is photolyzed. CO moves to a docking site and is parallel to the heme plane. Conformational substates are called B states.

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17 The origin of the A states is the hydrogen bonding conformations to CO

18 A view of the distal pocket Distal L29 V68 43 H64 Proximal Protein Data Bank 2MGK

19 Wild-type has multiple CO bands Distal L29 V68 43 H64 uillin, Phillips et al. JMB 1993, 234, Proximal

20 Distal histidine is key Distal L29 V68 43 H64 Proximal

21 The substrate of DHP binding site is in the heme pocket The enzyme dehaloperoxidase also provides an interesting case Study. Since the substrate can bind in an internal binding pocket One can see effects of the substrate on bound CO frequencies. Bound substrate Lebioda et al., J.Biol.Chem. (2) 275, 18712

22 A-state and B-state CO vibrations in DHP

23 DT computational study of ν CO The interpretation of the frequency shifts of bound CO in terms of the electrostatic environment in the heme pocket has been studied by DT calculation of various hydrogen bonding geometries (shown in the following pages) compared to calculation of the frequency in an applied electric field. The results permit comparison of the experimentally measured Stark tuning rate with the frequency shifts observed in mutant myoglobins and DHP. Model porphine complex ranzen JACS, 22, 124, 13271

24 DT calculation of ν CO frequencies Multiple hydrogen bonding interactions

25 DT calculation of ν CO frequencies Single hydrogen bonding interaction

26 DT calculation of ν CO frequencies No hydrogen bonding interaction

27 DT calculation in an applied electric field ranzen JACS, 22, 124, 13271

28 Electric field effect by DT MV/cm e-c C-O q C q O q C q O q C -q O ν CO Eqn. 1 ν CO Eqn. 2 ν CO Eqn Correlation is based on distance or Mulliken charge. ν CO = (R CO -R CO ) (1) ν CO = { (q C q O )} cm -1 (2)

29 DT calculation of ν CO frequencies Stark tuning rate is 2.4 cm -1 /(MV/cm). This is value predicted from correlations shown on right. Park and Boxer JPC 1999, 13, 913 ranzen JACS, 22, 124, 13271