Vibrational Stark Effect: Theory and Analysis NC State University
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
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.
Potential energy surface model Brewer, S. H., ranzen, J. Chem. Phys. 23, 119, 851-858
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, 851-858
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, 851-858
Anharmonic wavefunctions Energy (x1 3 ) (cm -1 ) 12 8 4 -.4 -.2..2.4 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, 851-858
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 2 1 1 = η µω α = = M M M M A 1 1 1 1 1 1 1 1 2 1 χ χ χ χ χ χ χ χ Brewer, S. H., ranzen, J. Chem. Phys. 23, 119, 851-858
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.253.437.69.756 CO.1.457.467.429 D CN -.19.24.223 ----- HCN.49.49.98 ----- E ACN.68.272.34.433 BCN.97.418.515.66 MVK.214.398.612.823 NMP.262.76.968 1.142 4-chlorobenzonitrile.126.554.68.584 3-chlorobenzonitrile.97.48.55.534 2-chlorobenzonitrile.97.359.456.514 4-methoxybenzonitrile.146.63.749.835 propionitrile.78.321.399.465 butyronitrile.97.34.437.475 valeronitrile.88.321.49.448 hexanenitrile.97.369.466.47 Brewer, S. H., ranzen, J. Chem. Phys. 23, 119, 851-858
Correlation of µ Experimental µ (cm -1 /MV/cm) 1..8.6.4.4.5.6.7.8.9 Calculated µ (cm -1 /MV/cm) Brewer, S. H., ranzen, J. Chem. Phys. 23, 119, 851-858
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 2.81 2.5 ----- CO 16.5 16.6 ----- CN - 37.45 37.46 ----- HCN 5.81 5.9 ----- IV ACN 6.61 6.63 17.7 BCN 17.1 17.1 33.4 MVK 4.2 1.33 ----- NMP 2.5 2.3 ----- 4-chlorobenzonitrile 2.91 21.28 32.3 3-chlorobenzonitrile 18.26 18.43 27.4 2-chlorobenzonitrile 15.4 15.38 29. 4-methoxybenzonitrile 21.31 21.85 16.3 propionitrile 7.28 7.29 17.3 butyronitrile 8.4 8.4 17.7 valeronitrile 8.54 8.54 7.67 hexanenitrile 8.86 8.86 8.34 Brewer, S. H., ranzen, J. Chem. Phys. 23, 119, 851-858
Correlation of A Brewer, S. H., ranzen, J. Chem. Phys. 23, 119, 851-858
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.
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
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.
The origin of the A states is the hydrogen bonding conformations to CO
A view of the distal pocket Distal L29 V68 43 H64 Proximal Protein Data Bank 2MGK
Wild-type has multiple CO bands Distal L29 V68 43 H64 uillin, Phillips et al. JMB 1993, 234, 14-155 Proximal
Distal histidine is key Distal L29 V68 43 H64 Proximal
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
A-state and B-state CO vibrations in DHP
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
DT calculation of ν CO frequencies Multiple hydrogen bonding interactions
DT calculation of ν CO frequencies Single hydrogen bonding interaction
DT calculation of ν CO frequencies No hydrogen bonding interaction
DT calculation in an applied electric field ranzen JACS, 22, 124, 13271
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. 2-1 1.7864 1.1569.19 -.237 -.47.427 221.4 221.8 215.7 -.5 1.7865 1.1572.19 -.238 -.48.428 218.7 22.3 215. 1.7861 1.1572.19 -.239 -.49.429 218.7 218.9 214.5.5 1.7861 1.1573.19 -.239 -.49.429 217.9 218.8 214.5 1 1.7858 1.1575.19 -.24 -.5.43 216.2 217.3 213.8 Correlation is based on distance or Mulliken charge. ν CO = 2168 8677 (R CO -R CO ) (1) ν CO = {294 1535(q C q O )} cm -1 (2)
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