Rotational Resonance

Problem

Create an alanine molecule using some reasonable assumptions about its geometry (use a z-matrix). Compute the R2 (rotational resonance) polarization exchange curves between CO and CA in a [CO,CA]-labeled sample and between CO and CB in a [CO,CB]-labeled sample for n=1 resonance (spinning frequency coincides with the chemical shift difference). Assume a1H 500 MHz spectrometer. Include in your simulation as many protons as you have time for to complete the simulation (either 4 or all 7). Assume that the CH3 and NH3 groups are hopping infinitely fast. Use a 100 kHz CW 1H decoupling field during the R2 exchange. Sample one point per rotor period. Start with the initial density matrix I1z – I2z.

Neglect the chemical shifts and CSA’s on protons and use the following 13C chemical shift parameters. Isotropic chemical shifts (ppm): 176.8 (CO), 50.9 (CA), 19.8 (CB). Chemical shift anisotropy (ppm): -71 (CO), -20 (CA) -12 (CB). Chemical shift asymmetry: 0.84 (CO), 0.44 (CA), 0.76 (CB). CSA orientation for the CO carbon: the most shielded direction is perpendicular to the sp2 plane; the least shielded direction is along the CO-CA bond. CSA orientation for the CA carbon: the most shielded direction is perpendicular to the H-CA-CB plane; the least shielded direction is 20º away from the H-CA bond towards the CA-CB bond. CSA orientation for the CB carbon: the most shielded direction is parallel to the CA-CB bond; the least shielded direction can be chosen as you please.

Hint: the most shielded direction coincides with the z principal component axis in all three CSA tensors above.

Repeat the simulations with a larger angles set for powder averaging. What can you say about the convergence?

 

Solution

Rotational Resonance simulation Rotational Resonance simulation
****** The System ***********************************
spectrometer(MHz)  500
spinning_freq(kHz) 10
channels           C13 H1
nuclei             C13 C13 H1 H1 H1 H1 H1 H1 H1
atomic_coords      *
cs_isotropic       176.8 50.9 19.8 0 0 0 0 0 0 0 ppm
csa_parameters     1 -71  0.84   0   0  0 ppm 1
csa_parameters     2 -20  0.44 -20   0  0 ppm 2
csa_parameters     3 -12  0.76   0 -90  0 ppm 3
j_coupling         *
quadrupole         *
dip_switchboard    *
csa_switchboard    *
exchange_nuclei    (4 5 6) (7 8 9)
bond_len_nuclei    *
bond_ang_nuclei    *
tors_ang_nuclei    *
groups_nuclei      (2 1 4) (7 2 3) (2 3 8)
******* Pulse Sequence ******************************
CHN 1
timing(usec)     (100)512
power(kHz)         0
phase(deg)         0
freq_offs(kHz)     0
CHN 2
timing(usec)      100
power(kHz)        100
phase(deg)         0
freq_offs(kHz)     0
******* Variables ***************************************
sys2ext_map=(["1 $n 7 8 9 10 11 12 13"])'
spinning_freq=cs_iso_$n-cs_iso_1
freq_1_1_1=(cs_iso_$n+cs_iso_1)/2
pulse_[1:2]_1_1=1000/spinning_freq
******* Options *****************************************
rho0               I1z-I2z
observables        I1z-I2z
EulerAngles        rep376
n_gamma            12
line_broaden(Hz)   *
zerofill           *
FFT_dimensions     *
options            -zxmatala.zxmat -re -xsysc3h10
*********************************************************
The option -macro'$n'= where  is either 2 or 3 must be
specified at the command line
ala.zxmat
C13 1
C13 2  1  1.50
C13 3  2  1.50  1  109.5
O   4  1  1.25  2  115.0  3  90  
O   5  1  1.25  2  115.0  3 -90
N   6  2  1.50  1  109.5  3  120
* H-CA
H1  7  2  1.10  1  109.5  3 -120
* H-CH3
H1  8  3  1.10  2  111.0  1  60
H1  9  3  1.10  2  111.0  1 -60
H1 10  3  1.10  2  111.0  1 180
* H-NH3
H1 11  6  1.09  2  111.0  1  60
H1 12  6  1.09  2  111.0  1 -60
H1 13  6  1.09  2  111.0  1 180