Ramped CP

Problem

Simulate a ramped cross-polarization (CP) from 1H to 13C and study how the degree of polarization transfer depends on the contact time (the duration of the ramp). Try to understand the results. Can this be described using a cross-relaxation matrix approach?

Assume the following conditions for your simulation. Make a linear ramp with the 13C RF field changing in 30 steps from 50 to 56 kHz and 1H field constant at 63 kHz. Use a spin system of one carbon and three protons: one directly bonded (1.1 Å distance), and the other two from a CH2 group directly bonded to the carbon (use a z-matrix). Neglect the chemical shifts. Set the spinning frequency to 10 kHz. Run the simulation with the option -t0 to disable the “turbo” algorithm; this will make the computations somewhat faster.

There are at least two ways to simulate this experiment: (1) using a 1D pulse sequence and no scan parameters and (2) using a 0D pulse sequence and a scan parameter. Make both versions. Verify that you get identical results in both cases. Which version works faster? Can you figure out why? Does the answer depend on the duration of the ramp? Make another input file to study the dependence of the polarization transfer on the crystallite orientation for a fixed contact time; use a 2 ms ramp for this simulation.

 

Solution

Ramped CP (cross-polarization) simulation

Ramped CP, version 1

****** The System ***********************************
spectrometer(MHz)  400                                                  
spinning_freq(kHz) 10
channels           C13 H1
nuclei             C13 H1 H1 H1
atomic_coords      *
cs_isotropic       *
csa_parameters     *
j_coupling         *
quadrupole         *
dip_switchboard    *
csa_switchboard    *
exchange_nuclei    *
bond_len_nuclei    *
bond_ang_nuclei    *
tors_ang_nuclei    *
groups_nuclei      *
******* Pulse Sequence ******************************
CHN 1
timing(usec)       [(0)64]30
power(kHz)         [0]30
phase(deg)         [0]30
freq_offs(kHz)     [0]30
CHN 2
timing(usec)       [(0)]30
power(kHz)         [0]30
phase(deg)         [0]30
freq_offs(kHz)     [0]30
******* Variables ***********************************
power_1_[1:30]_1=50+[0:29]*6/29
power_2_[1:30]_1=63
pulse_1_[1:30]_1=1
pulse_2_[1:30]_1=1
sys2ext_map=(["1 3 4 5"])'
******* Options *************************************
rho0               F2x
observables        I1x
EulerAngles        rep376
n_gamma            5
line_broaden(Hz)   *
zerofill           *
FFT_dimensions     *
options            -zxmatrampcp.zxmat -re -t0
 

Ramped CP, version 2

****** The System ***********************************
spectrometer(MHz)  400                                                  
spinning_freq(kHz) 10
channels           C13 H1
nuclei             C13 H1 H1 H1
atomic_coords      *
cs_isotropic       *
csa_parameters     *
j_coupling         *
quadrupole         *
dip_switchboard    *
csa_switchboard    *
exchange_nuclei    *
bond_len_nuclei    *
bond_ang_nuclei    *
tors_ang_nuclei    *
groups_nuclei      *
******* Pulse Sequence ******************************
CHN 1
timing(usec)       [0]30
power(kHz)         [0]30
phase(deg)         [0]30
freq_offs(kHz)     [0]30
CHN 2
timing(usec)       [0]30
power(kHz)         [0]30
phase(deg)         [0]30
freq_offs(kHz)     [0]30
******* Variables ***********************************
power_1_1=50+(["0:29"])'*6/29
power_2_1=63
scan_par ctime/0:0.03:2/
pulse_[1:2]_1=1000*ctime/30
sys2ext_map=(["1 3 4 5"])'
******* Options *************************************
rho0               F2x
observables        I1x
EulerAngles        rep376
n_gamma            5
line_broaden(Hz)   *
zerofill           *
FFT_dimensions     *
options            -zxmatrampcp.zxmat -re -t0 -v1
rampcp.zxmat
C13 1
C13 2 1 1.5
H1  3 2 1.1 1 109.47
H1  4 2 1.1 1 109.47 3 120
H1  5 1 1.1 2 109.47 3 60
 

Ramped CP: efficiency variation with the crystallite orientation

  rampcp - hist
****** The System ***********************************
spectrometer(MHz)  400                                                  
spinning_freq(kHz) 10
channels           C13 H1
nuclei             C13 H1 H1 H1
atomic_coords      *
cs_isotropic       *
csa_parameters     *
j_coupling         *
quadrupole         *
dip_switchboard    *
csa_switchboard    *
exchange_nuclei    *
bond_len_nuclei    *
bond_ang_nuclei    *
tors_ang_nuclei    *
groups_nuclei      *
******* Pulse Sequence ******************************
CHN 1
timing(usec)       [0]30
power(kHz)         [0]30
phase(deg)         [0]30
freq_offs(kHz)     [0]30
CHN 2
timing(usec)       [0]30
power(kHz)         [0]30
phase(deg)         [0]30
freq_offs(kHz)     [0]30
******* Variables ***********************************
*save(euler_CR',"rep376.dat")
rep376=(load("rep376.dat"))'
sys2ext_map=(["1 3 4 5"])'
power_1_1=50+(["0:29"])'*6/29
power_2_1=63
scan_par i/1:376/
ctime=2
pulse_[1:2]_1=1000*ctime/30
euler_CR(["1:2"],1)=rep376(["1:2"],i)
******* Options *************************************
rho0               F2x
observables        I1x
EulerAngles        *
n_gamma            *
line_broaden(Hz)   *
zerofill           *
FFT_dimensions     *
options            -zxmatrampcp.zxmat -re -t0