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, 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"] fig_title="Linear-Ramp Cross-Polarization in C$_1$H$_3$ Spin System" ******* Options ************************************* rho0 F2x observables I1x EulerAngles rep376 n_gamma 5 line_broaden(Hz) * zerofill * FFT_dimensions * options -zxmatrampcp.zxmat -re -py
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 time/0:0.03:2/ pulse_[1:2]_1=1000*time/30 sys2ext_map=["1 3 4 5"] fig_title="Linear-Ramp Cross-Polarization in C$_1$H$_3$ Spin System" ******* Options ************************************* rho0 F2x observables I1x EulerAngles rep376 n_gamma 5 line_broaden(Hz) * zerofill * FFT_dimensions * options -zxmatrampcp.zxmat -re -reframpcp1 -py
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
****** 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")
sys2ext_map=["1 3 4 5"]
power_1_1=50+(0:29)*6/29
power_2_1=63
time=2
pulse_[1:2]_1=1000*time/30
rep2000=(load("rep2000.dat"))'
scan_par i/1:2000/
euler_CR(1:2,1)=rep2000(1:2,i)
fig_options ="--hist 25 --colorsx navy"
x_label = "$^{13}$C polarization after CP"
fig_title="Histogram of ramped CP efficiency for a set of 2000 crystallite orientations"
******* Options *************************************
rho0 F2x
observables I1x
EulerAngles *
n_gamma *
line_broaden(Hz) *
zerofill *
FFT_dimensions *
options -zxmatrampcp.zxmat -re -py