1
Observation of proximities between spin-1/2 and quadrupolar nuclei: which hetero-nuclear
dipolar recoupling method is preferable?
X. Lu, O. Lafon,* J. Trébosc, G. Tricot, L. Delevoye, F. Méar, L. Montagne, J.P. Amoureux*
UCCS (CNRS-8181), Lille North of France University, Villeneuve d’Ascq 59652, France
I.
Figures S1 to S11.
II. Demonstration of Eq.7.
III. Interferences from terms proportional to appI(t)
IV. Demonstration of Eq.10 for SFAM-1reg.1
V. Implementation of the pulse sequence in Fig.1a.
2
Fig.S1. Variations of (a) app, x (Eq.S8), (b) app, y (Eq.S7), (c) ωappI and (d) ωappI / C1 as function
max
max
of  nutI
and  refI
for SFAM-1, with R = 20 kHz. The contour lines are spaced by 0.8 from -8 (clear
blue) to +8 (red) in (a) and (b), from 0.8 (clear blue) to 20 (red) in (c), from 0.8 (clear blue) to 80
max
max
(red) in (d). In (d), the dashed black straight line corresponds to nutI
( = 1), the dotted
 refI
max
max
yellow lines to refI  nutI R and nutI
 refI
R , the dotted-dashed yellow lines to
max
max
max
max
max
max
refI
 2 nutI
R and nutI
 2 refI
R , and the white zones to ωappI / C1 > 80. In (d), high
efficiency is observed in the blue zones, which correspond to small ωappI / C1 values.
3
Fig.S2. Trajectories of I-spin magnetization during the basic element of SFAM-1 irradiation, which
lasts one TR. Only the rf-field interaction is considered and R = 20 kHz. At t = 0, the magnetization
max
max
points in the B0 direction, i.e. the +z-axis. The trajectories are presented for ( nutI
,  refI
) = (a)
(31,0) kHz = (1.5,0)R (no frequency sweep); (b) (31,15) kHz = (1.5,0.75)R = SFAM-1reg.1; (c)
(50,70) kHz = (2.5,3.5)R = SFAM-1reg.2; (d) (100, 96) kHz = (5,4.8)R = SFAM-1reg.2. In opposite to
(b-d), conditions (e) (60,20) kHz = (3,1)R and (f) (15,40) kHz = (0.75,2)R, do not lead to an efficient
recoupling. These figures show that SFAM-1 is only efficient when its basic element is cyclic: the Ispin magnetization comes back to its initial orientation along the +z-axis every TR. Conversely, low
recoupling efficiency is obtained when after TR the SFAM-1 irradiation tilts the I-spin magnetization
max
max
max
max
either into the transverse plane (  refI
, (e)), or along –z (  refI
, (f)). As all the
  nutI
  nutI
elements of SFAM-1 are identical, the inversion of the I-spin magnetization each TR produces a
hetero-nuclear decoupling, instead of a recoupling. It must be noted that the trajectories of this
figure open an avenue for the design of symmetry-based recoupling methods built from basic
elements combining simultaneous amplitude and carrier frequency modulations.38 Trajectories were
calculated and plotted using the Spin-Dynamica code for Mathematica, programmed by M.H. Levitt,
available at www.spindynamica.soton.ac.uk.
4
Fig.S3. Simulated efficiency of
max
max
Al-{31P} D-HMQC using SFAM-1, as function of  nutI
and  refI
,
27
0
with  31P
= CSA31P = 0, at R = 10 (a), 20 (b), 40 (c) and 60 (d) kHz. The other parameters are
max
max
identical to those of Fig.4a. The straight dashed blue lines correspond to  nutI
=  refI
( = 1).
Fig.S4. Simulated efficiency of
27
Al-{31P} D-HMQC using (a) SFAM-1 and (b) SFAM-2, as function of
max
0
max
 nutI
and  refI
, with  31P
= CSA31P = 0, and R = 20 (a) or 10 (b) kHz, with  = 5 (a) or 7.2 (b) ms.
5
Fig.S5. Simulated efficiency of 27Al-{31P} D-HMQC using (a) SFAM-1 and (b) SFAM-2, as function of
max
0
max
 nutI
and  refI
, with  31P
= CSA31P = 0, and R = 40 (a) or 20 (b) kHz, with  = 5 (a) or 7.2 (b) ms.
Fig.S6. Simulated efficiency of
Al-{31P} D-HMQC of Na7(AlP2O7)4PO4 versus recoupling time ,
27
with R = 20 kHz and CSA27Al = 0. The recoupling sequence is SR 412 (▲), SFAM-1reg.1 (♦), SFAMmax
max
1reg.2 (■) and SFAM-2reg.1 (●). ( nutI
,  refI
) = (30,5), (50,70), (60,10) kHz for SFAM-1reg.1, SFAM-
1reg.2 and SFAM-2reg.1, respectively. The spin system consists in one aluminum atom above a regular
tetrahedron of four phosphorous. The
31P/(2)|=
27
Al nucleus was dipolar coupled to a single
31
P with |b27Al-
409 Hz, whereas all the four phosphorous atoms are coupled to each other with identical
dipolar coupling constant of |b31P-31P/(2)| = 800 Hz. The quadrupolar parameters of
27
Al were CQ =
5.33 MHz, ηQ = 0.43, and this interaction was considered to the second order. The angle between
quadrupolar and dipolar tensors was  = 120°. The recoupling sequence has always been applied
to the non-observed channel (Fig.1a). The irradiation on
27
Al channel has always been applied on-
resonance, including the quadrupolar induced shift in the S channel.
6
Fig.S7. Normalized experimental efficiency of
27
Al-{31P} D-HMQC of Na7(AlP2O7)4PO4 versus
recoupling time , with R = 20 kHz at 18.8T on a 3.2mm probe. The recoupling sequences are
SR 412 (
), SFAM-1reg.1 (
), SFAM-1reg.2 (
),SFAM-2reg.1 (
) and SFAM-2reg.2 (
max
max
). ( nutI
,  refI
) = (30,10), (40,60), (60,15), (80,80) kHz for SFAM-1reg.1, SFAM-1reg.2, SFAM-
2reg.1 and SFAM-2reg.2, respectively. Intensities are extracted from integration of the single
27
Al site in
1D spectrum.
Fig.S8. Experimental buildup stack plot of
Al-{31P} D-HMQC of Al(PO3)3 (monoclinic) [1-2] with R
27
= 20 kHz at 18.8T on a 3.2mm probe. The recoupling sequences are SFAM-1reg.2 (right red peak),
max
max
and SFAM-2reg.1 (left black peak) with ( nutI
,  refI
) = (60,60) kHz for both.
Al T2’ is about 3.2 ms.
27
1 - Z. Kanene, Z.A. Konstant, V. Krasnikov, Neorg. Mat. 21 9 (1985) 1552.
2- G. Tricot, D. Coillot, E. Creton, L. Montagne, J. Eur. Ceram. Soc. 28 (2008) 1135–1141.
7
Fig.S9. Scheme of the chemical structure of Na7(AlP2O7)4PO4 around the Al site.
8
Fig.S10. 2D D-HMQC spectrum of Na7(AlP2O7)4PO4 recorded at R = 20 kHz on 3.2mm triple
resonance probe and AVANCE-III 18.8T spectrometer. 27Al Slices for the three 31P sites are
max
extracted from 2D spectrum recorded using SR 412 (nutI = 40 kHz,  = 1.6ms), SFAM-2 reg1 ( nutI =
max
max
57 kHz,  refI
= 20 kHz, = 1.6ms) and SFAM-1reg1 ( nutI = 29 kHz,  refI
= 20 kHz, = 0.8 ms)
max
recoupling schemes. Distortions depend on the relative angle between dipolar and quadrupolar
tensors, and they are characteristic of the recoupling sequence. SR 412 and SFAM-2 that are
formally identical exhibit similar line-shapes and intensities.
9
Fig.S11. Schematic of the orientations in I spin-space of the contributions to first-order Hamiltonian
for SFAM-1reg.1. The analytical expressions for the Hamiltonians of DIS, CSAI, frequency modulation,
 I0 and JIS coupling are given by Eqs.10, and S14 to S20.
II Demonstration of Eq.7
From Eqs. 1, 3 and 4, it is possible to show that



max
max
max
max
inf nutI
, refI
 effI (t )  sup nutI
, refI

(S1)
where inf and sup denote the infimum and supremum. Eqs. 5 and S1 entail that
max
max
nutI
refI
N R
max
max
sup nutI
, refI

2
 appI (t ) 
max
max
nutI
refI
NR
max
max
inf nutI
, refI

2
(S2)
Therefore, the condition effI(t) >> appI(t),5 is fulfilled when
max
max
max
max
nutI
refI
NR  inf nutI
, refI

3
(S3)
which can be recast as
max
max
refI
NR  nutI

max
max
when nutI
and
 refI
2
(S4)
10
max
max
nutI
NR   refI

2
(S5)
max
max
when refI
. Eqs. S4 and S5 can then be recast as Eq.7.
 nutI
III Interferences from terms proportional to appI(t)
Expanding the theoretical description of SFAM-N introduced by Fu et al.,5 it can be shown that the
term proportional to appI(t) contributes to the first-order average Hamiltonian by
Hˆ app
(1)
 appI, y Iˆy  appI, x Iˆx
(S6)
where
appI, y 
N
r
r / N

0
appI t  cos effI t  dt
(S7)
appI t sin  effI t  dt
(S8)
and
appI, x 
N
r
r / N

0
The angle  effI t  is defined by
effI t    effI t ' dt '
t
(S9)
0
We also define the norm

2
2
ωappI  appI
, x  appI , y

1/ 2
(S10)
max
max
The variations of appI, x , appI, y , ωappI and ωappI / C1 as function of  nutI
and  refI
are displayed
in Fig.S1. The value ωappI / C1 provides an estimation of the relative magnitude of Ĥ app
Eq.S6 and Hˆ D ,IS
(1)
(1)
given by
given by Eq.15. The SFAM-1reg.2 recoupling mechanism corresponds to the
max
max
regions where ωappI / C1 is small. Globally, ωappI / C1 decreases when both nutI
and refI
increase. Furthermore, most of the SFAM-1reg.2 regions are enclosed within the boundaries
max
max
max
max
refI
 nutI
R and nutI
 refI
R . Conversely there are some regions within this
boundaries where SFAM-1reg.2 recoupling cannot be achieved owing to interferences of Ĥ app
max
max
These interferences occur especially for  nutI
and
  refI
     
max 2
nutI
max 2
refI
     
max 2
nutI
max 2
refI
(1)
.
/ R  k i.e.
/ R  63, 126 and 188 kHz (see Fig.S1). Note that these regions also
correspond to the zeros of Eq.14 showing the link between SFAM-1reg.1 and SFAM-1reg.2. The
11
max
max
max
max
boundaries refI
 2 nutI
R and nutI
 2 refI
R exclude most of the interferences but also
max
max
some regions of low nutI
and refI
frequencies, where the SFAM-1reg.2 recoupling is efficient.
Therefore, the criterion of Eq.7 is not accurate enough for the practical optimization of SFAM-1reg.2
max
recoupling at R = 20 kHz and  nutI
< 100 kHz. Conversely Fig.S1d shows that there are no
(1)
interference of Ĥ app
max
max
for 40 kHz   nutI
 100 kHz, when  refI
is chosen according to Eq.17.
Nevertheless, Fig.S1d shows that there are regions where SFAM-1reg.2 recoupling is efficient even if
Eq.17 is not valid. Finally note that the other undesired terms in the average Hamiltonian
proportional to bIS 2Iˆx Sˆz and bIS 2 Iˆy Sˆ z are usually smaller than Hˆ D ,IS
(1)
by a factor of 10 and can be
disregarded.
IV Demonstration of Eq.10 for SFAM-1reg.1
The demonstration of Eq.10 for SFAM-1reg.1 follows the derivation of the first-order average
Hamiltonian for SFAM-2reg.1, which has been presented in the Supporting Information of ref.[6b]. For
the SFAM-1reg.1 recoupling, the frequency sweep is small compared to the rf-amplitude and this
recoupling can be described as a C110 sequence using as basic cyclic element a sine modulated rf
pulse. The carrier frequency modulation is included in the internal interaction Hamiltonian. For a
C110 sequence, the symmetry does not restrain the number of terms in the average Hamiltonian: all
combination of quantum numbers {l,m, ,} are symmetry-allowed. Therefore, the contributions to
first-order average Hamiltonian have to be calculated using:
(1)
̅̅̅̅
̂Λ = 1 ∫𝜏𝑟 𝑅𝐼𝑥 [−𝛽𝑟𝑓𝐼 (𝑡)]𝐻
̂Λ (𝑡) 𝑅𝐼𝑥 [−𝛽𝑟𝑓𝐼 (𝑡)]𝑑𝑡
𝐻
𝜏 0
𝑟
(S11)
(1)
̂Λ is the contribution of Hamiltonian 𝐻
̂Λ (𝑡) corresponding to the spin interaction .
where ̅̅̅̅
𝐻
𝑅𝐼𝑥 [−𝛽𝑟𝑓𝐼 (𝑡)] = exp[𝑖𝛽𝑟𝑓𝐼 (𝑡)𝐼𝑥 ] with 𝐼𝑥 = ∑𝑛𝑘=1 𝐼𝑘𝑥 is the operator for the rotation of I spins 1 to n
through the angle −𝛽𝑟𝑓𝐼 (𝑡) around the x-axis. The tilt angle 𝛽𝑟𝑓𝐼 (𝑡) is defined as
𝜏
𝛽𝑟𝑓𝐼 (𝑡) = ∫0 𝑅 𝜔𝑛𝑢𝑡𝐼 (𝑡)𝑑𝑡
(S12)
where 𝜔𝑛𝑢𝑡𝐼 (𝑡) is defined in Eq.1. The CSAI and I-S dipolar interactions evolve identically under
sample rotation and the rf irradiation of a I channel. Therefore, their contributions to the first-order
average Hamiltonian have similar forms. Using Eqs. S11 and S12, we found that the hetero-nuclear
dipolar coupling between a pair of nuclei I-S and the CSAI contributes to first-order average
Hamiltonian by
(1)
̅̅̅̅
̂Λ = ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=1 + ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=2
𝐻
𝐻
𝐻
Λ
Λ
(S13)
12
̅̅̅̅̅̅̅̅̅
̂ |𝑚|=1 and
where  = D,IS for hetero-nuclear dipolar interaction and  = CSA,I for CSAI. The terms, 𝐻
Λ
̅̅̅̅̅̅̅̅̅
̂ |𝑚|=2 , correspond to the contributions of space components, |m| = 1 and 2 of the recoupled
𝐻
Λ
̅̅̅̅̅̅̅̅̅
̂ |𝑚|=1 term is given by Eq.10, whereas the ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=2 has the following expression
interaction. The 𝐻
𝐻
𝐷,𝐼𝑆
𝐷,𝐼𝑆
̅̅̅̅̅̅̅̅̅
|𝑚|=2
̂ |𝑚|=2 = 𝜔𝐷,𝐼𝑆
𝐻
[cos(𝜓)2𝐼̂𝑧 𝑆̂𝑧 + sin(𝜓)2𝐼̂𝑦 𝑆̂𝑧 ]
𝐷,𝐼𝑆
(S14)
̅̅̅̅̅̅̅̅̅
𝑚=2
̂ |𝑚|=1 and ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=2 terms are given by
where 𝜔𝐷,𝐼𝑆
is given by Eq.12 and  = -J2()/2. The 𝐻
𝐻
𝐶𝑆𝐴,𝐼
𝐶𝑆𝐴,𝐼
̅̅̅̅̅̅̅̅̅
|𝑚|=1
̂ |𝑚|=1 = 𝜔𝐶𝑆𝐴,𝐼
𝐻
[sin(𝜓)𝐼̂𝑧 − cos(𝜓)𝐼̂𝑦 ]
𝐶𝑆𝐴,𝐼
(S15)
̅̅̅̅̅̅̅̅̅
|𝑚|=2
̂ |𝑚|=2 = 𝜔𝐶𝑆𝐴,𝐼
𝐻
[cos(𝜓)𝐼̂𝑧 + sin(𝜓)𝐼̂𝑦 ]
(S16)
and
𝐶𝑆𝐴,𝐼
with
𝑅
|𝑚|=𝑘
0
𝜔𝐶𝑆𝐴,𝐼 = 𝜅 |𝑚|=𝑘 Re {[𝐴𝐶𝑆𝐴,𝐼
2|𝑚| ] exp[−𝑖𝑚(𝛼𝑅𝐿 − 𝜔𝑟 𝑡0 )]}
(S17)
and the scaling factor  m 1  2 J1   / 3 and m = -2J2()/3. In Eq.S17, Re denotes the real part
𝑅
of a complex number, [𝐴𝐶𝑆𝐴,𝐼
2|𝑚| ] is the space component m = k with k = 1 or 2 of interaction CSAI with
𝑅
space rank l = 2, expressed in the rotor-fixed frame, R. The expressions of [𝐴𝐶𝑆𝐴,𝐼
2|𝑚| ] can be found in
ref. [6b]. The carrier frequency modulation contributes to the first-order average Hamiltonian by
̅̅̅̅̅̅̅
𝑚𝑎𝑥
̂𝑟𝑒𝑓,𝐼 = −Δ𝜔𝑟𝑒𝑓,𝐼
𝐻
𝐽1 (𝜓)[sin(𝜓)𝐼̂𝑧 − cos(𝜓)𝐼̂𝑦 ] .
(S18)
The contribution of isotropic chemical shift is
̅̅̅̅̅
̂ 0 = 2𝜋𝜈𝐼0 𝐽0 (𝜓)[cos(𝜓)𝐼̂𝑧 + sin(𝜓)𝐼̂𝑦 ]
𝐻
𝜈𝐼
(S19)
and that of hetero-nuclear JIS coupling has the following form
̅̅̅̅̅̅
̂𝐽,𝐼𝑆 = 2𝜋𝐽𝐼𝑆 𝐽0 (𝜓)[cos(𝜓)𝐼̂𝑧 + sin(𝜓)𝐼̂𝑦 ]
𝐻
(S20)
The SFAM-1reg.1 sequence also reintroduces the homo-nuclear dipolar interactions between I nuclei.
However, the expression of this recoupled interaction will not be given here. Fig.S8 summarizes the
orientations in I spin space of the contributions to first-order Hamiltonian for DIS coupling, CSAI,
frequency modulation, 𝜈𝐼0 and JIS coupling for SFAM-1reg.1 sequence. From Fig.S8, it is obvious that
̅̅̅̅̅̅̅̅̅
̅̅̅̅̅
̂ |𝑚|=1 , ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=1 and ̅̅̅̅̅̅̅
̂𝑟𝑒𝑓,𝐼 do not commute with ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=2 , ̅̅̅̅̅̅̅̅̅
̂ |𝑚|=2 , 𝐻
̂ 0 and ̅̅̅̅̅̅
̂𝐽,𝐼𝑆 . In particular, the
𝐻
𝐻
𝐻
𝐻
𝐻
𝐻
𝐷,𝐼𝑆
𝐶𝑆𝐴,𝐼
𝐷,𝐼𝑆
𝐶𝑆𝐴,𝐼
𝜈
𝐼
̅̅̅̅̅̅̅̅̅
̂ |𝑚|=1 , but commutes neither with the space components |m|
frequency modulation commutes with 𝐻
𝐷,𝐼𝑆
= 2 of DIS, CSAI nor with the isotropic chemical shift or JIS coupling. Therefore, when Eq.8 is valid,
̅̅̅̅̅̅̅̅̅
̂ |𝑚|=1 and we obtain
the recoupled dipolar interaction for SFAM-1reg.1 sequence is restricted to 𝐻
𝐷,𝐼𝑆
Eq.10. The above theoretical treatment explains how the frequency modulation in SFAM-1reg.1
recoupling improves the robustness to offset and suppresses the JIS coupling. Nevertheless, in
13
SFAM-1reg.1 recoupling, the frequency modulation is limited by the fulfillment of the conditions
max
max
max
max
 1.57R . Hence, refI
and nutI
cannot exceed a fraction of R and SFAM-1reg.1 is
nutI
 refI
not robust for resonance offset larger than this fraction of R.
V. Implementation of Fig. 1.a) pulse sequence.
Note : the pulse program requires include files that can be found at :
http://rmn800.univ-lille1.fr/pp/includesJT/decouple.incl
http://rmn800.univ-lille1.fr/pp/includesJT/presat.incl
;hmqcIR.jt
; hmqc with indirect dipolar recoupling
; ---------------; DESCRIPTION :
; hmqc experiment using SFAM (simultaneous frequency and
; amplitude modulation) or SR4 to generate heteronuclear multiple
; quantum correlation spectra
; you need to run SFAM AU program to generate correct shape pulse
;
;AUTHOR
; Julien TREBOSC
;$COMMENT=HMQC with dipolar recoupling on indirect channel
;$CLASS=Solids
;$DIM=2D
;$TYPE=
;$SUBTYPE=
;$OWNER=Trebosc
; -----------;PARAMETERS:
;ns : 8*n min, 32*n max
;d1 : recycle delay
;pl1 : =119 dB, not used
;pl21 : RF power level p3/p4
;pl3 : RF power level p1
;pl23 : SFAM/SR4 power level
;p3 : 90 degree pulse @ pl21
;p4 : 180 degree pulse @ pl21
;p1 : 90 degree pulse @pl3
;p16 : SFAM/SR4 dipolar recoupling time
;cnst3 : shape pulse resolution in ns (300ns)
;cnst30 : SFAM offset amplitude
;cnst31 : =MAS spin rate
;cnst0 : factor for second pulse
;l3 : SFAM mode (l3=1 or 2 for homo dipol decoupl)
;FnMODE : States or States-TPPI
;
;ZGOPTNS : PRESAT decF3 decF2t1 decF2aq _DFS
; PRESAT : send presaturation pulses on F1 can be replaced with DS=1 or 2
; decF3 : applyies decoupling during aq on F3
; decF2aq : applyies decoupling during aq on F2 (1H)
; decF2t1 : applyies decoupling during t1 on F2 (1H)
; _SR4 : use SR4 recoupling
; _SFAM : use _SFAM recoupling (default)
; _DFS : add DFS enhancement pre-pulse
;*********************** PRESAT *****************
#ifdef PRESAT
#include "presat.incl"
#else
#define PRESAT1(f1)
#define presatPH
#endif
#ifdef decF3
#define dec
#define decF3on cpds3:f3
#define decF3off do:f3
14
#else
#define decF3on
#define decF3off
#endif
#ifdef decF2t1
#define decF2
#define decF2t1on cpds2:f2
#else
#define decF2t1on
#endif
#ifdef decF2aq
#define decF2
#define decF2aqon cpds2:f2
#else
#define decF2aqon
#endif
#ifdef decF2
#define dec
#define tppm
#define decF2off do:f2
#else
#define decF2off
#endif
#ifdef dec
#include "decouple.incl"
#endif
#ifdef _DFS
;p2 DFS/HS pulse
;cnst1 : (kHz) Start DFS sweep freq.
;cnst2 : (kHz) End DFS sweep freq.
;cnst3 : (ns) time resolution of shape sp1
;spoffs1 HS offset (spoffs1 < 1/cnst3)
;spnam1 DFS/HS shape : use HS.jt of DFS.jt to regenerate
;sp1 DFS/HS shape power
define delay showInASED
"showInASED=cnst1+cnst2+cnst3"
#define DFSpulse (5u p2:sp1 ph0 5u):f1
#else
#define DFSpulse
#endif
#ifndef _SR4
#define _SFAM
#endif
"cnst0=2"
"p4=p3*cnst0"
;**************** calculation of t1 delays ******************
define delay Dmin
define loopcounter lmin
define delay delA
define delay delAa
define delay delB
"Dmin=(2*p1+d0+2u)"
"lmin=trunc(Dmin*cnst31)+1"
"delA=(((1s*lmin)/cnst31)-2u-p4)/2.0"
"delB=(((1s*lmin)/cnst31)-2u-d0-p1*2.0)/2.0"
"delAa=0.5s*(lmin%2)/cnst31+1u"
define loopcounter LCounter
define delay dummy
#ifdef _SFAM
"p6=1s/cnst31"
"LCounter=trunc(p16*cnst31/1e6+0.5)"
"dummy=cnst31+cnst30+cnst3+l3"
#endif
#ifdef _SR4
15
"p6=(0.25s/cnst31)"
"LCounter=trunc(p16*cnst31/1e6+0.5)"
;"dummy=cnst31"
; counter for cycling SR4
"l0=0"
#endif
"in0=inf1"
;*************** experiment block ********************
1 ze
2 100m decF2off decF3off
"Dmin=(2*p1+d0+2u)"
"lmin=trunc(Dmin*cnst31)+1"
"delA=(((1s*lmin)/cnst31)-2u-p4)/2.0"
"delAa=0.5s*(lmin%2)/cnst31+1u"
"delB=(((1s*lmin)/cnst31)-2u-d0-p1*2.0)/2.0"
#ifdef _SR4
;SR4 manual phase cycling
10u iu0
"cnst46=180*(((l0-1)/16)%2)"
"cnst47=180*(((l0-1)/4)%2)"
10u ip16+cnst46
10u ip17+cnst47
#endif
PRESAT1(f1)
d1
DFSpulse
5u pl21:f1 pl23:f3
(p3 ph1):f1
delAa decF2t1on
#ifdef _SFAM
SFAMl1, (p6:spf5 ph4):f3
lo to SFAMl1 times LCounter
#endif
#ifdef _SR4
sr4_1, (p6 ph16^):f3
(p6 ph16^):f3
(p6 ph16^):f3
(p6 ph16^):f3
lo to sr4_1 times LCounter
#endif
1u
(delB pl3 p1 ph11 d0 p1 ph12 delB):f3 (delA p4 ph2
1u pl23:f3
#ifdef _SFAM
SFAMl2, (p6:spf5 ph5):f3
lo to SFAMl2 times LCounter
#endif
#ifdef _SR4
sr4_2, (p6 ph17^):f3
(p6 ph17^):f3
(p6 ph17^):f3
(p6 ph17^):f3
lo to sr4_2 times LCounter
#endif
delAa decF2off
go=2 ph31 decF2aqon decF3on
1u decF3off decF2off
100m mc #0 to 2 F1PH(ip11,id0)
exit
#ifndef opt1D
;phase cycling for 2D
ph0=0
delA ):f1
16
ph1={0 0 2 2}*2 {1 1 3 3}*2
ph2=0
ph4={0}*16 {2}*16
ph5={0}*4 {2}*4
ph11=0
ph12=0 2
ph30=0
ph31={0 2 2 0}*2 {3 1 1 3}*2
ph16=(360) 90 270 90 270 270 90 270 90
ph17=(360) 90 270 90 270 270 90 270 90
#else
; phase cycling for 1D optimization
ph0=0
ph1={0 0 0 0 2 2 2 2}*2 {1 1 1 1 3 3 3
ph2=0
ph4={0}*32 {2}*32
ph5={0}*8 {2}*8
ph11=0
ph12=0 2 1 3
ph30=0
ph31={0 2 1 3 2 0 3 1}*2 {3 1 1 3 1 3
ph16=(360) 90 270 90 270 270 90 270 90
ph17=(360) 90 270 90 270 270 90 270 90
#endif
210 30 210 30 30 210 30 210 330 150 330 150 150 330 150 330
210 30 210 30 30 210 30 210 330 150 330 150 150 330 150 330
3}*2
3 1}*2
210 30 210 30 30 210 30 210 330 150 330 150 150 330 150 330
210 30 210 30 30 210 30 210 330 150 330 150 150 330 150 330
; set phases for presat : ph19 and ph20
presatPH
Phase cycling explanation:
First ph12 is cycled on 2 phases to ensure ±1Q coherence order selection on the indirect dimension,
then ph1 is cycled on 2 phases, and then the reconversion recoupling train is cycled on 2 phases.
This minimal 8 phase cycling usually provides clean spectra. If more scans are required then
additional phase cycling is performed: ph1 is cycled on 2 more phases, the excitation recoupling is
cycled on 2 phases leading to maximal 32 phase cycling.