How Many Nuclear Spins Are

Coupled With Each Other In Condensed Matter At Room Temperature?

 Shangwu Ding, Cheng Lung Chen

丁尚武，陳正隆Department of Chemistry,

National Sun Yat-Sen University國立中山大學化學系

大連，2002.10.11.

Quantum Mechanically

The System

N spin-1/2 nuclei in a liquid- or solid- state sample

Room Temperature

N

ji

couplingsij

N

i

izi Ie

1,

id

in

ii

n

ji

couplingsij

izi

n

i

H BIHIHe

11,

Or

One System, Two Formulae

“Full Quantum”

Semi-Classical

Which Is Better?

Are They Equivalent?

“Mainstream” Opinions

Both are correct and they are equivalent

Full quantum description is more consistent but classical description easier in calculation

Never proved

Consistent but incorrect?

Consequences of “Full Quantum” Picture

NMR theory has to be reformulated High temperature approximation invalid

Coherences may be created among uncorrelated spins

ij

N

N

N

b

a

b

a

b

a

2

2

1

1

21

Example

Two distant spins (maybe a billion light years apart)

1

1

1

1

1

1

1

1

:spineach toapplied pulse 90 aAfter

2/1

2/1

2/1

2/1

41

41

o

21

Double quantum coherences!

“Counter-intuition” ORquantum superstition?

Resolution

Two distant spins (maybe a billion light

years apart) can retain their correlation

IFF they have never interacted with other

objects.

Nuclear spins in liquids or solids, however,

are in very noisy environments.

Correlation Evaluation(1)

Uncorrelated spins should not be considered as in the same quantum system!

jiji IIII

:spins edUncorrelat

Correlation Evaluation(2) Two spins are uncorrelated if their interaction

does not contribute to observable evolution

],[

],[

:evolution

],[

|||||||| If

ofn fluctuatio

],[

)(

)(

)(

,

,,

)(

jjjdt

Id

iiidtId

jijjiidt

IId

ijji

jiji

jiijjjiidt

IId

IHH

IHH

eduncorrelat

IIHHHH

HH

HH

IIHHHHH

j

i

ji

ji

Correlation Evaluation(3)

Two spins are uncorrelated if their

dipolar interaction is immersed in the

intrinsic linewidth.

3/121

:Nuclei 1/2-Spin Two of

Lengthn CorrelatioDipolar

cd Intrinsic linewidth

Correlation Evaluation(4)

Intrinsic proton linewidith >0.01 HzMaximum correlation length of two

protons: o

cd A20

<1000 spins are possibly quantum mechanically correlated

Quantum Measurement (1)

Hz(solids)),10Hz(liquids 100R rate Sampling

)sec(solidss)10sec(liquid10

olids)),100kHz(sHz(liquids1

6

62

t

δEhδEδt

Quantum Measurement (2)

!Reasonable

(solids) liquidsin spin states/per )(10 10

)10(10 rate sampling

states,10system,spin 100 of mole aFor

1-3

)23263023-2-2-30

30

Quantum Measurement (3)

le!Unreasonab

(solids) liquidsin spin states/per )(10 10

)10(10 rate sampling

states,10system,spin 200 of mole aFor

2933

)23266023-2-2-60

60

Conclusions

At Around Room Temperature

1. “Full Quantum Treatment” Not Only Unnecessary But Also Incorrect

2. Spin Clusters Are Small, Even in Solids (<100)

Acknowledgments

Discussion:

Guo Wei WEI (MSU)

Chaohui YE(WIPM)

Lian-Pin HWANG (NTU)

Funding:

NSC, MOE

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