inorganic chemistry

foreign metal ion concentration ( 96 ). Most Ln^3 þ–macrocycles are
highly water soluble, thermodynamically stable, kinetically inert
at physiological pH, cell permeable, and nontoxic, making them
ideal for use asin vivobioprobes. The facile derivatization of lig-
ands bound to lanthanides also makes them easily tailored to bind
specific biomolecules such as antigens and proteins.
As described previously, nonradiative decay due to solvent
interactions can severely reduce lanthanide luminescence
through energy dissipation by vibronic modes, with the OH
oscillator being the most common and efficient quencher.
However, if these O H oscillators are replaced with lower-
frequency O D oscillators, the efficiency of vibronic deactivation
decreases substantially. Therefore, the rate constants for
luminescence lifetimes (tH 2 O) of lanthanide excited states in water
or alcoholic solvents are often much shorter than those in analo-
gous deuterated solvents (tD 2 O). This property can be utilized to
determine the degree of solvation for luminescent lanthanides.
The hydration number, or the number of bound water molecules
in the lanthanide coordination sphere, can be calculated using a
method introduced by Horrocks and Sudnick for terbium and
europium complexes ( 50 ). The relationship between Tb or Eu
excited state lifetimes (t), which are experimentally determined
in H 2 O and D 2 O, and the hydration number (q) is given in Eq.(1)

q¼ALn

1

tH 2 O



1

tD 2 O



ð 1 Þ

All lifetimes are in milliseconds, and the ALn constant is a
proportionality factor specific to a given lanthanide that takes
into account the energy gap between the ground and excited
state manifolds. This equation was later modified by Parker to
include quenching effects from coordinated N H oscillators
(Eq. 2), wherexis the number of NH oscillators) and outer-
sphere water molecules ( 97 ).

qEu¼AEu

1

tH 2 O



1

tD 2 O

!

 0 : 25  0 : 075 x

"#

qTb¼ATb

1

tH 2 O



1

tD 2 O

!

 0 : 06

"#ð 2 Þ

The effect of the DO2A ligand, which contains two NH
oscillators, results in a proportionality factor of 4.60.5 ms when
coordinated to Tb^3 þ, assuming slow exchange with D 2 O( 98 ).

14 MORGAN L. CABLEet al.