Basics of Lanthanide Photophysics

TLDR: In this article, Gschneidner et al. outline the principles underlying the simplest models used for describing the electronic structure and spectroscopic properties of trivalent lanthanide ions LnIII (4f n ) with special emphasis on luminescence.

Abstract: The fascination for lanthanide optical spectroscopy dates back to the 1880s when renowned scientists such as Sir William Crookes, LeCoq de Boisbaudran, Eugene Demarcay or, later, Georges Urbain were using luminescence as an analytical tool to test the purity of their crystallizations and to identify potential new elements. The richness and complexity of lanthanide optical spectra are reflected in an article published in 1937 by J.H. van Vleck: The Puzzle of Rare Earth Spectra in Solids. After this analytical and exploratory period, lanthanide unique optical properties were taken advantage of in optical glasses, filters, and lasers. In the mid-1970s, E. Soini and I. Hemmila proposed lanthanide luminescent probes for time-resolved immunoassays (Soini and Hemmila in Clin Chem 25:353–361, 1979) and this has been the starting point of the present numerous bio-applications based on optical properties of lanthanides. In this chapter, we first briefly outline the principles underlying the simplest models used for describing the electronic structure and spectroscopic properties of trivalent lanthanide ions LnIII (4f n ) with special emphasis on luminescence. Since the book is intended for a broad readership within the sciences, we start from scratch defining all quantities used, but we stay at a descriptive level, leaving out detailed mathematical developments. For the latter, the reader is referred to references Liu and Jacquier, Spectroscopic properties of rare earths in optical materials. Tsinghua University Press & Springer, Beijing & Heidelberg, 2005 and Gorller-Walrand and Binnemans, Rationalization of crystal field parameters. In: Gschneidner, Eyring (eds) Handbook on the physics and chemistry of rare earths, vol 23. Elsevier BV, Amsterdam, Ch 155, 1996. The second part of the chapter is devoted to practical aspects of lanthanide luminescent probes, both from the point of view of their design and of their potential utility.

Figures

Table 4 Experimentally observed hypersensitive transitions for LnIII ions in optical spectra [5]. Energies/wavelengths are approximate

Table 3 Number of Stark levels versus the value of quantum number J

Fig. 16 Stern–Volmer plots for the quenching of the luminescence of [Eu2(L C2)3] by acridine orange (left) and ethidium bromide (right) in Tris–HCl buffer (pH 7.4). Open squares: lifetimes, solid squares: intensities. Redrawn after [47]

Fig. 10 Relationships between the triplet state energy of the feeding ligand and the quantum yields of 39 EuIII (top) and TbIII (middle) polyaminocarboxylates [24] and of EuIII Schiff bases (triangles, [25]) and b-diketonates (squares, [26])

Fig. 5 Left: Absorption spectrum of [Ce(H2O)9] 3+ and right: its assignment (D3h symmetry)

Fig. 7 Schematic representation of energy absorption, migration, emission (plain arrows) and dissipation (dotted arrows) processes in a lanthanide complex. 1S* or S = singlet state, 3T* or T = triplet state, A = absorption, F = fluorescence, P = phosphorescence, k = rate constant, r = radiative, nr = nonradiative, IC = internal conversion, ISC = intersystem crossing, ILCT (or IL) = intra-ligand charge transfer, LMCT (or LM) = ligand-to-metal charge transfer. Back transfer processes are not drawn for the sake of clarity

Full text

Basics of Lanthanide Photophysics
Jean-Claude G. Bu
¨
nzli and Svetlana V. Eliseeva
Abstract The fascination for lanthanide optical spectroscopy dates back to the 1880s
when renowned scientists such as Sir William Crookes, LeCoq de Boisbaudran,
Euge
`
ne Demarc¸ay or, later, Georges Urbain were using luminescence as an analytical
tool to test the purity of their crystallizations and to identify potential new elements.
The richness and complexity of lanthanide optical spectra are reflected in an article
published in 1937 by J.H. van Vleck: The Puzzle of Rare Earth Spectra in Solids.After
this analytical and exploratory period, lanthanide unique optical properties were taken
advantage of in optical glasses, filters, and lasers. In the mid-1970s, E. Soini and
I. Hemmila
¨
proposed lanthanide luminescent probes for time-resolved immunoassays
(Soini and Hemmila
¨
in Clin Chem 25:353–361, 1979) and this has been the starting
point of the present numerous bio-applications based on optical properties of lantha-
nides. In this chapter, we first briefly outline the principles underlying the simplest
models used for describing the electronic structure and spectroscopic properties of
trivalent lanthanide ions Ln
III
(4f
n
) with special emphasis on luminescence. Since the
book is intended for a broad readership within the sciences, we start from scratch
defining all quantities used, but we stay at a descriptive level, leaving out detailed
mathematical developments. For the latter, the reader is referred to references Liu and
Jacquier, Spectroscopic properties of rare earths in optical materials. Tsinghua Uni-
versity Press & Springer, Beijing & Heidelberg, 2005 and Go
¨
rller-Walrand and
Binnemans, Rationalization of crystal field parameters. In: Gschneidner, Eyring
(eds) Handbook on the physics and chemistry of rare earths, vol 23. Elsevier BV,
Amsterdam, Ch 155, 1996. The second part of the chapter is devoted to practical
aspects of lanthanide luminescent probes, both from the point of view of their design
and of their potential utility.
J.-C.G. Bu
¨
nzli (*) and S.V. Eliseeva
Laboratory of Lanthanide Supramolecular Chemistry, E
´
cole Polytechnique Fe
´
de
´
rale de Lausanne,
BCH 1402, 1015 Lausanne, Switzerland
e-mail: Jean-Claude.Bunzli@epfl.ch
P. Ha
¨
nninen and H. Ha
¨
rma
¨
(eds.), Lanthanide Luminescence: Photophysical, Analytical
and Biological Aspects, Springer Ser Fluoresc (2010), DOI 10.1007/4243_2010_3,
#
Springer-Verlag Berlin Heidelberg 2010

Keywords Crystal-field analysis  Energy transfer  f–f Transition  Intrinsic
quantum yield  Lanthanide bioprobe  Lanthanide luminescence  Lanthanide
spectroscopy  Lifetime  Luminescence sensitization  Population analysis 
Quantum yield  Radiative lifetime  Selection rule  Site symmetry  Stern–Volmer
quenching
Contents
1 Electronic Structure of Trivalent Lanthanide Ions
1.1 Atomic Orbitals
1.2 Electronic Configuration
1.3 The Ions in a Ligand Field
2 Absorption Spectra
2.1 Induced ED f–f Transitions: Judd–Ofelt Theory [5, 6]
2.2 4f–5d and CT Transitions
3 Emission Spectra
4 Sensitization of Lanthanide Luminescence
4.1 Design of Efficient Lanthanide Luminescent Bioprobes
4.2 Practical Measurements of Absolute Quantum Yields
5 Information Extracted from Lanthanide Luminescent Probes
5.1 Metal Ion Sites: Number, Composition, and Population Analysis
5.2 Site Symmetry Through Crystal-Field Analysis
5.3 Strength of Metal–Ligand Bonds: Vibronic Satellite Analysis
5.4 Solvation State of the Metal Ion
5.5 Energy Transfers: Donor–Acceptor Distances and Control of the Photophysical
Properties of the Acceptor by the Donor
5.6 FRET Analysis
5.7 Ligand Exchange Kinetics
5.8 Analytical Probes
6 Appendices
6.1 Site Symmetry Determination from Eu
III
Luminescence Spectra
6.2 Examples of Judd–Ofelt Parameters
6.3 Examples of Reduced Matrix Elements
6.4 Emission Spectra
References
Abbreviations
AO Acridine orange
CF Crystal field
CT Charge transfer
DMF Dimethylformamide
DNA Deoxyribonucleic acid
dpa Dipicolinate (2,6-pyridine dicarboxylate)
dtpa Diethylenetrinitrilopentaacetate
EB Ethidium bromide
ED Electric dipole
J.-C.G. Bu
¨
nzli and S.V. Eliseeva

EQ Electric quadrupole
FRET Fo
¨
rster resonant energy transfer
hfa Hexafluoroacetylacetonate
ILCT Intraligand charge transfer
ISC Intersystem crossing
JO Judd–Ofelt
LLB Lanthanide luminescent bioprobe
LMCT Ligand-to-metal charge transfer
MD Magnetic dipole
MLCT Metal-to-ligand charge transfer
NIR Near-infrared
PCR Polymerase chain reaction
SO Spin–orbit
tta Thenoyltrifluoroacetylacetonate
YAG Yttrium aluminum garnet
1 Electronic Structure of Trivalent Lanthanide Ions
1.1 Atomic Orbitals
In quantum mechanics, three variables depict the movement of the electrons around
the positively-charged nucleus, these electrons being considered as waves with
wavelength l ¼ h/mv where h is Planck’s constant (6.626  10
34
Js
1
), m and v
the mass (9.109  10
31
kg) and velocity of the electron, respectively:
– The time-dependent Hamiltonian operator H describing the sum of kinetic and
potential energies in the system; it is a function of the coordinates of the
electrons and nucl eus.
– The wavefunction, C
n
, also depending on the coordinates and time, related to
the movement of the particles, and not directly observable; its square (C
n
)
2
though gives the probability that the particle it describes will be found at the
position given by the coordina tes; the set of all probabilities for a given
electronic C
n
, is called an orbital.
– The quantified energy E
n
associated with a specific wavefunction, and indepen-
dent of the coordinates.
These quantities are related by the dramatically simple Schro
¨
dinger equation,
which replaces the fundamental equations of classical mechanics for atomic sys-
tems:
HC
n
¼ E
n
C
n
: (1)
Energies E
n
are eigenvalues of C
n
, themselves called eigenfunctions. In view
of the complexity brought by the multidimensional aspect of this equation
Basics of Lanthanide Photophysics

(3 coordinates for each electron and nucleus, in addition to time) several simplifica-
tions are made. Firstly, the energy is assumed to be constant with time, which
removes one coordinate. Secondly, nuclei being much heavier than electrons, they
are considered as being fixed (Born–Oppenheimer approximation). Thirdly, since
the equation can only be solved precisely for the hydrogen atom, the resulting
hydrogenoid or one-electron wavefunction is used for the other elements, with a
scaling taking into account the apparent nucleus charge, i.e., including screening
effects from the other electrons. Finally, to ease solving the equation for non-H
atoms, the various interactions occurring in the electron-nucleus system are treated
separately, in order of decreasing importance (perturbation method).
For hydrogen, the Hamiltonian simply reflects Coulomb’s attraction between
the nucleus and the electron, separated by a distance r
i
, and the kinetic energy of the
latter:
1
H
0
¼
1
r
i

1
2
D
i
D ¼
@
2
@x
2
þ
@
2
@y
2
þ
@
2
@z
2

: (2)
Each wavefunction (or orbital: the two terms are very often, but wrongly, taken
as synonyms) resulting from solving (1) is defined by four quantum numbers
reflecting the quantified energy of the two motions of the electrons: the orbital
motion, defined by the angular momentum
~
‘, and the spin, characterized by the
angular momentum
~
s. If polar coordinates (r, #, ’) are used, wavefunctions are
expressed as the product of a normalizing factor N, of a radial function <
n;‘
,ofan
angular function F
ℓ,m
ℓ
, and of a spin function S
m
s
:
C
n;‘;m
‘
;m
s
¼ N <
n;‘
ðrÞF
‘;m
‘
ð#; ’ ÞS
m
s
: (3)
The principal quantum number n is an integer (1, 2, 3, ...) and represents the
radial expansion of the orbital. The angular quantum number ℓ varies from 0 to
(n  1) and characterizes the shape of the orbital (designed by letters: s, p, d, f, g,...
for ℓ ¼ 0, 1, 2, 3, 4, ...). The magnetic quantum number m
ℓ
is the projection of the
vector
~
‘ onto the z axis and is linked to the orientation of the orbital in space; it
varies between ℓ and þℓ. Finally, m
s
is the projection of the vector
~
s and takes
values of  ½. Pauli’s principle requires that two electrons of the same atom must
at least differ by the value of one quantum number; this implies that only two
electrons of opposite spin can be associated with a given orbital. An electronic shell
consists in all electrons having the same quantum numb er n. A sub-shell regroups
electrons with same n and ℓ numbers, has therefore (2ℓ þ 1) orbitals, and may
contain a maximum of (4ℓ þ 2) electrons. The shapes of the seven 4f orbitals
(n ¼ 4, ℓ ¼ 3) are represented on top of Fig. 1.
1
We use the atomic system units (a.u.) in order to simplify the equations as much as possible.
J.-C.G. Bu
¨
nzli and S.V. Eliseeva

1.2 Electronic Configuration
The ground state ele ctronic configuration of Ln
III
ions is [Xe]4f
n
(n = 0–14).
It is energetically well separated from the [Xe]4f
n1
5d
1
configuration (DE
> 32,000 cm
1
). A far reaching fact is the shielding of the 4f orbitals by the
xenon core (54 electrons), particularly the larger radial expansion of the 5s
2
5p
6
subshells, making the valence 4f orbitals “inner orbitals” (bottom of Fig. 1). This is
the key to the chemical and spectroscopic properties of these metal ions.
r
2
Ψ
2
/a.u.
r/a.u.
0123
4f
3
Xe core
Nd
III
Fig. 1 Top: Shape of the one-electron (hydrogenoid) 4f orbitals in a Cartesian space. From top to
bottom and left to right:4f
x(x
2
 3y
2
)
,4f
y(3y
2
 x
2
)
,4f
xyz
,4f
z(x
2
y
2
)
,4f
xz
2
,4f
yz
2
, and 4f
z
3
(combina-
tions of Cartesian coordinates represent the angular functions). Bottom: Radial wavefunction of the
three 4f electrons of Nd
III
compared with the radial wavefunction of the xenon core (a.u. = atomic
units); redrawn after [1]
Basics of Lanthanide Photophysics

Frequently asked questions

Q1. What is the time dependence of the luminescence decay?

if the chemical exchange process occurs at a rate comparable to the de-excitation rate, the time dependence of the luminescence decay is a function of both the excited state lifetimes and the interconversion rate. 

Q2. What are the contributions in "Basics of lanthanide photophysics" ?

The richness and complexity of lanthanide optical spectra are reflected in an article published in 1937 by J. H. vanVleck: The Puzzle of Rare Earth Spectra in Solids. The second part of the chapter is devoted to practical aspects of lanthanide luminescent probes, both from the point of view of their design and of their potential utility. 

Q3. What are the candidates for a lanthanide luminescent bioprobe?

aminocarboxylates, phosphonates, hydroxyquinolinates, and hydroxypyridinones are good candidates, while bdiketonates which have excellent photophysical properties have the tendency to be less stable. 

Q4. What is the reason why the ligands are mainly electrostatic?

As a result of the poor expansion of the 4f orbitals, the Ln–ligand bonds are mainly electrostatic and only some minute mixing of metal and ligand electronic wavefunctions contributes to covalency. 

Q5. What is the time dependence of the luminescence emission following an excitation pulse?

The timedependence of the luminescence emission following an excitation pulse will depend on the rate of chemical exchange relative to the photophysical deactivation rates. 

Q6. What is the importance of a standard calibrated lamp?

It is also essential that emission spectra are corrected for the instrumental function established with a standard calibrated lamp. 

Q7. What is the spectral overlap integral of the absorption spectrum of the acceptor A and?

Once the ligand is excited, subsequent intramolecular energy migrations obey Fermi’s golden rule governing resonant energy transfer (24), whereby WDA is the probability of energy transfer, ODA is the spectral overlap integral between the absorption spectrum of the acceptor A and the emission spectrum of the donor D, while H0 is the perturbation operator in the matrix element < D AjH0jDA > . 

Q8. What is the way to minimize vibration-induced deactivation processes?

The best way to minimize vibration-induced deactivation processes is to design a rigid metal–ion environment, devoid of high-energy vibrations and protecting the LnIII ion from solvent interactions. 

Q9. How many rate constants are needed to model the entire energy-converting mechanism?

In fact a workable model of the entire energy-converting mechanism has shown that considering as many as 20–30 rate constants (including those describing back transfers) may be necessary [20]. 

Q10. How many times does the Dexter mechanism extend over the same distance?

Their specific dependences on the distance d separating the donor D from the acceptor A, i.e., e bd for double-electron exchange and d 6 for dipole–dipolar processes, respectively, often limit Dexter mechanism to operate at short distance (typically 30–50 pm) at which orbital overlap is significant, while Förster mechanism may extend over much longer distances (up to 1,000 pm). 

Q11. What are the requirements for building efficient lanthanide luminescent bioprobes?

The ligand design for building efficient lanthanide luminescent bioprobes (LLBs) must meet several requirements, both chemical, photophysical, and biochemical: (1) efficient sensitization of the metal luminescence, (2) embedding of the emitting ion into a rigid and protective cavity minimizing nonradiative deactivation, (3) long excited state lifetime, (4) water solubility, (5) large thermodynamic stability, (6) kinetic inertness, (7) intense absorption above 330 nm, and (8) whenever relevant, ability to couple to bioactive molecules while retaining their photophysical properties and not altering the bio-affinity of the host. 

Q12. What is the important information to extract for symmetries close to axial?

In this case, three important pieces of information can be extracted for symmetries close to axial symmetry: (1) the sign of the B02 crystal-field parameter which depends on the relative energetic position of the A and E sublevels of 7F1, (2) its value thanks to a phenomenological relationship between DE(A–E) and this parameter [34], and (3) the extent of the deviation from the idealized symmetry given by the splitting of the E sublevel. 

Q13. What is the effect of vibrational quenching on the emission intensity?

Although detrimental to the emission intensity, vibrational quenching allows one to assess the number of water molecules q interacting in the inner-coordination sphere. 

Q14. What is the angular quantum number of a sub-shell?

A sub-shell regroups electrons with same n and ℓ numbers, has therefore (2ℓ þ 1) orbitals, and may contain a maximum of (4ℓ þ 2) electrons. 

Q15. What is the simplest definition of the interaction between photons and matter?

Description of the interaction between photons (massless elemental particles of light) and matter considers the former behaving as waves comprised of two perpendicular fields, electric and magnetic, oscillating in time (henceforth the denomination of electromagnetic wave or radiation). 

Q16. What are the selection rules for induced ED transitions?

The selection rules are derived under several hypotheses which are not always completely fulfilled in reality (in particular 4f wavefunctions are not completely pure), so that the terms “forbidden” and “allowed” transitions are not accurate. 

Q17. What is the way to measure the emission spectrum of the unknown sample?

Regarding the standard, it is best when its emission spectrum overlaps the emission spectrum of the unknownsample; a safe way to proceed is to use two different standards and to measure them against each other as well. 

Q18. Why are the energy levels of the ligand-field sublevels not yet fully explored?

2. Due to their large number, energy levels may extend up to 190,000 cm 1 for n = 6, 7, 8, and are not yet fully explored, although an extension of Carnall’s diagram up to this energy has been recently published [4]. 

Q19. What are the parity rules for induced ED transitions?

Mathematical treatment of the parity mixing by the crystal-field perturbation leads to the selection rules for f–f transitions reproduced in Table 5.JO parameters are adjustable parameters and they are calculated from the absorption spectrum e (~n).