Frequency-Domain and Wide-Pulse Time-Domain Measurements of Lanthanide Luminescence and Lanthanide-Based Resonance Energy Transfer

Resonance energy transfer (RET) is a non-radiative transfer of the excitation energy from the initially excited luminescent donor to an acceptor. The requirements for the resonance energy transfer are: i) the spectral overlap between the donor emission spectrum and the acceptor absorption spectrum, ii) the close proximity of the donor and the acceptor, and iii) the suitable relative orientations of the donor emission and the acceptor absorption transition dipoles. As a result of the RET process the donor luminescence intensity and the donor lifetime are decreased. If the acceptor is luminescent, a sensitized acceptor emission appears. The rate of RET depends strongly on the donor–acceptor distance (r) and is inversely proportional to r6. The distance dependence of RET is utilized in binding assays. The proximity requirement and the selective detection of the RET-modified emission signal allow homogeneous separation free assays. The term lanthanide-based RET is used when luminescent lanthanide compounds are used as donors. The long luminescence lifetimes, the large Stokes’ shifts and the intense, sharply-spiked emission spectra of the lanthanide donors offer advantages over the conventional organic donor molecules. Both the organic lanthanide chelates and the inorganic up-converting phosphor (UCP) particles have been used as donor labels in the RET based binding assays. In the present work lanthanide luminescence and lanthanide-based resonance energy transfer phenomena were studied. Luminescence lifetime measurements had an essential role in the research. Modular frequency-domain and time-domain luminometers were assembled and used successfully in the lifetime measurements. The frequency-domain luminometer operated in the low frequency domain ( 100 kHz) and utilized a novel dual-phase lock-in detection of the luminescence. One of the studied phenomena was the recently discovered non-overlapping fluorescence resonance energy transfer (nFRET). The studied properties were the distance and temperature dependences of nFRET. The distance dependence was found to deviate from the Förster theory and a clear temperature dependence was observed whereas conventional RET was completely independent of the temperature. Based on the experimental results two thermally activated mechanisms were proposed for the nFRET process. The work with the UCP particles involved the measurement of the luminescence properties of the UCP particles synthesized in our laboratory. The goal of the UCP particle research is to develop UCP donor labels for binding assays. In the present work the effect of the dopant concentrations and the core–shell structure on the total up-conversion luminescence intensity, the red–green emission ratio, and the luminescence lifetime was studied. Also the non-radiative nature of the energy transfer from the UCP particle donors to organic acceptors was demonstrated for the first time in aqueous environment and with a controlled donor–acceptor distance.

Luminescent Lanthanide Reporters: New Concepts for Use in Bioanalytical Applications

Lanthanides represent the chemical elements from lanthanum to lutetium. They intrinsically exhibit some very exciting photophysical properties, which can be further enhanced by incorporating the lanthanide ion into organic or inorganic sensitizing structures. A very popular approach is to conjugate the lanthanide ion to an organic chromophore structure forming lanthanide chelates. Another approach, which has quickly gained interest, is to incorporate the lanthanide ions into nanoparticle structures, thus attaining improved specific activity and binding capacity. The lanthanide-based reporters usually express strong luminescence emission, multiple narrow emission lines covering a wide wavelength range, and exceptionally long excited state lifetimes enabling timeresolved detection. Because of these properties, the lanthanide-based reporters have found widespread applications in various fields of life. This study focuses on the field of bioanalytical applications. The aim of the study was to demonstrate the utility of different lanthanide-based reporters in homogeneous Förster resonance energy transfer (FRET)-based bioaffinity assays. Several different model assays were constructed. One was a competitive bioaffinity assay that utilized energy transfer from lanthanide chelate donors to fluorescent protein acceptors. In addition to the conventional FRET phenomenon, a recently discovered non-overlapping FRET (nFRET) phenomenon was demonstrated for the first time for fluorescent proteins. The lack of spectral overlap in the nFRET mechanism provides sensitivity and versatility to energy transfer-based assays. The distance and temperature dependence of these phenomena were further studied in a DNA-hybridization assay. The distance dependence of nFRET deviated from that of FRET, and unlike FRET, nFRET demonstrated clear temperature dependence. Based on these results, a possible excitation mechanism operating in nFRET was proposed. In the study, two enzyme activity assays for caspase-3 were also constructed. One of these was a fluorescence quenching-based enzyme activity assay that utilized novel inorganic particulate reporters called upconverting phosphors (UCPs) as donors. The use of UCPs enabled the construction of a simple, rather inexpensive, and easily automated assay format that had a high throughput rate. The other enzyme activity assay took advantage of another novel reporter class, the lanthanidebinding peptides (LBPs). In this assay, energy was transferred from a LBP to a green fluorescent protein (GFP). Using the LBPs it was possible to avoid the rather laborious, often poorly repeatable, and randomly positioned chemical labeling. In most of the constructed assays, time-resolved detection was used to eliminate the interfering background signal caused by autofluorescence. The improved signal-to-background ratios resulted in increased assay sensitivity, often unobtainable in homogeneous assay formats using conventional organic fluorophores. The anti-Stokes luminescence of the UCPs, however, enabled the elimination of autofluorescence even without time-gating, thus simplifying the instrument setup. Together, the studied reporters and assay formats pave the way for increasingly sensitive, simple, and easily automated bioanalytical applications.

Instability of a square sheet under symmetric biaxial loading

An early experiment found that a square rubber sheet under symmetric biaxial loading may not remain square. This curious result has been one of the most instructive examples in finite elasticity. Here thermodynamic considerations are used to analyze this instability.

Numerical study on mixed convection in a horizontal flow past a square porous cavity using UNIFAES scheme

Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained.

Switchable lanthanide fluorescence probes in homogenous molecular diagnostics

The number of molecular diagnostic assays has increased tremendously in recent years.Nucleic acid diagnostic assays have been developed, especially for the detection of human pathogenic microbes and genetic markers predisposing to certain diseases. Closed-tube methods are preferred because they are usually faster and easier to perform than heterogenous methods and in addition, target nucleic acids are commonly amplified leading to risk of contamination of the following reactions by the amplification product if the reactions are opened. The present study introduces a new closed-tube switchable complementation probes based PCR assay concept where two non-fluorescent probes form a fluorescent lanthanide chelate complex in the presence of the target DNA. In this dual-probe PCR assay method one oligonucleotide probe carries a non-fluorescent lanthanide chelate and another probe a light absorbing antenna ligand. The fluorescent lanthanide chelate complex is formed only when the non-fluorescent probes are hybridized to adjacent positions into the target DNA bringing the reporter moieties in close proximity. The complex is formed by self-assembled lanthanide chelate complementation where the antenna ligand is coordinated to the lanthanide ion captured in the chelate. The complementation probes based assays with time-resolved fluorescence measurement showed low background signal level and hence, relatively high nucleic acid detection sensitivity (low picomolar target concentration). Different lanthanide chelate structures were explored and a new cyclic seven dentate lanthanide chelate was found suitable for complementation probe method. It was also found to resist relatively high PCR reaction temperatures, which was essential for the PCR assay applications. A seven-dentate chelate with two unoccupied coordination sites must be used instead of a more stable eight- or nine-dentate chelate because the antenna ligand needs to be coordinated to the free coordination sites of the lanthanide ion. The previously used linear seven-dentate lanthanide chelate was found to be unstable in PCR conditions and hence, the new cyclic chelate was needed. The complementation probe PCR assay method showed high signal-to-background ratio up to 300 due to a low background fluorescence level and the results (threshold cycles) in real-time PCR were reached approximately 6 amplification cycles earlier compared to the commonly used FRET-based closed-tube PCR method. The suitability of the complementation probe method for different nucleic acid assay applications was studied. 1) A duplex complementation probe C. trachomatis PCR assay with a simple 10-minute urine sample preparation was developed to study suitability of the method for clinical diagnostics. The performance of the C. trachomatis assay was equal to the commercial C. trachomatis nucleic acid amplification assay containing more complex sample preparation based on DNA extraction. 2) A PCR assay for the detection of HLA-DQA1*05 allele, that is used to predict the risk of type 1 diabetes, was developed to study the performance of the method in genotyping. A simple blood sample preparation was used where the nucleic acids were released from dried blood sample punches using high temperature and alkaline reaction conditions. The complementation probe HLA-DQA1*05 PCR assay showed good genotyping performance correlating 100% with the routinely used heterogenous reference assay. 3) To study the suitability of the complementation probe method for direct measurement of the target organism, e.g., in the culture media, the complementation probes were applied to amplificationfree closed-tube bacteriophage quantification by measuring M13 bacteriophage ssDNA. A low picomolar bacteriophage concentration was detected in a rapid 20- minute assay. The assay provides a quick and reliable alternative to the commonly used and relatively unreliable UV-photometry and time-consuming culture based bacteriophage detection methods and indicates that the method could also be used for direct measurement of other micro-organisms. The complementation probe PCR method has a low background signal level leading to a high signal-to-background ratio and relatively sensitive nucleic acid detection. The method is compatible with simple sample preparation and it was shown to tolerate residues of urine, blood, bacteria and bacterial culture media. The common trend in nucleic acid diagnostics is to create easy-to-use assays suitable for rapid near patient analysis. The complementation probe PCR assays with a brief sample preparation should be relatively easy to automate and hence, would allow the development of highperformance nucleic acid amplification assays with a short overall assay time.

Switchable Lanthanide Luminescence for Detection of Biomolecules

Binary probes are oligonucleotide probe pairs that hybridize adjacently to a complementary target nucleic acid. In order to detect this hybridization, the two probes can be modified with, for example, fluorescent molecules, chemically reactive groups or nucleic acid enzymes. The benefit of this kind of binary probe based approach is that the hybridization elicits a detectable signal which is distinguishable from background noise even though unbound probes are not removed by washing before measurement. In addition, the requirement of two simultaneous binding events increases specificity. Similarly to binary oligonucleotide probes, also certain enzymes and fluorescent proteins can be divided into two parts and used in separation-free assays. Split enzyme and fluorescent protein reporters have practical applications among others as tools to investigate protein-protein interactions within living cells. In this study, a novel label technology, switchable lanthanide luminescence, was introduced and used successfully in model assays for nucleic acid and protein detection. This label technology is based on a luminescent lanthanide chelate divided into two inherently non-luminescent moieties, an ion carrier chelate and a light harvesting antenna ligand. These form a highly luminescent complex when brought into close proximity; i.e., the label moieties switch from a dark state to a luminescent state. This kind of mixed lanthanide complex has the same beneficial photophysical properties as the more typical lanthanide chelates and cryptates - sharp emission peaks, long emission lifetime enabling time-resolved measurement, and large Stokes’ shift, which minimize the background signal. Furthermore, the switchable lanthanide luminescence technique enables a homogeneous assay set-up. Here, switchable lanthanide luminescence label technology was first applied to sensitive, homogeneous, single-target nucleic acid and protein assays with picomolar detection limits and high signal to background ratios. Thereafter, a homogeneous four-plex nucleic acid array-based assay was developed. Finally, the label technology was shown to be effective in discrimination of single nucleotide mismatched targets from fully matched targets and the luminescent complex formation was analyzed more thoroughly. In conclusion, this study demonstrates that the switchable lanthanide luminescencebased label technology can be used in various homogeneous bioanalytical assays.

From Molecular Blocks To Bioanalytical Assays: Combining Lanthanide Luminescence and Bioaffinity Binders for Protein Detection

Measuring protein biomarkers from sample matrix, such as plasma, is one of the basic tasks in clinical diagnostics. Bioanalytical assays used for the measuring should be able to measure proteins with high sensitivity and specificity. Furthermore, multiplexing capability would also be advantageous. To ensure the utility of the diagnostic test in point-of-care setting, additional requirements such as short turn-around times, ease-ofuse and low costs need to be met. On the other hand, enhancement of assay sensitivity could enable exploiting novel biomarkers, which are present in very low concentrations and which the current immunoassays are unable to measure. Furthermore, highly sensitive assays could enable the use of minimally invasive sampling. In the development of high-sensitivity assays the label technology and affinity binders are in pivotal role. Additionally, innovative assay designs contribute to the obtained sensitivity and other characteristics of the assay as well as its applicability. The aim of this thesis was to study the impact of assay components on the performance of both homogeneous and heterogeneous assays. Applicability of two different lanthanide-based label technologies, upconverting nanoparticles and switchable lanthanide luminescence, to protein detection was explored. Moreover, the potential of recombinant antibodies and aptamers as alternative affinity binders were evaluated. Additionally, alternative conjugation chemistries for production of the labeled binders were studied. Different assay concepts were also evaluated with respect to their applicability to point-of-care testing, which requires simple yet sensitive methods. The applicability of upconverting nanoparticles to the simultaneous quantitative measurement of multiple analytes using imaging-based detection was demonstrated. Additionally, the required instrumentation was relatively simple and inexpensive compared to other luminescent lanthanide-based labels requiring time-resolved measurement. The developed homogeneous assays exploiting switchable lanthanide luminescence were rapid and simple to perform and thus applicable even to point-ofcare testing. The sensitivities of the homogeneous assays were in the picomolar range, which are still inadequate for some analytes, such as cardiac troponins, requiring ultralow limits of detection. For most analytes, however, the obtained limits of detection were sufficient. The use of recombinant antibody fragments and aptamers as binders allowed site-specific and controlled covalent conjugation to construct labeled binders reproducibly either by using chemical modification or recombinant technology. Luminescent lanthanide labels were shown to be widely applicable for protein detection in various assay setups and to contribute assay sensitivity.

Chi-square analysis of the reduction of ATP levels in L-02 hepatocytes by hexavalent chromium

This study explored the reduction of adenosine triphosphate (ATP) levels in L-02 hepatocytes by hexavalent chromium (Cr(VI)) using chi-square analysis. Cells were treated with 2, 4, 8, 16, or 32 μM Cr(VI) for 12, 24, or 36 h. Methyl thiazolyl tetrazolium (MTT) experiments and measurements of intracellular ATP levels were performed by spectrophotometry or bioluminescence assays following Cr(VI) treatment. The chi-square test was used to determine the difference between cell survival rate and ATP levels. For the chi-square analysis, the results of the MTT or ATP experiments were transformed into a relative ratio with respect to the control (%). The relative ATP levels increased at 12 h, decreased at 24 h, and increased slightly again at 36 h following 4, 8, 16, 32 μM Cr(VI) treatment, corresponding to a "V-shaped" curve. Furthermore, the results of the chi-square analysis demonstrated a significant difference of the ATP level in the 32-μM Cr(VI) group (P < 0.05). The results suggest that the chi-square test can be applied to analyze the interference effects of Cr(VI) on ATP levels in L-02 hepatocytes. The decreased ATP levels at 24 h indicated disruption of mitochondrial energy metabolism and the slight increase of ATP levels at 36 h indicated partial recovery of mitochondrial function or activated glycolysis in L-02 hepatocytes.

Spectrally Tuned Lanthanide Photoluminescence for Point-of-Care Testing

Point-of-care (POC) –diagnostics is a field with rapidly growing market share. As these applications become more widely used, there is an increasing pressure to improve their performance to match the one of a central laboratory tests. Lanthanide luminescence has been widely utilized in diagnostics because of the numerous advantages gained by the utilization of time-resolved or anti-Stokes detection. So far the use of lanthanide labels in POC has been scarce due to limitations set by the instrumentation required for their detection and the shortcomings, e.g. low brightness, of these labels. Along with the advances in the research of lanthanide luminescence, and in the field of semiconductors, these materials are becoming a feasible alternative for the signal generation also in the future POC assays. The aim of this thesis was to explore ways of utilizing time-resolved detection or anti-Stokes detection in POC applications. The long-lived fluorescence for the time-resolved measurement can be produced with lanthanide chelates. The ultraviolet (UV) excitation required by these chelates is cumbersome to produce with POC compatible fluorescence readers. In this thesis the use of a novel light-harvesting ligand was studied. This molecule can be used to excite Eu(III)-ions at wavelengths extending up to visible part of the spectrum. An enhancement solution based on this ligand showed a good performance in a proof-of-concept -bioaffinity assay and produced a bright signal upon 365 nm excitation thanks to the high molar absorptivity of the chelate. These features are crucial when developing miniaturized readers for the time-resolved detection of fluorescence. Upconverting phosphors (UCPs) were studied as an internal light source in glucose-sensing dry chemistry test strips and ways of utilizing their various emission wavelengths and near-infrared excitation were explored. The use of nanosized NaYF :Yb3+,Tm3+-particles enabled the replacement of an external UV-light source with a NIR-laser and gave an additional degree of freedom in the optical setup of the detector instrument. The new method enabled a blood glucose measurement with results comparable to a current standard method of measuring reflectance. Microsized visible emitting UCPs were used in a similar manner, but with a broad absorbing indicator compound filtering the excitation and emission wavelengths of the UCP. This approach resulted in a novel way of benefitting from the non-linear relationship between the excitation power and emission intensity of the UCPs, and enabled the amplification of the signal response from the indicator dye.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Heats of formation of some hydrates /|nA. Phillipson. -- 260 St. Catharines, Ont. : [s. n.],

A great deal of data on the heats of formation of various hydrates has been compiled i n the J.A.N.A.F. and other tables such as the National Bureau of Standards circulars. Comparison of the heat of f ormation of a hydrate with that of the corresponding anhydrate exposes anomalies i n a surprising number of cases. Some of the results are so discordant that i t is apparent that one or the other value is seriously mistaken. No attempt has been made i n this work to determine which value may be correct, but measurements have been made of the difference between these two values. The procedure adopted has been to dissolve the hydrate and the anhydrate, to achieve the same final concentration of the compound in solution, and so to measure the difference in heats of solution .. Measurements were made at OOC in a modified Bunsen ice calorimeter, well insulated and surrounded by an icewater mixture . The observed differences in heats of solut ion were corrected t o 25°0 by using appropriate heat capacity data. These differences offer a direct measure of the enthalpy involved in binding a mole of water into the crystal structure and so should shed light on the nature of binding involved. The following hydrates were studied : MgS04.nH20 (n = 1,4,7), MnC12.nH20 (n = 1, 2), LiI. nH20 (n = 1,3), MnS04. nH20 (n = 1,4), CaC12. nH20 (n = 2,6) , K2C03.1~H20, LiCl.H20, LiBr.2H20, CdC12.2t H2o, and N2H4eH20.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.