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# INTERMEDIATE Vietmse 2

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This 42 page Class Notes was uploaded by Cassidy Kuvalis IV on Saturday September 12, 2015. The Class Notes belongs to Vietmse 2 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 62 views. For similar materials see /class/201880/vietmse-2-university-of-california-irvine in Vietnamese at University of California - Irvine.

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THE JOURNAL OF CHEMICAL PHYSICS 127 214511 2007 Vibronic dynamics of l2 trapped in amorphous ice Coherent following of cage relaxation V Senekerimyan Goldschleger and V A Apkariana Department 0f Chemistry University 0f Califarnia Irvine Califarnia 926972025 USA Received 10 September 2007 accepted 8 October 2007 published online 7 December 2007 Fourwave mixing measurements are carried out on lzdoped ice prepared by quench condensing the premixed vapor at 128 K Coherent vibrational dynamics is observed in two distinct ensembles The rst is ascribed to trapping in asymmetric polar cages in which as in water the valence absorption of the molecule is blueshifted by 3500 cm l predissociation of the B state is complete upon the rst extension of the molecular bond and the vibrational frequency in the ground state observed through coherent antiStokes Raman scattering is reduced by 65 The effect is ascribed to polarization of the molecule The implied local e and the ionicity of the molecule are extracted to conclude that the molecule is oxygen bonded to one water molecule on one side and hydrogen bonded on the other side The second ensemble is characterized by the transient grating signal which shows coherent vibrational dynamics on the B state The small predissociation rate in this site suggests a symmetric cage in which the local electric eld undergoes effective cancellation and consistent with this the extracted blueshift of the valence transition in this site 1500 cm l coincides with that observed in clathrate hydrates of iodine Remarkably in this site the vibrational period of the B state packet coherently stretches from an initial value of 245 fs to 325 fs in the course of ve oscillations 13 ps indicative of vibrationally adiabatic following of the cage expansion The dynamics is characteristic of a molecule trapped in a tight symmetric cage with a soft cage coordinate that relaxes without eliciting elastic response in lowdensity amorphous ice is concluded 2007 American Institute of Physics Enclathration DOL 10106312803922 INTRODUCTION We employ molecular halogens as reporters of local structure and dynamics to investigate their various hydrated environments with particular interest in developing spectro scopic probes of clathrate hydrates The ultravioletvisible UVVis absorption spectra of halogens undergo distinct blueshift and broadening when hydrated as already reported for bromine 39 and iodine The shift is associated primarily with the extent of oxygen bonding The 11 HZOX2 complex is oxygen bonded with the lonepair electrons of oxygen overlapping the empty 0 orbital on the halogen 6 Since the visible absorption spectra of halogens consist of 0 H 7 transitions they undergo a blueshift due to the bound repulsive interaction along the HZOXZ coordinateia shift that can be regarded as a marker for the extent of oxygen bonding in the ground electronic state While in water and amorphous ice the spectra are dramatically shifted in the clathrates where all oxygen atoms of the lattice are fully hydrogen bonded smaller blueshift characteristic of the vari ous clathrate structures is observed 39 The vibrational fre quency of the halogen molecule is another marker of the local structure as was recently demonstrated in the identi cation of polymorphs of bromine clathrate hydrates7 This may be most directly related to the ionicity of the hydrated halogen bond Electronic structure calculations on H20Br2 3Electronic mail aapkaria uciedu 0021 960620071 2721 214511 82300 127 2145111 and HZOC12 complexes show that although there is no in termolecular charge transfer the molecular halogen is strongly polarized HZOXampXamp with a partial charge 8 004700 6 The extent of polarization of the molecule will be controlled by the local electric eld which in mm can be expected to be directly correlated with the vibrational frequency of the probe molecule as amply demonstrated in simulations of water8 These spectroscopic markers of local structure are reinforced in the present investigations of io dine doped in amorphous ice Our principal aim is the char acterization of cage dynamics through timeresolved mea suremenm Timeresolved measurements of hydrated bromine have proven rather informative 39 In what is spectroscopically characterized as BrZdoped amorphous ice we observe a subensemble of molecules that evolve quantum coherently on the electronically excited B state of the molecule The vibrational coherence of the molecule was imaged through the Brz HZOJ39 charge transfer state taking advantage of the sharp nature of this transition The insulation of the molecule from the dielectric disorder of ice and the decoupling of its vibrational dynamics from the rest of the solid are taken as demonstrations of enclathrationitrapping in highly symmet ric cages that are assembled by the molecule in the ice This is consistent with the ndings that air trapped in ice sheets and ice cores impresses the clathrate structure locally10 lo dine is known to not make clathrate structures directly but can be induced to occupy clathrate cages when assisted by a 2007 American Institute of Physics Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpljcpaip0rgjcpcopyrightjsp 2145112 Seneken39myan Goldschleger Apkarian help molecule such as tetra hydro furan THF3 It would then be useful to interrogate what distinguishes the local iodineice interactionsia query that we address in the present study through timeresolved fourwave mixing spec troscopy Indeed the measurements reveal that 12 can be found in a variety of sites in the amorphous solid including selfimposed clathratetype structures Most remarkably in such sites we observe coherent vibrational dynamics that undergoes period elongation which we interpret as coherent following of the cage coordinate as it relaxes Vibronic dynamics of caged dihalogens has been exten sively studied in rare gas matrices11 13 Cage motion can be directly seen when the molecule is prepared on dissociative molecular potentials which are strictly cage bound Alter natively cage dynamics in the form of zoneboundary phonons can be seen when the probe transition is modulated by the motion 16 Where the molecular spring constant is signi cantly larger than the characteristic frequencies of the lattice phonons the molecular vibrational coherence under goes period compression due to vibrational relaxation in the anharmonic molecular potential The period compression under the assumption of linear anharmonicity Morse poten tial is the principal source of characterization of vibrational dissipation rates The signature of cage dilation has been observed as a faint elongation 5 elongation after 15 cycles of motion of the molecular vibrational period when 12 is prepared near the bottom of the B state in solid Ar in a region where the vibrational relaxation rate of the mol ecule is small15 In the present for 12 enclathrated in ice we see a dramatically larger effect of cage accommodation we observe the vibrational period of the molecule to stretch from 245 to 325 fs in the course of ve oscillations 13 ps with out loss of vibrational coherence This rather unusual cage dynamicsithe opening of a soft cage mode in slow enough motion to allow the molecule to follow with full retention of vibrational coherenceipresumably re ects the very local nature of the cage which is supported by a bulk of low density amorphous ice EXPERIMENT The samples are prepared by vapor deposition of the premixed vapor in the ratio 11000 of IZHZO on a 500zmthick sapphire substrate held at 128 K A second bulb containing pure water vapor is used to cover the sample to ensure that 12 does not leach under vacuum Sample thick nesses used was on the order of 200 Mm Measurements were conducted at the deposition temperature of 128 K bo before and after annealing at 155 K The experimental setup used in these measuremenm has been described in detail elsewhere1 Brie y the laser system consists of a Tisapphire oscillator operating at 790 nm The output is ampli ed re generatively to deliver 06 mJ pulses at 1 kHz and is split in 70 30 ratio with the stronger arm used to pump an optical parametric ampli er OPA to generate tunable visible pulses The leftover is used for second harmonic generation in a 200 rm beta barium borate BBO crystal The OPA output is compressed down to 60 fs using a pair of SF10 J Chem Phys 127 214511 2007 prisms The pulse elongation of the second harmonic at 395 nm is precompensated using a pair of quartz prisms The experimental time resolution is 90 fs as measured by four wave mixing on a 500 rm sapphire substrate in the same geometry of the experiments The fourwave mixing FWM measurements are carried out using three noncollinear beams in the boxcar geometry using a single f15 cm achromatic lens to focus onto the sample Two coincident visible beams are used to write the optical grating and the second harmonic is used to read the grating along k4k1 k2k3 Since 12 the detected ra diation is at A43 ie at the same color as the probe laser The FWM under this phase matching condition contains con tributions from transient grating TG and coherent anti Stokes Raman scattering CARS on the electronically ex cited and ground states respectively A monochromator coupled to a photomultiplier tube is used for spectrally inte grated detection Improvement of the signaltonoise ratio is obtained by synchronously chopping one of the visible beams at 500 Hz using a phaselocked loop referenced to the Pockels cell of the regenerative ampli er The signal is then collected with a boxcar integrator operating in toggle mode alternating polarity of the input ampli er and aver aged for 1000 pulses Frequency resolved measurements are conducted using a monochromator coupled to a charge coupled device camera Measurements were carried out on gratings prepared at 12512 493 and 550 nm always probed at A32395 nm In the data reported here all three input beams have the same polarization RESULTS AND ANALYSIS The absorption spectra of gaseous iodine iodine in clathratehydrates in water and in ice are shown in Fig 1 The absorption which is dominated by the B3Hu 9X02 electronic transition peaks at 450 nm in water and in ice and at 490 nm in the clathrate The spectra are blue shifted by 3500 cm 1 in the former and by 1500 cm 1 in the latter Note 12 does not form a clathrate on its own It is prepared as a mixed hydrate with THF or CHZClz as the main guest and iodine as a minority component which oc cupies 51264 cages3 While 12 isolated in rare gas solids uo resces over a variety of transitions183919 attempts at observing uorescence in hydrated iodine failed The measuremenm in ice reveal signi cant sample inho mogeniety The FWM signal intensity and the observed dy namics vary from spot to spot on the same sample with spot size determined by the beam waist of the laser of 50 Mm In certain spots sharp coherent oscillations are observed sug gesting the existence of ordered domains Two distinct be haviors are identi able when pumped at 512 nm and probed at 395 nm 1 oscillatory signal with Bstate periods and 2 oscillatory signal with Xstate periods along with regions in which both signals coexist Note the Braggdiffracted signal along k4k1 k2k3 allows the observation of Bstate dy namics through resonant TG when the pump excitation is resonant with the BHX transition1 or Xstate vibrational dynamics through CARS when the pump excitation is pre resonant with the B HX transition as extensively reported in Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpljcpaip0rgjcpcopyrightjsp 2145113 Vibronic dynamics of 2 in amorphous ice 550 I 512 39493 1 um I l I I I 21000 24000 cmquot 15000 18000 FIG 1 Absorption spectra a 12 in gas phase at 295 K b IzTHF clath rate hydrate at 273 K Ref 3 c aqueous solution of 12 at 273 K d 12 in amorphous ice at 128 K Dash dot horizontal lines show the base line in each measurement The arrows show the excitation wavelengths used in the FWM measurements IZdoped rare gas solids20722 The observation of one or other of these signals with the same pump and probe lasers but in different spots of the solid clearly re ects site inhomogeniety and the dramatic site induced shift in the Blt X resonance It can be seen from Fig 1 that 512 nm excitation corresponds to the peak of the Blt X absorption in the clathrate structure and to the tail of the band in ice Indeed the observed X state dynamics betrays a strongly polarized molecule consistent with trapping in frozen water while the observed Bstate dynamics selects an ensemble of molecules that is isolated in an immediate cage structure that is clathratelike We should note that the observed signal intensities from the different ensembles are comparable in magnitude suggesting that the strengths of transitions involved in the pump and probe reso nances are comparable Xstate dynamics In the present experimental scheme the two coincident beams that prepare the grating at a given color have suf cient bandwidth to create vibrational superposition on the ground electronic state Thus for degenerate excitation at Apumpksmkes5l2 nm vibrational states within the convo lution width of the laser 2Aw1aser350 cm l can be pre pared coherently Given the gas phase harmonic frequency we2l45 cm 1 and anharmonicity wexe06l4 cm 1 of J Chem Phys 127 214511 2007 FWM Signal au Q FWM Signal au 1000 2000 b Time fs FIG 2 FWM signal of 12 in ice a at the deposition temperature of 128 K before annealing and b signals recorded at annealing temperature of 155 K solid line and at 128 K after annealing dotted line The observed oscillations are due to the vibrational coherence on the ground X state In both cases a peak is observed at 100 fs with amplitude eight times higher than subsequent oscillations after multiplying the signal by 01 solid black line I2X23 24 coherent preparation of principally the v0gtv 1 superposition is to be expected The CARS signal arises from the scattering of the probe beam on the vibrational co herence phase grating while the transient grating signal arises from the population amplitude grating prepared on various electronic surfaces The two contributions appear in the signals of Figs 2 and 3 as the oscillatory CARS signal riding over the TG signal from the incoherent population FWM Signal au l I 0 2000 4000 Time fs FIG 3 FWM signal in 12 enclathrated in ice Measurement in a sample prepared under similar conditions as in Fig 2 recorded at 155 K The insert shows the period of oscillations obtained from six measurements carried out in three different samples excitation wavelength is 512 nm The dashed horizontal line shows the average period of 167 fs Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpjcpaip0rgjcpcopyrightjsp 2145114 Senekerimyan Goldschleger Apkarian background The measurement shown in Fig 2a is recorded at the deposition temperature of 128 K before annealing the sample the two measurements shown in Fig 2b are at the annealing temperature of 155 K and postannealing at 128 K The preannealed sample is subject to structural instability that leads to light scattering events an example of which is captured in the trace in Fig 2a shaded area Quench con densation of water below 130 K is known to result in the formation of predominantly lowdensity amorphous ice253926 and annealing at 155 K is known to lead to crystallization into cubic ice IE27 28 The intensity jump in the preannealed sample which must be associated with the motion of micrometersize grains takes place on the time scale of 1 min the scan time of the entire trace is 4 min The effect is suggestive of sintering or Ostwald ripening29 30 which can occur if defects have signi cant mobility At 128 K while defects in ice are locked a glass transition is known to con nect the lowdensity amorphous phase to the frozen water B phase27 It is quite likely that such a transition can be triggered photothermally during laser irradiation What is clear is that structural change on macroscopic scales occurs during the measurements in preannealed samples Once an nealed lowering the temperature back to 128 K eliminates the instability The signals shown in Figs 2 and 3 contain a response limited coherence peak which arises from both resonant and nonresonant contributions This is followed by the oscillatory part that rides over an incoherent background The amplitude of the rst recursion peak observed at 100 fs Fig 2b is eight times stronger than subsequent oscilla tions This appearance time of this peak is 15 longer than the halfperiod of subsequent oscillations and must arise from the predissociative B state see below Despite the variation of the incoherent background a meaningful analy sis of the oscillations is possible To be systematic the signal is tted as a multiGaussian to extract the position ampli tude and width of the peaks The insert in Fig 3 shows the average periods of oscillations obtained from six measure ments performed in three different samples that were pre pared under similar conditions The error bars shown are for the set otherwise the uncertainty in determining peak posi tions is approximately 7 fs The average period extracted from all six measurements is 167 3 fs and does not show a measurable variation with time The oscillations decay with a time constant of 12 ps independent of annealing history It is reasonable to assign the observed coherence to the 0 11 superposition in which case the period of 167 fs would translate into a level spacing of w101996 cm l which is 64 shorter than that of the free molecule 110sz 2wExE21327 cm l This is a signi cant reduction in the molecular spring constant larger than what is observed for iodine dissolved in strongly interacting liquids such as dioxane313932 In contrast the vibrational frequency of iodine in the clathrate hydrate is nearly identical to that of the free molecule In the series of studied solvents by Kiefer the spectral blueshift of the visible absorption band and the re duction in the vibrational frequency are directly correlatedi they take a jump between polar multipolar and nonpolar solvents Rather than intermolecular charge transfer the sig ni cant weakening of the molecular bond can be associated J Chem Phys 127 214511 2007 with electrostatics as recognized by the far IR measurements33 This is directly con rmed in the present system In the ice structure where the absorption band is shifted by 3500 cm l we observe a very large softening of the molecular bond in contrast in the symmetric clathrate cages where the blueshift is less than half as large the spring constant of the molecule is essentially unperturbed The ef fect can be directly related to the polarization of the molecule by the local electric eld Let us estimate the implied ionicity of the observed mol ecule and the required electric eld to induce such a polar ization Thus if we were to ascribe the softening of the mo lecular bond entirely to the admixture of ionpair character in the ground electronic state then for an electronic wavefunc tion given as altjgtlz3 gtll the potential energy of the mixed state may be constructed as V 012V12 BZVII where 042BZ 1 This is in the spirit of diatom ics in ionic systems which has been successfully applied to analyze vibrational redshifts34 and to reproduce details of potential energy surfaces for molecular halogens and hy drogen bonding in HF Refs 36 and 37 and H2038 The lowest ionpair state which is dipole coupled to the ground is the D0 state39 We note that in the free molecule the ion pair states are split by exchange energy which would be absent in the broken symmetry of a strong eld As such for VII we use the mean of the exchange split pair VD0 VE0 2 Using the known Morse parameters for the ion pairs and the ground X state we vary the ionic admixture and solve for the vibrational eigenvalues A bond ionicity of 322005 reproduces the observed value of mm 2200 cm l This value is consistent with what is obtained in ab initio treatments of H20Br2 and HZOC12 complexes4 6 Besides softening 5 ionicity stretches the bond from its equilibrium value of r82266 to r27 and implies an induced dipole of M12065 D Assuming this to be induced by the permanent dipole of a water molecule Mp18 D the required H2042 separation can be calculated as l 204LpLI13385 A in which 11034 1amp3 is the polar izability of iodine This is too short in comparison to what would be expected based on the van der Waals contact sepa ration of 48 A Were we to assume 12 to be sandwiched between a pair of water molecules with their dipoles aligned such that 12 is O bonded on one end and H bonded on the opposite end as in the motif seen in small clusters40 then the required separation would be 2485 Aia rather reasonable value It is safe to conclude that the molecules observed on the X state are trapped in asymmetric polar cages It is also safe to conclude that both in water and in amorphous ice 12 is strongly polarized by oxygen bonding to one water mol ecule and hydrogen bonding to another along its molecular axrs B state dynamics The Bstate dynamics is followed in the preannealed samples in what is expected to be the lowdensity amor phous ice In regions where the Bstate signal is observed exclusively the solid is not subject to the instabilities noted above The TG signals obtained for populations prepared at Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpljcpaip0rgjcpcopyrightjsp 2145115 Vibronic dynamics of 2 in amorphous ice E u E T E m E 0 1000 2000 Time fs FIG 4 Color online FWM signal of 12 enclathrated in ice a TG signal at 512 nm excitation solid line and t using Eq 2 in the text dash dot line simulation signal according to the cage following model discussed in text dashed line The change in the period of oscillations for six measurements in two different samples along with the t to the average of all the six measurements is shown on the insert 512 and 493 nm while probed at A395 nm are shown in Figs 4 and 5 respectively Measurements were also at tempted at a pump wavelength of 550 nm but no signal could be observed At t0 a response limited peak saturates the signal While at 512 nm Fig 4 fully modulated damped oscillations are observed for ve to six periods at 493 nm a single peak delayed by 300 fs is observed Fig 5 In both cases the observed signal can be uniquely assigned to arise from the B state The absorption spectra in Fig 1 make it clear that the cross section for exciting into the B state is larger at 493 nm than at 512 nm therefore the prepa ration of a population grating is unavoidable The disappear ance of the signal after the rst large amplitude excursion of the molecular bond halfperiod of 300 fs must be ascribed to complete predissociation when the molecule is prepared at 493 nm above the dissociation limit of the free molecule This is not too surprising since the B state of IQ is subject to solvent induced predissociation41L and the effect can be ex pected to be larger in polar solvents since dipolar coupling is the leading term in determining the electronic mixing in the main predissociation channel the crossing between the B31Tu and the a1g surfaces42 Evidently when prepared at FWM Signal au 600 800 Time fs I 39 39 39 I 39 200 400 FIG 5 TG signal obtained with 493 nm excitation A single recursion is observed at t300 fs J Chem Phys 127 214511 2007 512 nm a signi cant fraction of the population remains trapped on the B state Based on the ratio of the intensity in the rst recursion and second recursion we can estimate that of the population promoted to the B state 50 undergoes curve crossing in the rst bond extension The population that survives undergoes coherent vibrational motion and leaks out on the time scale of 1 ps see below This leakage rate is nearly ve times smaller than in simple liquids such as CCI443 44 and a factor of 2 larger than what is observed in cryogenic Kr matrices44 The large survival probability of the population in the present in cages constructed of water mol ecules is only possible if the cage were highly symmetric such that dipolar coupling among electronic states is effec tively cancelled electronic caging by symmetry44 As we expand below energetics dynamics and spectroscopy of this ensemble identify it to be in clathratetype cages The rather remarkable feature of the vibrational coher ence observed at 512 nm is that the period of motion stretches with time The insert to Fig 4 shows the observed recursion times as a function of recursion number obtained from six measurements and recorded in two different samples prepared under similar conditions The trend of pe riod elongation is similar in all six measurements even though the values show a spread that is outside measurement error Through a multiGaussian t of the data peak posi tions are determined with a precision of 6 fs however the spread in oscillation periods may be as large as 40 fs Fig 4 insert We attribute the observed dispersion to the inhomo geneity of the distribution of trap sites Two related effects may contribute to the dispersion in vibrational periods the spread in the spectral shift of the Blt X transition which controls the prepared initial vibrational energy and the local cage potential that may modify the spring constant of the trapped molecule In all cases the time dependence of the period elongation chirp is similar The mean chirp for the full data set can be represented by an exponential 7t70A7l em 1 with initial period of 70245 fs amplitude A780 fs and chirp rate a083 ps l The observed nal period after six cycles has a mean value 700325 fs Contrary to a vibra tional packet evolving in an anharmonic potential where re laxation would lead to period contraction we see a dramatic period elongation The observed period elongation would im ply a time dependent reduction in the effective spring con stant in the B state of 71722k2k1053 We ascribe the effect to relaxation of the con ning cage and note that the molecular vibrations seem to follow this slow coordinate with retention of coherence To characterize the extent of coherence during the mo tion we t the signal to the form of a Gaussian packet de tected under a stationary Gaussian window Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpjcpaip0rgjcpcopyrightjsp 2145116 Senekerimyan Goldschleger Apkarian Sm Aft78f e x xz5zZe x xc6X2dx A M Wee mt xCA27 where A 5120 52x 2 with the trajectory of the molecular bond x r re given as a damped oscillator 27139 xt x e wcos 3 l ltgt This tting scheme allows the assessment of contributions of electronic population decay Te time dependent spread of the packet 50 vibrational relaxation rate 1 that allows for the packet to fall out of the detection window and a time depen dent period of the oscillator 7t taken from the t to the experimental data Eq The nite pulse width of the laser is taken into account by convoluting Eq 2 with a Gaussian of FWHM90 fs As shown in Fig 4 dashdot line the procedure reproduces the signal with good delity The exception is the amplitude of the rst peak which is two times larger in the experiment which was argued above to be the effect of predissociation The reproduction assumes a xed packet width the packet retains its coherence without any evidence of anharmonic dispersion or dephasing and requires 710 implying that the decay of the signal ampli tude is entirely due to predissociation of the electronic popu lation with time constant 781 ps the detection window is wide 5xx003 and situated on the attractive side of the potential DISCUSSION The absorption spectrum of iodine in ice is nearly iden tical to that of iodine in water It would seem that the disor der of the liquid is frozen out in the quenchcondensed ice at 128 K The variation in the observed signal in different parts of the same sample and the direct observation of grain mo tion would suggest photothermally driven annealing and the establishment of ordered domains at least in the irradiated parts of the sample The doped molecule can be expected to trap in a variety of sites from strictly amorphous to crystal line domains and at grain boundaries The fact that in such an inhomogeneous sample we should observe coherent vibra tional dynamics is noteworthy The variation between ob serving X state CARS versus B state TG in different parts of the same sample would indicate a signi cant variation in the separation between X and B states in different trapping sites Indeed the successive 1500 cm 1 shift between the free mol ecule versus clathrate hydrate and then again between clath rate and ice indicates the same In effect we are selectively observing two identi able ensembles The observation of ex clusively Xstate CARS in certain regions is consistent with selecting molecules trapped in amorphous ice frozen water where the shift in electronic origin precludes access of the Bstate In this ensemble the molecular vibrational fre quency is reduced by 64 an effect that is explained in terms of the polarization of the molecule by the local electric J Chem Phys 127 214511 2007 18000 I a 1r0 I 3972 12000 1 3 f 113 ps c lt N gt 6000 o FIG 6 Time dependent effective potential of 12 enclathrated in ice a Morse potential of free 12 effective potential at i0 and t 13 ps with the exponentially repulsive cage potential Cage diameter d098 A and d13 p5 1068 A eld and therefore trapping in a highly asymmetric site with at least one water molecule oxygen bonded to iodine The observation of exclusively Bstate dynamics in other regions suggests the selective interrogation of an ensemble in which the B state is accessible at 512 nm moreover based on the rate of predissociation it is clear that the molecules in this case are isolated in highly symmetric cages Both of these observations indicate that the Bstate coherence is due to molecules trapped in a clathratetype structure where the water molecules of the cage are hydrogen bonded and un available to donate an electron pair to iodine This assign ment is further bolstered on energetic grounds as we expand below in modeling the strongly chirped vibrational coher ence in these sites At 512 nm in the free molecule 1139 of the B state would be prepared where the period of vibration is 516 fs Instead we observe an initial period of 24520 fs with a spread re ecting sitetosite variation If we were to assume that the electronic origin of the B state is shifted by 3500 cm l as seen in the absorption spectrum then the excitation would reach the very bottom of the B potential where the free molecule period is 1cw102685 fs This would seem plausible until we consider the observed termi nal period of vibration of 32520 fs which would now cor respond to reaching 11 14 It is not likely that we are observ ing vibrational uppumping There could not be a physical model that explains the period elongation if the initial prepa ration is at the bottom of the potential If we were to assume that the observed molecules are trapped in a clathratetype structure then the blueshift of 1500 cm 1 would prepare the molecule near 1128 where the free molecule period is 410 fs The much shorter observed initial period would have to be ascribed to the molecule being constrained in a tight cage with the subsequent period elongation to be associated with cage relaxation We consider a model that is constrained to account for both spectral shift of the transition and the observed periods We assume that the molecule is initially in a cage of time dependent diameter dt with an exponentially repulsive po tential between cage wall and I atoms Fig 6 The effective potential experienced by the molecule is Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpjcpaip0rgjcpcopyrightjsp 0 1 e For the reasonable esti mate of 10298 A given by the sum of the 12B equilibrium bond length 3024 A and the van der Waals radii of iodine and oxygen atoms the parameters of the exponential po tential A2956 X 107 cm 1 and 12111 A4 are adjusted to obtain simultaneously a blueshift of 1500 cm 1 and the observed initial period of motion The trajectory of the Gaussian packet is then obtained by solving the equation of motion WW Mrt 77r T 0 With initial conditions r r0 033 A r0 0 5 Assuming no dissipation 770 for the assumed cage poten tial the cage diameter must expand from its initial value of d098 A to dt13 ps 21068 A to reproduce the chirped signal Figure 5 makes it clear that at this terminal distance the molecule is still squeezed Yet the chirp rate is monotonic there is no evidence of rebound suggesting de formation that lacks elasticity on this time scale If so one would expect the cage to fully release such that the B state reaches its free molecule parameters That can be accom plished by now including a nonzero value for the friction constant in Eq 5 We adjust 77 such that the observed ter minal period of oscillation is realized upon complete relax ation of the cage potential d1125 A The signal can be reproduced equally well with either model There are inter esting differences between the two For the case 770 the molecule is prepared in 010 of the effective potential it loses 250 cm 1 of kinetic energy due to cage deformation and reaches 014 in the terminal potential While for the case of full relaxation the molecule loses 800 cm 1 of ki netic energy and remains in 010 throu hout The second model corresponds to the vibrationally adiabatic limit which is more realistic than the assumption of no dissipation The analysis suggests fully coherent vibrationally adiabatic fol lowing of the cage coordinate Note although the cage does not show any elasticity on the time scale of 2 ps it must retuni to its compressed ge ometry between pulses in time less than 1 ms The mono tonic dilation of the cage by 14 A on a time scale of 13 ps without eliciting any rebound indicates a soft lattice mode of heavy mass for which a frequency less than 6 cm 1 can be estimated This suggests a cage assembled around the guest molecule in a glassy solid which based on the prepa ration conditions is expected to be lowdensity amorphous ice The fact that the con ning cage mode is soft neverthe less the molecule is strongly caged such that the effective spring constant it experiences initially is 50 stiffer could be understood if the low frequency of the mode is deter mined by its heavy effective mass and small spring constant J Chem Phys 127 214511 2007 CONCLUSIONS The dynamical investigations of iodine trapped in what is nominally a lowdensity amorphous ice along with spec troscopic UVVis and Raman measurements previously re ported allow for deeper insights in the nature of the guest molecules trapped in ice The measuremenm clearly identify two main ensembles The rst which we associate with amorphous ice consists of asymmetric trap sites in which the molecule is strongly polarized through oxygen bonding to one water molecule with the spectroscopic signatures of a reduced vibrational frequency by 64 and a dramatic blue shift of 3500 cm 1 in the valence band transitions The solid in which this site is exclusively observed is structurally un stable at the deposition temperature of 128 K but the insta bility can be eliminated by annealing at 155 K Moreover the only Bstate signal observed in this site shows complete predissociation after one extension of the bond We offer a simple analysis of the vibrational downshift in terms of bond ionicity to conclude that the molecule must be in a highly polar cageioxygen bonded on one end and hydrogen bonded on the other The second site is associated with glassy amorphous ice in which the molecule is trapped in highly symmetric clathratetype cages where the molecular vibrational frequency is unperturbed and the UVVis spec trum is blueshifted by 1500 cm 1 as in the previously pre pared mixed clathrates Consistent with the concept of sym metry induced electronic caging we observe the B state to predissociate in 1 ps only a factor of 2 faster than in cryo genic rare gas solids The remarkable observation in this site is that vibrational coherences prepared on the excited B state undergo a dramatic period elongation without losing coher ence and with negligible dissipation The effect is associated with vibrationally adiabatic following of the con ning cage coordinate which undergoes dilation without feedback into the molecule ACKNOWLEDGMENTS This work was supported by the US National Science Foundation Grant No CHE0404743 The authors thank Professors N Schwentner P Devlin W Kuhs and KC J anda and Dr G Kerenskaya for helpful discussions 1I Goldschleger V Senekerimyan M S nge H Seferyan K C Janda and V A Apkarian J Chem Phys 124 204507 2006 2G Kerenskaya I U Goldschleger V A Apkarian and K C Janda J Phys Chem A 110 13792 2006 3G Kerenskaya I U Goldschleger V A Apkarian E Fleischer and K C Janda J Phys Chem A 111 10969 2007 A C Legon J M A Thumwood and E R Waclawik ChemrEur J 8 940 2002 J B Davey A C Legon and J M A Thumwood J Chem Phys 114 6190 2000 5R Hern ndeeramoneda V Hugo U Rosas M I Bemal Uruchurtu and K C Janda Twordimensional HZOrClz and HZOrBrZ potential surr faces An ab initio study of ground and valence excited electronic statesquot J Phys Chem A to be published 7I Golsdchleger G Kerenskaya K C Janda and V A Apkarian Polyr morphism in Brz clathrate hydratesquot J Phys Chem A to be published 8S A Corcelli C P Lawrence and J L Skinner J Chem Phys 120 8107 2004 9I Goldschleger V Senekerimyan and V A Apkarian unpublished 10F Pauer J Kipfstuhl W F Kuhs and H Shoji J Glaciol 45 149 4 Downloaded 15 Feb 2008 to 1282007848 Redistribution subject to AIP license or copyright see httpljcpaip0rgjcpcopyrightjsp Chapter 2 Limits and Rates of Change 22 The Limit of a Function I Limit of a function Review the method to nd the tangent to a curve or the velocity of an object we need to nd the limit of slopes or average velocities to nd the tangent or instant velocityi In this section we will turn our attention to limits in general Example Investigate the function 12 7 z 2 for values of 1 near 2 and nd the limit of as I approaches 2 The following table gives values of for values of I close to 2 but not equal to 2 M w fltzgt 20000000 30 80000000 20750000 25 50750000 30440000 22 40640000 30710000 21 40310000 195 30852500 205 40151500 199 30970100 201 40030100 10995 30985025 20005 40015025 10999 30997001 20001 40003001 TABJEl HHHHH 300010 From the table we see that when I is close to 2 is close to 4 In fact it appears that we can make the values of as close as we like to 4 by taking 1 sufficiently close to 2 We express this by saying the limit of the function 12 7 z 2 as I approaches 2 is equal to 4 The notation of this is lim127z2 4 EH2 In general we have the following notation De nition 1 We write lim L xaa and say the limit of as I approaches a equals L77 if we can make the values of arbitrarily close to L as close to L as we like by taking 1 to be sufficiently close to a on either side of a but not equal to a Note 1 Roughly speaking limgc a L means that the values of get closer and closer to the number L as 1 gets closer and closer to the number a from either side of a but I f at 2 A more precise de nition will be given in Section 24 3 We need I approaches to a from either side of a but I f at 1 4 The phrase but I f a in the de nition of limit means that in nding the limit of as I approaches a we never consider I a 1n fact7 need not even be de ned when I a The only thing that matters is how f is de ned near a See example of Figure 2 page 71 An alternative notation for lim L 7gt L as I 7gt a which is usually read fz approaches L as I approaches an Example 1 Guess the value of 131 I2 7 1 Solution Notice that the function I 7 1z2 7 1 is not de ned when I 17 but we can nd the limit as I approaches 1 from the values that I approach 1 as following z lt 1 z gt 1 015 01666667 115 0140000 019 01526316 111 01476190 0199 01502513 1101 01497512 01999 01500250 11001 01499750 019999 01500025 110001 01499975 TAB 4E 2 Example 2 Estimate the value of W2 7 3 11m t7gt0 72 Answer Mt 7 3 1 11m 7 zao t2 6 Note If you try to nd the answer on your own calculator7 you might get different values7 but eventually you will get the value 0 if you make t suf cientl small The problem is that the calculator gave false values because V12 9 is very close to 3 when t is smalli Example 3 Guess the value of Answer Example 4 lnvestigate FIGURE 1 Graph of fz as at 1 at 1 0 25 1 12 0 29 1 13 0 213 1 14 0 217 1 0 1 0 2101 1 0101 0 21001 1 TABLE 3 Solution Since the values of do not approach a xed number as I approaches 0 see Table 37 7T hm sm 7 does not eX1st 140 z FIGURE 2 Graph of sing Example 5 Find hm 13 cos5 z 1H0 10000 Answer 1 lt 3 cos 5 Igt 1 1m x 7 Ho 10000 10000 We had to be very careful in guessing the value of a limit using a calculator Sometimes calculators and computers give the wrong values In the next two sec tions however we will develop foolproof methods for calculating limits Example 6 The Heaviside function H is de ned by 0 if t lt 0 HO i 1 if t 2 0 As t approaches 0 from the left Ht approaches 0 As t approaches 0 from the right Ht approaches 1 There is no single number that Ht approaches as t approaches 0 Therefore limtno Ht does not exist II Oneside Limits De nition 2 We write lim f L EH07 and say the lefthand limit of fr as r approaches a or the limit of fr as r approaches a from the left is equal to L if we can make the values of arbitrarily close to L by taking 1 to be sufficiently close to a and 1 less than a Similarly the righthand limit of fr as r approaches a is equal to L if we can make the values of arbitrarily close to L by taking 1 to be sufficiently close to a and z greater than a and denoted as 3 W L From the de nition we have 139 Ht 0 d l39 Ht 1 3 0 7 an 3 0 We have the following Theorem lim L if and only if limi L and limJr L III In nite Limits 1 Example 8 Find liming 7 if it ex1stsi 1 Solution As I become close to 0 112 can be make arbitrarily large by taking 1 close enough to 0 Thus the values of do not approach a number so lim n0l12 does not exist Figure 3 D To indicate the kind of behavior exhibited in example 8 we use the notation 1 lim 7 00 1H0 12 100 FIGURE 3 Graph of 0712 Caution This does not mean that we are regarding 00 as a number Nor does it mean that the limit exists It simply expresses the particular way in which the limit does not exist 112 can be made as large as we like by taking 1 close enough to 0 De nition 4 Let f be a function de ned on both sides of a7 except possibly at a itself Then lim 00 raa means that the values of can be made arbitrarily large as large as we please by taking 1 suf ciently close to a7 but not equa t Another notation for limgcha 00 is A 00 as r A a Again the symbol 00 is not a number7 but the expression limgcha 00 is often read as the limit of as I approaches a7 is infinity77 or fz becomes in nite as I approaches a77 or fz increase without bound as I approaches a77 A similar sort of limit7 for functions that become large negative as 1 gets close to a7 is de ned as follows De nition 5 Let f be de ned on both sides of a7 except possible at a itself Then lim 700 raa means that the values of can be made arbitrarily large negative by taking 1 suf ciently close to a7 but not equal to al The symbol limina 700 can be read as the limit of as I approaches a7 is negative infinity77 or decreases without bound as I approaches alll Similar de nition can be given for the onesided in nite limits limi 00 limJr 00 limi 700 limJr 700 remembering that z A a means that we consider only values of I that are less than a7 and similarly z A a4r means that we consider only I gt a De nition 6 The li e z a is called a vertical asymptote of the curve n y if at least one of the following statements is tru lim 00 lim 00 lim 00 149a xeea 149a lim 700 lim 700 lim 700 meea xeea 149a For instance7 yaxis is a vertical asymptote of the curve y 112 because limgcno IQ 00 Example 9 Find 1 2 I 139 cl 139 7 13173 an 13131173 Answer 2 z 2 1 lim 7 00 and lim 700 H3x73 xHS I S 400 200 35 4 7200 7400 FIGURE 4 23 Calculating Limits Using the Limit Laws Limit Laws Suppose that c is a constant and the limits existl Then 1 2 3 4 5 6 7 8 9 10 11 lim and lim 91 lim 5 5 lim 1 a min 9ltzgtl hm fltzgt um gltzgt min 7 m gig fltzgt 7 mm 0113 W c gig fltzgt mmmw gig fltzgt mm fz 7 11mm fzgt 13 7 limxaa 9W if lim 91 0 where n is a position integer lim 1 a where n is a positive integer 1uz limtfquotE where n is a positive ineter if n is even we assume that a gt 0 gig mac 40113 fltzgt where n is a positive integer if n is even we assume that limxna gt 0 12 If 91 when 1 f a then Note lim lim 91 1 In the Limit Laws the conditions that limgcna and limgcna91 exist are necessary 2 The Limit Laws also hold for oneside limitsl Example 2 Evaluate the following limits ai lim n5 2 12 7 31 4 b lim H72 13212il 5731 8 Solution a lim2w2 a 3w 4 11m2w2 a 11m3w lim 4 was was was was 2 lim127Slimzlim4 17gt5 17gt5 17gt5 252 a 35 4 39 bl 13 212 71 7 limgcn2z3 212 71 wanalQ 5 7 31 7 lim H25 7 31 lim 472 13 2 lim 472 12 7limxn21 lim H72 5 7 3 lim H2 z 723 2722 71 5 7 372 E D Direct Substitution Property If f is a polynomial or a rational function and a is in the domain of f7 then 0113 M fltagt Not all limits can be evaluated by direct substitution Example 3 Find 1 z 71 wlani I71 Solution We can t nd the limit by substituting z 1 because isnlt de nedl 2 7 7 lim I 1 lim 1 1 1 1 wa1 w a1 wai w 1 lim 1 1 wa1 11 2 Example 4 Find w2 73 lim zao t2 9 Solution We can7t apply the Quotient Law immediately7 since the limit of the denominator is i 1 27973 7 1 V7524 73 xt293 31 t2 7 31 t2 Ixt27l39797l3973 t2 9 7 9 hm 1H0 t2lt t293 2 t lim 1H0 t2lt t293 1 1 1m Ho W s 1 1 1 hm oaug 3 33 7 D Some limits are best calculated by rst nding the left and righthand limitsl To this end7 we have the following Theorem 1 lim L if and only if limi L limJr 1051 Example 8 Prove that limgcno does not exist 1 Example 9 If 8 7 2 1 if1 lt 4 determine whether lim n4 exists The next two theorems give two additional properties of limits fx if1gt4 Theorem 2 1f S 91 when 1 is near 9 except possible at a and the limits of f and 9 both exist as 1 approaches a t en lim S lim 91 Theorem 3 The Squeeze Theorem lf f1 g 91 g h1 when 1 is near 9 except possibly at a and lim lim h1 L then lim 91 L Example 11 Show that 1 lim 12 sin 7 0 170 1 Solution First note that we cannot use 1 1 l1m 12 s1n 7 l1m 12 l1m s1n 7 170 1 170 170 1 10 because lim ho sin1z does not exist However we have 1 712 S 12 sin7 S 12 z and lim 12 0 and lim 712 0 ma xao Thus we have from the Squeeze Theorem 2 1 sin7 0 1 lim 1 xao FIGURE 5 25 Continuity We notice in Section 23 that the limit of a function as I approaches a can often be found simply by calculating the values of the function at a Functions With this property are called continuous at a De nition 1 A function f is continuous at a number a if gg mfw Note 1 Notice that Definition 1 implicitly requires three things if f is continuous at a o fa is de ned that is7 a is in the domain of o limgcna exists 0 limgcna fa 2 The definition says that f is continuous at a if approaches fa as I approac es a 3 If f is defined near a in other words7 f is defined on an open interval containing a except perhaps at a7 we say that f is discontinuous at a or f has a discontinuity at a if f is not continuous at a Example 2 Where are each of the following functions discontinuous ey mi33 2 127172 cy m1w2 1 the largest integer that is less than or equal to If Solution ai fis quot 39 atg 1 LI p W b f is discontinuous at 0 in nite discontinuity c f is quot 39 at 2 1 u u W Cl 161 I can be de ned as follows I n if n zlt n17 here n is an integer Thus f is discontinuous at all of the integers jump discon tinuity i De nition 2 A function f is continuous from the right at a number a is lim fr fa xaai and f is continuous from the left at a if 11mg f I f a mall Example 3 At each integer n7 the function is continuous from the right but discontinuous from the efti De nition 3 A function f is continuous on an interval if it is continuous at every number in the interval If f is de ned only on one side of an endpoint of the interval we understand continuous at the endpoint to mean continuous from the right or continuous from the left Example 4 Show that the function l 7 xl 7 12 is continuous on the interval 71 Solution lf 71 lt a lt 1 then gr fltzgt fa At the endpoint of the interval we have E 113111 2071 71gt 113 fz1 f1 Theorem 4 If f and g are continuous at a and c is a constant then the following functions are also continuous at a l fg 2 f7g 3 cf 4 fg 5 ifga7 0 Exercise Try to prove the Theorem 4 by yourself Theorem 5 a Any polynomial is continuous everywhere that is it is continuous on R 700 co b Any rational function is continuous wherever it is de ned that is it is continuous on its domain Exercise Try to prove the Theorem 5 by your self Example 5 Find 13 2 12 7 1 1m 772 5 7 31 Solution Consider the function 13 212 71 161 7 5 7 31 the domain of is I f Therefore 3 27 lim HI 1f727i 772 5731 Theorem 7 The following types of functions are continuous at every number in their domains polynomials rational functions root functions trigonometric functions Another way of combing continuous functions f and g to get a new continuous function is to form the composite functionf o g 13 Theorem 8 If f is continuous at b and lirngcna 91 b then lirngcna In other words hm fltgltzgtgt f hm gm EH11 EH11 Theorem 9 If g is continuous at a and f is continuous at 9a then the composite function f o 9 given by o g is continuous at a Example 7 Where are the following functions continuous ai hz sin12 Fz W Solution a Let 91 12 and sinz Then hz and is continuous on R b Let 205 gltzgtzi4 hltzgt man then Fz Each of these functions is continuous on its domain Hence F is continuous on its domain IER 1274I Ii3 The Intermediate Value Theorem Suppose that f is continuous on the closed interval a b and let N be any number between fa and fb where fa Then there exists a number 5 in a 12 such that Ni Example 8 Show that there is a root of the equation 41376z231720 between 1 and 2 Solution Because 413 7 6x2 31 7 2 is continuous on 12 and 71 lt 0f2 12 gt 0 From the intermediate value theorem there is a number 5 6 12 such that 0 D Assignments 1 Find the limit if it exists If the limit does not exist explain why You need to write down each step while answer the questions N2005 TRA CK II Potin 2102009 111201 AM Imaging Genetics Brain Imaging Center Staff amp Faculty Arthur Lander Fabio Macciardi Ann Carlof and fBIRN T N2005 TRA CK II Potin 2102009 111201 AM 1 Review QT strategy using brain imaging as a QT 2 New GWAS combined imaging identifies new candidates 3 Systems biology approach to evaluate these candidates oKnowledge of Candidates From Pathophysiology of Neuronal s Circuits Microsateite Surveys 39Candidates From dentifying Hotspmsv amp oNeurotransmitter Systems and Genes in ROI oPharmacology of Disease oCandidates From oMicroarray Studies in Animals oeg PCP amphetamine oTreatment Models 0 eg neuroleptics Plus validation with In situ hybridization N2005 TRA CK II Potin 2102009 111201 AM Variability in human Variability is the law of life and as no two faces are the same so no two bodies are alike and no two individuals react alike and behave alike under the abnormal conditions which we know as diseasequot Sir lliam Osler 13491919 The candidate gene approach 0F Collins N2005 TRA CKII Patin 2102009 111201 AM Candidate Gene Approach Biological face validity is reassuring but potentially dangerous Limited by current knowledge and concepts 12 million polymorphism requiring between 5 and 15 million SNPs to adequately represent genetic variation 111e genome wide association approach A it it it N2005 TRA CK II Potin 2102009 111201 AM iI dlr quot i a 0 1 PostTest Probabil39 2 o I I u I I 30 ii Personalized medicine in the near future Computer analysis Probabilities of medication response and development of side effects Eiiicacy Negative Cognitive DM Weight Suicide Clozapine Olanzapine 80 70 20 70 90 4 Ziprasidone 10 7 85 75 30 20 Men 9 39 m M u AnlzeIe imagin Bloodsamplein r 7 t physician s office Gene Chip Pntkin et al 2002 N2005 TRA CK II Potin 2102009 111201 AM Imaging Genetics Imaging Genetics combination of imaging genetic and clinical data Candidate approach begins with a gene of interest and use brain imaging to understand the gene effects Imaging as a strategy to nd unknown risk genes Fundamentally different from a standard candidate gene approach New approach uses brain imaging as a quantitative phenotype and identifies wun SNP influence u m the context of a GWS N2005 TRA CK II Potkin 2102009 111201 AM A HOLD change Memory Load 0 Healthy Control Len Hermsphere mu ma mu 5 N2005 TRA CK II Potin 2102009 111201 AM Why Brain Imaging Quantitative and qualitative changes in brain function often predate or precede clinical changes and thus can be im ortant in earl diagnosis and monitoring of treatment Current diagnostic system based on subjective patient reports may be inadequate to distinguish meaningful biological differences and subtypes New Approach Imaging Phenotype Genotype Imaging Phenotype is activation in ROI eg BOLD signal left DLPFC during working memory task Genotype SNP1 Determine which SNPs or genotypes influence these functional differences by a series of GLM N2005 TRACK II Potkin 2102009 111201 AM naasea nonsnxs nsmi nosian nonnua nunszz nnxnm naniosi naneen nwssis nszma nzzssei nosiisk nanxosz noxsasi nnszmx nxsznss nissszi nim nmsxu nma nusnz nimis nsosizi n nmzi naninsx nainzss nsxisss Munoz ninixsb nennnn nsonmi nnssis nsoxnn nosnsiz nwszs nsszonr nnsosss neziini naesesz nsnsm nnnneu nsssixs nsmsm nnzsm ninms nxwm nznme n nxnsso niszizz nsoszos nmazz nzemi nawu nsxzus nosszsx nsnnn nzsznz nnssza nxizses nssisss nossoxi mama naisasz nsxsnis nenisix n see nisss nmosz nimso nunne nsiozzi nzzmn nisissi nixezi nmzxi nunnvs nissxu nizsiss nmzza nsxosm menus nasxixs mama nsiisss nxixmi nazssne naeuz nnenm nsosnss nmixs nnszsz nsnzans nmusi nmnn nabsns n nzosszi naiszsi nzisx naenzm nzmzo nxzsms nsnsu nxuxix nszaxss nszzm nsonsxx niszsos nassm n enae nsbsxa ne uni nsnxzao nsozasz naaannn nsxnuz nosxnzs nonssza naxsixz nssms n nsxsssi nsnmsi nsiisis neonnz nnm nxozsn nzsnass nonisso amiss nzm ninnn M33333 nsvz nusixs noissos neevasa nnnenes nzzsxss nbxmx nooxzsi nossisa nmssss nsszses nnmza n nnunas nisnsnz naismx nziinsz nsssxii ms nxmis nisuso nssmi nasesu nzzxzxz naxnzu nxsmss nseseen naasans nezuna n 5979 amino n susz naanene nnizxn nisnnss nssme nixzxi n newnes nzssm ninnsz nxmxs nisisss n ms n27232 niuzzx nxossze nsssosa nzxszzs nmisi Mamas nzixses mum names nbazsi nissbsi nnxsz nosisn nssisix nsnsos nxzxns nsnnxz n nxszsx nenisis nmsna nnessoz nesnm nansm M32952 nisxnnx nszwsz nzuasa nzmsz nomi nanann nmees nwxszs nnxxsxi nmav nsbnss nznze nixim naiszn nisaxsz nbsnszi ena nznsss nsasis nnmx nma 35 nmm nmsu nzxsnzi nisioso nzsoxii naeeene nxonsiz nsssxsl nxssm oxsxs usissso same nmsiz nisnxu nzsixsx nissixz nmzzn nixsais nssuai nusna nixoszi nxnzsu nmisi nzexsi Emu nannii neizxm nusizz nzzms nmnz nizsm nsmm nnissn n zen nszsiz nmizs nnzsoso nzxsm nozzm nxssxoz nmsns nisssxs nsssisi n nnnennn neznnea mum nxsinsa neiniss nnnnn nnsssbs nnsgsso nnesssz nnxaxzs niszixs nnaesss nssosil n 92772 nwssm nnnnsos n 22225 n 75m 233 naisam nmnae nnenzi nsszisa noxssz nmnzi nsssnes nnaozss nxazxm nszsus nziisiz nauxxz nanness nszsu nusam nnnzis nossms nuzzn n 5532 nxinisi nnsassz nxsmi nmnsu nnnsnis nsisizs nonssu nnseees nnensae neonxb n nnsneea nuzsns nxuxos nussm nszsiis nzsxsn snsm nszsns nszsoz usis nisosis nnennan nsxnssr nzzssis nszsxa nnzssz nbnsbs nszms nssxsis nsixssi nmssax nesnxu ninsxsa nsmsns n nsssons nxxasix nemea nssbssz noxssaz ninxsnz nwme nzszaxo nnsssee nnnzsz nsoisxo nnsnsx nxnsns niosnza n mo nzzmi n xsxi nsonins nanni nxnmx nsssws nssuzs moms ninsz n nzssos nozxsis naosaxs nnisu nozzssx nzsnzi nzsanm nxszsis nozzise nsnmsi nxzaixa nimis nszinu nsanzss nmnes nzssxes nszsii nisnsse naissss nsonsi usisziz nssisis nssm nisbxzx n nxaxozs nsxwz nssusi nzisssx niismz nnszsix naossis ninssii nnasm naenenn nssxios nonsiss nnseese amiss nnzssn nnsem nzssxss n een nnszssi nszms nsxszns nusm nwxasi nsniszi nmsns nazsnse nnnsisz nmnna ninius noszesi nsnisu nssznzs nmnn nmsxs nsnss usissao nssisix nsnssn nxmix num nmoxss 9232 nma nwznnx naznmx neanes nozzzs nixissi n nzxasos nsmxn nzsaim nsnszi nansm e ninssss n27ssl niszim numb nnnxu nusuz muses nsisnsx nxnosx nmzi nissnu nssosii nn 252 names nesneaa nsnme nosssos nnanm nzonsn mums nxsxsxz nnosxs nxms 7 nvnvnnn nssnnsi noxaiso nnssiss nmsnnx nsisisz nxisio nzensnz nzzms nbsuzz usinso nxaszzs nsssws nzsaxxs nansxxi nsixssx neauns nsueea nsnsxza nisbxnz nenms nssxixs nossns niaaiss nssises nwxsze nisssis nnznnn nmszaz nuam nsxaxza nxzssss nssinn noxsszi nsoxiis nznnss nizsnz nsosuo nssbzni neensen nzsnnis nziossz nxsasm naessso nnzissi n 7 usisxi noasssi usizns nixssaz nxsssis nmzi ninssn nss nse smns nssnssi n nne neeasnn Misses nisoszi nnaaenn nnesssi nxizxss mm m e nsmsz nixsizs nseane iassii nisiosi nmnna nnsxm nsnana nussw nsnsm ususis nannsu i323 ess amen nenszxz neaaeae nasms nsssxxi nbnzsiz nsisizi nneanna um nme mama usixnss nasnnx nneaens nmnzs nzssaxs nxmsi nexzim nssissz nnsznx nnsnsu nwnz naisnu nmeea nmisx n asne nisxsns nbsissa nxossso nemae nzsissz nzssu s eane nzmas nissiiz nxssxis nixssss nsnsxis nesnnu nisbssz naesniz e nsasozs nosuxs nssszii nzmxo usaszxx nnnm n nsmee nsenenn nus nawu amuse nisnzz ammo nsnzsss nzeszsi nnnena nxmso amass n 7253 nnzzes 957 usim nxsms nxxmso ammo nnneee nzszasx nxssszz nnusiz nnm nszsu n2 737 nsosasi naisni nusnzs nxosxsx nsnixxi nnsma nsszzio no nsnsu nnvn nassus n 232x uszsa nanzsiz nnaane neseun nasmzi nxsissi usazsxs nxxizss names n eaee nnsxxs nisxszs n nnes nzsiinz man nsszios noesini nssxmo nzssisa nsnssi nosssm nsnissi nneenee nsnxos mums nosnnii names nmxos n xinsz nms nnszosz n nnsxozs nsszsss nosinx masses nnssene nsnsszz n ean sasinz nisnsm nxsisxi niissis nensnnn n naxmsi nmwe nnesinz nsosnsx nzbsxo nnsnsi nssxzxs nssizni masses nisassa nszssu nnsxzsi n naneenn nsinsz naeneee nswssi nuxssi nmesa nsnsxzz nonsis nissxsi na 733x nssms nzsszxi n nnnsei nnssozs nmms nissm nssxisz nsiszz msi nososas n 2x2 nazim nn nnzs nwnm n usisnsz nnxunx nsznsii nnzniss nxsasaz nsxmi nasisss nsossio nxaznxs nzsisu namxo nan mason n namsi ninxnz nszsss n 7xxo nxzssei nzssszx nzzxssx nsxzaxr nmiso nn 3329 nauso nsueee nixsozs nmzsm nnbnss nnxazso nsmi nxxzso nmaz nsmm nsszsoz nsxizsz naiisis nmxzis H3255 nxsisas niisiso nxsnini nzissio n nzissw nssnsoz niswss me nnvnen M72923 nissnik naxxsaz nmssi naxisns nssisn nimnz nismx nxixsso n nxsesb n ism niznnsa nzzaszb nmazs nsxam naeneee naszvnn nmsix n ssnz nmaz nisxam nsnmm 5329 nisuss n nnsbxzx nsmsi nmzu nxmss nasuas nainssx mum nimxw nsnmm n 32m naizw nnnso nuzzxo name nnssxz n neeaan nexzisz 9952 n uzzi nisssos nxssm nzxszis nnsezs nssuns neeenae nsainnx nisxssz naisxze nxsnzs nxszn nixxm nsizsso n nuxsns nmzs nnaaasa nbxst nxmxs nsssisz nxznxs nsissis nznssao nmszx nnsneze nsxssz neznsb nnsiso nnsoxs naixsis n nasazsi nzxsxs nzssini nxsssiz nxsnni nixszzx nsenm nmnne nosnsxo nxxomk nixsssi n mss nzwsa nnxu nssixsz nsznm nzssis n nissws naism nnnasn nnnnnna nwees moms nnsm mosses nzixm nsosinz noxissz nnsisok nixssxs nnzisz nemsn nssszis amass nssszns menus nsznsiz nassus nnssszz nnseun n nsssoss nznnws nsssaos nosissb nonsm nesnsxi nixxnss nzsiiss nisnin nnssox nunm naiozxs nznsaos niswzs nssnss nnszsz nemne nomsz nzznszx nasnsai nsnnzi neensee nmsoss nwms n We mmm Drklllmm DL Prevanlal 1 oLooking down 10 million base pairs on Chromosome 6 to discover the genes that cause schizophrenia ew gene detected in white bracket oPeaks point to SNPs that N2005 TRA CK II Potin 2102009 111201 AM Discovery sample Gws with Imaging as Quantitative Phenotype 27 of47 SNPs on 19 of58 SNPs on fquot 3 gene Chromo 5 gene 18 of the 19 measured in Veri cation sample 17 of the 27 measured in Veri cation sample 6 of 18 positive in case control Verification study 13 of 17 positive in case control Verification study DOPAMINE RECEPTOR SIGNALING mm H L rum 7 rPostsynaptic neuron N2005 WCKII Po dll 2102009 111201 AM GLUTAMINE RECEPTOR SIGNALING Postsynaptic neuron QTs increase power and reduce needed sample sizes Power Distribution Curves case contro QTL o zoo 400 600 800 1000 12110 1400 1600 1800 2000 Sample Size N2005 TRA CK II Patkin 2102009 111201 AM fBIRN Sample UCSD UCLA UCI BWH MGH Duke Universities of New MexicoMIND Iowa Minnesota N Carolina and Yale University Gender Male 719 608 ns right handed 875 919 ns Mean age 373 378 ns NARRT Premorbid IQ 1052 1133 lt0001 SAPS global 893 SANS global 645 Calgary Depression 523 Analysis 0 Regression on every SNP Phenotype effect of SNP effect of diagnosis What affects the phenotype one way in 2 and some other way in controls 12 N2005 TRA CK II Potkin 2102009 111201 AM lRN Analysis Plan o Illumina HumanHap300 genotyping tag SNP a After QC 302 783 autosomal markers to analyze a Stratification assessed by EIGENSTRAT47 a PLINK used to assess interaction term a Additive model c There are no definitive methods for determining a statistical threshold for a QT interaction 9 Given 302783 SNPs set threshold at 106 QT analysis for the interaction between right DLPFC and GWAS SNP At least two SNPs at a 10396 significance level CHR GENE SNP TYPE MAFCTRL MAFSZ PValue R0302 3 R0301 rs7610746 INTERGENIC 031 041 756E06 R0302 3 R0301 r59836484 INTERGENIC 032 041 423E06 3 TNIK r52088885 INTRONIC 047 045 624E06 3 TNIK rs7627954 INTRONIC 047 045 624E06 CTXN3 5 SLc12A2 r5245178 INTERGENIC 032 030 122E06 5 SLc12A2 r5245201 INTERGENIC 032 030 931E08 1 N2005 WCK II Potkin 2102009 111201 AM QT analysis for the interaction between right DLPFC and GWAS SNP At least one SNPs at a 10396 significance level and putatively belonging to a previous pathway CHR GENE SNP TYPE MAFCTRL MAFSZ Pvaluequot 2 GPC1 rs1574192 INTERGENIC 038 030 392E06 6 POU3F2 59491640 INTERGENIC 006 002 923E06 14 TRAF3 rs10133111 o 02 477E06 Overexpression of TNIK causes cytoskeleton disruption announcesu on w 5 a D in N u procaspasg 9 S 4 Stress CRH N2005 TRA CK II Potkin 2102009 111201 AM The role of stress 339 em 393 TNIK 3q2631 Stressactivated serinethreonine kinase that may play a role in the response to environmental stress and LTP 14 of 79 lt1o5 Also suggestive were the TRAF ndings a gene which interacts with TNIK in the HPA axis function and TNF alpha TNIK and TRAF3 both interact with DISC1 Camargo etal 2007 POU3F2 transcriptional factor regulates CRH TRAF3 POU3F2 TNIK rs10133111 rs9491640 fS7627954 i T 3 APT Hi 3 it 17 i acinrimneaam 39 ammsm taa ittt I ramorrrg msn 15 N2005 TRA CK II Potin 2102009 111201 AM Neurodevelopment ROBO1ROBOZ 3p123 13 of70 lt105 Involved in neuronal midline axon crossing May also be involved in developmental dyslexia In an area implicated In SZ Not quite previous linkage studies pointed to 3p2224 SYNZ or 3q26 lL12A but not 3p12 Neurodevelopment CTXN3SLC12A2 5q232 5q233 13 SNPslt10 5 CTXN3 cortexin enriched fetus and post natal increase SLC12A2 is also NKCC1 sodiumpotassiumchloride co transporter and regulates GABA Differentially expressed postmortem SZ brains Dean 2007 May be involved with epilepsy infarct and inflammation In the 5q22 region implicated repeatedly in SZ Almasy et al 2008 5q22 related to cognitive function measures in SZ 0005 TRACK I Patin 2102009 111201 AM GPC1 51574192 acmmiagnnsis Scmznnhmma Mm nghl uwc actnrs1 741 2 Human GWAS egatydata Hum n PMHUWD N2005 TRA CK II Potkin 2102009 111201 AM Human GWAS legacy data Human Phenotype Neuronal Vquotquot ll function Human GWAS legacy data Human Phenotype I gt Neuronal my function Bioinformatics 18 N2005 TRACK II Potkin 2102009 111201 AM Human GWAS legacy data Animal models k Neuronal quotl function Bioinformatics Systems biology addresses links between SNPs and human phenotype originally identified by GWAS Human Phenotype DISC1 Interactions LM Camargo et al Mol Psych 2007 Bait Tami number afinteractians High confidence interactions DISC1DSC1 134 16 DISC1 Nlerm 140 26 DISC1 379 39 Discllrunc 80 16 Discllrunc 134 14 FLJ13386 210 22 Cep63 79 10 TRAFSI P1 1 23 17 NDEL1 81 17 SEC3L1 92 13 SHSBP5 58 Z TNIK 105 15 CDC5L 80 17 CDK5RAP3 25 0 DTNBP1 97 17 Physical binding doesn t necessarily mean in vivo functionality 19 N2005 TRA CK II Potlrin 2102009 111201 AM Gene interaction network inferred from prefrontal cortex gene expression in 42 different inbred mouse strains Schizophrenia candidate genes from GWAS are in yellow Some unexpected connections DACT3 circled encodes regulator of Wnt signaling that has been linking to schizophrenia413943 Inferred Networks mm Currant MAP 12x10 s oquot 011 pvalue in two independent imaging genetics GWAS datasets C2 refers to canonical pathways and chemical and genetic perturbations C3 refers to motif gene sets C4 to computational gene sets and C5 Gene sets enriched analysis Subramanain PANS 2005 to GO gene sets MicroRNA datasets are indicated by mir MSigDB Gene se 24 SCZ dataset SIRP datasel Number category Gene 53 name MannWhitney KS logmp MannWhitney KS logmp of genes Zscore value Zscore value 03mir ATATGCAMlR448 88657 171214 69348 97769 177 CZCgp UCTTDALLDN 86874 129778 74691 99803 318 c21cgp UVCXPCSALlDN 81193 125773 79788 12225 419 c2cgp UVCXPCSBHRDN 76156 103729 75681 107036 359 chgp UVCTTD8HRDN 73774 60467 64656 66742 144 cZcgp UCTTD4HRDN 73072 102440 61085 71162 262 c3111 VOCT103 67830 81680 26201 16422 147 c2cgp UVCXPCS4HRDN 66389 96161 57022 71296 208 c2cgp 945575754909 66375 98099 52192 45020 203 c3mir AAGCACAMIR21B 65172 78408 69509 110283 332 03111 YNGTTNNNATTUNKNOWN 59645 66110 73309 127903 235 c3mir AAGCAATMlRtS 58681 72371 65203 76126 168 0361 VNKX2502 58142 71266 47564 39708 181 GNF clusterGNF105 57840 65692 63786 75820 187 c3tft VCART101 57749 63817 54727 78015 157 c3tft V0CT107 56725 92947 38748 35030 107 031mir TTGCCAAMlR182 56675 52286 57457 81750 263 c3mir TCCAGAGMlR51 BC 55932 72030 31213 25984 124 c3mir CAGTAWMlRZODBMIR200CMIR429 55687 61427 60432 62270 363 03111 VFOXJ202 55746 53850 59776 65761 160 c3mir TATTATAMIR374 55734 51674 56163 60237 233 05bp NERVOUSSYSTEMDEVELOPMENT 55395 60857 51776 63565 331 c3mir GTATTATMlR3693P 55370 92865 36326 42507 170 c2cgp BOQUESTCD31PLUSVSCD31MNUSDN 55227 54404 56424 45051 217 c3mir ACTGTGAMlR 27AMlR27B 54877 57890 59505 68975 381 20 N2005 774CKII Potkin 2102009 111201 AM microRNA and Schizophrenia Scandinavian sample 840 SCZ 1476 HC rs17578796 and rs1700 in mir206 and mir198 showed nominal significant allelic assocuation Hansen et al 2007 BDNFregulating microRNAs miR195 and miR30a5p decreased in PRC of SCZ n20 Mellios 2008 miR181b increased in superior temporal gyrus n2L may regulate calcium sensor gene visininlike 1 VSNL1 and the ionotropic AMPA glutamate receptor subunit GRIA2 schizophrenia Beveridge NJ 2008 Decreases miR 26b 30b 29b 195 92 30a5p 30d 20b 29c 29a 212 72430e 93p and increased 106b Perkins 2007 Phenotypes of glypicanl Gpc mutant mice Lander Pysn SprouIyISproulyZ 21 N2005 TRA CK II Potin 2102009 111201 AM Ra mlgha Ntmolmmmupr Ade r39jrwyl 0mm mmmm mmplm duve anmom p bely ncwmnl a p 0 myclmanon N mumquot v pummypu Hzlemlop ag Mkls om m mowed mye n Colrzlduon mween ahuwed In unhtgml upmaxmn mmcl mduumn m numva 19 M unset nl luchhmma xdlhnphmnin vumudu reK m mama 039 ulandendnxyles and sexual mnunavian R v Schixophrenia quot u eummnsmmer 0llgndendrncyle 0m2 e1 Reee nr dwelnpmenl puheny essinn myein nn ED 2 7 2 Pllulla v7 oua ELM Cnrrerlinn between age nl unset nlschiznphreniz n manned mrelin neummnsmmer quotEdna n number enemmexpressmn n1nllgndendrncylus and sexual malumt nn mam mm Ennas zuuaumme Newnsmence

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