3._CRD Experimental_AJ0 view_NN1 of_PRF plasmons_NN2 
In_PRP the_AT0 past_NN1 several_DT0 decades_NN2 ,_PUN new_AJ0 synthetic_AJ0 approaches_NN2 have_VHB produced_VVN hundreds_CRD of_PRF distinct_AJ0 atomically_AJ0 precise_AJ0 noble_AJ0 metal_NN1 nanoclusters_NN2 coated_VVN with_PRP a_AT0 ligand_NN1 shell_NN1 ,_PUN ranging_VVG in_PRP size_NN1 from_PRP tens_CRD to_PRP hundreds_CRD of_PRF metal_NN1 atoms_NN2 ._SENT Depending_VVG on_PRP the_AT0 size_NN1 ,_PUN shape_NN1 ,_PUN metal_NN1 composition_NN1 ,_PUN and_CJC ligands_NN2 ,_PUN these_DT0 nanoclusters_NN2 may_VM0 exhibit_VVI either_AV0 plasmonic_AJ0 or_CJC excitonic_AJ0 properties_NN2 ._SENT Spectroscopic_AJ0 studies_NN2 have_VHB shown_VVN that_CJT there_EX0 are_VBB features_NN2 that_CJT distinguish_VVB plasmonic_AJ0 from_PRP excitonic_AJ0 behavior_NN1 in_PRP two_CRD main_AJ0 areas_NN2 :_PUN (_PUL 1_CRD )_PUR the_AT0 instantaneous_AJ0 optical_AJ0 properties_NN2 and_CJC (_PUL 2_CRD )_PUR the_AT0 dynamics_NN0 following_AJ0 absorption_NN1 ._SENT This_DT0 section_NN1 does_VDZ not_XX0 cover_VVI every_AT0 experimental_AJ0 distinction_NN1 between_PRP plasmonic_AJ0 and_CJC excitonic_AJ0 systems_NN2 ,_PUN which_DTQ have_VHB been_VBN reviewed_VVN more_AV0 extensively_AV0 elsewhere_AV0 ._SENT Instead_AV0 ,_PUN we_PNP focus_VVB on_PRP two_CRD main_AJ0 goals_NN2 :_PUN (_PUL 1_CRD )_PUR relating_VVG the_AT0 key_AJ0 features_NN2 that_CJT are_VBB seen_VVN experimentally_AV0 to_PRP their_DPS classical_AJ0 electrodynamics_NN1 explanation_NN1 ,_PUN and_CJC (_PUL 2_CRD )_PUR laying_VVG the_AT0 necessary_AJ0 groundwork_NN1 so_AV0 that_CJT it_PNP is_VBZ clear_AJ0 in_PRP the_AT0 next_ORD section_NN1 what_DTQ similarities_NN2 and_CJC differences_NN2 exist_VVB between_PRP the_AT0 properties_NN2 used_VVN experimentally_AV0 vs._PRP in_PRP quantum_NN1 mechanical_AJ0 models_NN2 to_TO0 distinguish_VVI between_PRP plasmonic_AJ0 and_CJC excitonic_AJ0 behavior_NN1 ._SENT 
The_AT0 first_ORD distinguishing_AJ0 feature_NN1 of_PRF plasmonic_AJ0 behavior_NN1 is_VBZ the_AT0 absorption_NN1 spectrum_NN1 ,_PUN reflecting_VVG the_AT0 instantaneous_AJ0 response_NN1 of_PRF the_AT0 nanocluster_NN1 to_PRP light_NN1 ._SENT As_CJS seen_VVN from_PRP the_AT0 classical_AJ0 electrodynamics_NN1 model_NN1 ,_PUN because_CJS plasmons_NN2 are_VBB collective_AJ0 oscillations_NN2 ,_PUN a_AT0 (_PUL nearly_AV0 )_PUR spherical_AJ0 plasmonic_AJ0 nanocluster_NN1 should_VM0 have_VHI only_AV0 one_CRD peak_NN1 in_PRP its_DPS absorption_NN1 spectrum_NN1 ,_PUN as_CJS seen_VVN for_PRP 22_CRD nm_AJ0 Au_NN0 nanoparticles_NN2 in_PRP Fig._NN1 1a_NN1 ._SENT In_PRP contrast_NN1 ,_PUN excitonic_AJ0 nanoclusters_NN2 may_VM0 have_VHI several_DT0 or_CJC many_DT0 absorption_NN1 peaks_NN2 involving_VVG transitions_NN2 between_PRP different_AJ0 molecular_AJ0 orbitals_NN2 ,_PUN such_DT0 as_PRP that_DT0 of_PRF the_AT0 Au6_CRD (_PUL PPh3_CRD )_PUR 62+_CRD nanocluster_NN1 in_PRP Fig._NN1 1b_NN1 ._SENT In_PRP larger_AJC nanoclusters_NN2 ,_PUN the_AT0 transition_NN1 from_PRP an_AT0 excitonic_AJ0 multi-peaked_AJ0 absorption_NN1 spectrum_NN1 to_PRP a_AT0 single-peaked_AJ0 plasmonic_AJ0 absorption_NN1 spectrum_NN1 is_VBZ visible_AJ0 as_PRP the_AT0 nanocluster_NN1 size_NN1 increases_VVZ from_PRP Au246_CRD (_PUL SR_NP0 )_PUR 80_CRD to_PRP Au279_CRD (_PUL SR_NP0 )_PUR 84_CRD ,_PUN though_CJS overlap_NN1 of_PRF the_AT0 intraband_AJ0 and_CJC intraband_AJ0 transitions_NN2 somewhat_AV0 obscures_VVZ the_AT0 intraband_AJ0 absorption_NN1 peaks_NN2 (_PUL Fig._NN1 1c_CRD )_PUR ._SENT 
Several_DT0 spectroscopic_AJ0 techniques_NN2 that_CJT probe_VVB the_AT0 dynamics_NN0 following_AJ0 absorption_NN1 also_AV0 reveal_VVB differences_NN2 between_PRP excitonic_AJ0 and_CJC plasmonic_AJ0 behavior_NN1 ._SENT To_TO0 understand_VVI the_AT0 reasons_NN2 for_PRP these_DT0 differences_NN2 ,_PUN we_PNP must_VM0 first_ORD examine_VVI the_AT0 typical_AJ0 decay_NN1 processes_NN2 ._SENT When_CJS plasmonic_AJ0 metal_NN1 nanoparticles_NN2 absorb_VVB light_NN1 ,_PUN the_AT0 initially_AV0 coherent_AJ0 plasmon_NN1 dephases_NN2 into_PRP individual_AJ0 hot_AJ0 charge_NN1 carriers_NN2 (_PUL hot_AJ0 electrons_NN2 and_CJC hot_AJ0 holes_NN2 )_PUR within_PRP a_AT0 few_DT0 femtoseconds_NN2 (_PUL Fig._NN1 2_CRD )_PUR ._SENT The_AT0 initial_AJ0 distribution_NN1 of_PRF hot_AJ0 carriers_NN2 is_VBZ relatively_AV0 uniform_AJ0 over_PRP a_AT0 broad_AJ0 range_NN1 of_PRF energies_NN2 ._SENT Because_CJS the_AT0 electron_NN1 –_PUN electron_NN1 scattering_NN1 rate_NN1 is_VBZ higher_AJC for_PRP charge_NN1 carriers_NN2 farther_AV0 from_PRP the_AT0 Fermi_NP0 energy_NN1 ,_PUN the_AT0 higher-energy_AJ0 charge_NN1 carriers_NN2 lose_VVB energy_NN1 more_AV0 quickly_AV0 than_CJS the_AT0 lower-energy_AJ0 carriers_NN2 ._SENT This_DT0 scattering_NN1 transforms_VVZ the_AT0 initial_AJ0 non-thermal_AJ0 hot_AJ0 carrier_NN1 distribution_NN1 into_PRP a_AT0 thermal_AJ0 distribution_NN1 within_PRP a_AT0 few_DT0 hundred_CRD femtoseconds_NN2 ,_PUN in_PRP a_AT0 process_NN1 called_VVN thermalization_NN1 ._SENT On_PRP the_AT0 scale_NN1 of_PRF a_AT0 few_DT0 ps_NN2 ,_PUN the_AT0 hot_AJ0 carriers_NN2 relax_VVB ,_PUN and_CJC the_AT0 excess_AJ0 energy_NN1 is_VBZ transferred_VVN into_PRP phonons_NN2 ._SENT 
In_PRP contrast_NN1 ,_PUN the_AT0 decay_NN1 of_PRF excitonic_AJ0 systems_NN2 depends_VVZ on_PRP the_AT0 specific_AJ0 electronic_AJ0 excited_AJ0 states_NN2 in_PRP the_AT0 nanocluster_NN1 ._SENT In_PRP the_AT0 prototypical_AJ0 Au_NN0 nanocluster_NN1 Au25_NP0 (_PUL SR_NP0 )_PUR 18−_CRD ,_PUN three_CRD distinct_AJ0 decay_NN1 time_NN1 scales_NN2 have_VHB been_VBN measured_VVN ,_PUN though_CJS the_AT0 details_NN2 of_PRF the_AT0 decay_NN1 depend_VVI on_PRP the_AT0 exact_AJ0 ligand_NN1 structure_NN1 ,_PUN the_AT0 excitation_NN1 energy_NN1 ,_PUN and_CJC other_AJ0 experimental_AJ0 factors_NN2 ._SENT First_ORD ,_PUN the_AT0 hot_AJ0 carriers_NN2 within_PRP the_AT0 metal_NN1 core_NN1 relax_VVB within_PRP several_DT0 hundred_CRD fs_NN2 ._SENT This_DT0 is_VBZ followed_VVN by_PRP transfer_NN1 of_PRF energy_NN1 from_PRP the_AT0 metal_NN1 core_NN1 to_PRP states_NN2 with_PRP ligand-to-metal_AJ0 charge-transfer_NN1 character_NN1 within_PRP a_AT0 few_DT0 ps84_NN1 and_CJC relaxation_NN1 to_PRP vibrational_AJ0 modes_NN2 on_PRP the_AT0 order_NN1 of_PRF 50_CRD –_PUN 200_CRD ns_NN2 ._SENT These_DT0 time_NN1 scales_NN2 are_VBB several_DT0 orders_NN2 of_PRF magnitude_NN1 larger_AJC than_CJS for_PRP similar_AJ0 decay_NN1 processes_NN2 in_PRP plasmonic_AJ0 systems_NN2 ._SENT Unlike_AJ0 in_PRP typical_AJ0 plasmonic_AJ0 systems_NN2 ,_PUN higher-energy_AJ0 excited_AJ0 states_NN2 in_PRP excitonic_AJ0 nanoclusters_NN2 may_VM0 have_VHI longer_AJC lifetimes_NN2 than_CJS the_AT0 low-energy_AJ0 excited_AJ0 states_NN2 of_PRF the_AT0 same_DT0 nanocluster_NN1 ._SENT Because_CJS there_EX0 are_VBB discrete_AJ0 excited_AJ0 states_NN2 ,_PUN decay_NN1 from_PRP one_CRD state_NN1 to_PRP another_DT0 occurs_VVZ on_PRP a_AT0 distinctive_AJ0 time_NN1 scale_NN1 ,_PUN and_CJC that_DT0 time_NN1 scale_NN1 varies_VVZ between_PRP different_AJ0 nanocluster_NN1 isomers88_NN2 or_CJC sizes_NN2 ._SENT 
Because_CJS of_PRF the_AT0 differences_NN2 in_PRP the_AT0 excited-state_AJ0 dynamics_NN0 ,_PUN plasmonic_AJ0 and_CJC excitonic_AJ0 noble_AJ0 metal_NN1 nanoclusters_NN2 have_VHB distinct_AJ0 emission_NN1 mechanisms_NN2 and_CJC time_NN1 scales_NN2 ._SENT Both_DT0 classes_NN2 of_PRF nanoclusters_NN2 typically_AV0 have_VHB two_CRD emissive_AJ0 transitions_NN2 :_PUN a_AT0 short-lived_AJ0 visible_AJ0 emission_NN1 attributed_VVN to_PRP the_AT0 decay_NN1 of_PRF an_AT0 excitation_NN1 in_PRP the_AT0 nanocluster_NN1 core_NN1 ,_PUN and_CJC a_AT0 longer-lived_AJC near-infrared_AJ0 emission_NN1 attributed_VVN to_PRP ligand_NN1 states_NN2 ._SENT For_PRP the_AT0 shorter-lived_AJC visible_AJ0 emission_NN1 ,_PUN plasmonic_AJ0 gold_NN1 nanoparticle_NN1 have_VHB fluorescence_NN1 lifetimes_NN2 <_NN1 50_CRD fs_NN2 ,_PUN which_DTQ is_VBZ faster_AJC than_CJS can_VM0 be_VBI resolved_VVN experimentally_AV0 ;_PUN this_DT0 rapid_AJ0 decay_NN1 reflects_VVZ the_AT0 fast_AJ0 dephasing_NN1 and_CJC thermalization_NN1 processes_NN2 (_PUL Fig._NN1 3a_CRD )_PUR ._SENT In_PRP contrast_NN1 ,_PUN excitonic_AJ0 gold_NN1 nanoclusters_NN2 have_VHB visible_AJ0 fluorescence_NN1 time_NN1 scales_NN2 on_PRP the_AT0 order_NN1 of_PRF 250_CRD –_PUN 350_CRD fs_NN2 ,_PUN reflecting_VVG the_AT0 slower_AJC decay_NN1 from_PRP the_AT0 initial_AJ0 excited_AJ0 states_NN2 into_PRP ligand_NN1 states_NN2 ._SENT 
The_AT0 differences_NN2 in_PRP the_AT0 decay_NN1 processes_NN2 of_PRF excitonic_AJ0 and_CJC plasmonic_AJ0 gold_NN1 nanoclusters_NN2 can_VM0 also_AV0 be_VBI observed_VVN in_PRP differences_NN2 in_PRP the_AT0 pump-power_AJ0 dependence_NN1 of_PRF their_DPS decay_NN1 time_NN1 scales_NN2 ,_PUN as_CJS observed_VVN by_PRP various_AJ0 time-resolved_AJ0 spectroscopic_AJ0 techniques_NN2 ._SENT For_PRP plasmonic_AJ0 nanoclusters_NN2 and_CJC nanoparticles_NN2 ,_PUN the_AT0 time_NN1 scale_NN1 of_PRF the_AT0 relaxation_NN1 of_PRF electronic_AJ0 energy_NN1 into_PRP phonons_NN2 depends_VVZ on_PRP the_AT0 intensity_NN1 of_PRF the_AT0 pump_NN1 laser_NN1 used_VVN to_TO0 excite_VVI the_AT0 system_NN1 :_PUN because_CJS a_AT0 high_AJ0 pump_NN1 power_NN1 can_VM0 cause_VVI one_CRD nanoparticle_NN1 to_TO0 absorb_VVI multiple_AJ0 photons_NN2 ,_PUN the_AT0 initial_AJ0 hot_AJ0 carriers_NN2 have_VHB a_AT0 higher_AJC effective_AJ0 temperature_NN1 ,_PUN and_CJC these_DT0 higher-energy_AJ0 hot_AJ0 carriers_NN2 decay_VVB more_AV0 quickly_AV0 ._SENT In_PRP contrast_NN1 ,_PUN in_PRP excitonic_AJ0 nanoclusters_NN2 ,_PUN the_AT0 relaxation_NN1 time_NN1 scale_NN1 is_VBZ independent_AJ0 of_PRF the_AT0 pump_NN1 power_NN1 because_CJS the_AT0 excitation_NN1 and_CJC decay_NN1 processes_NN2 involve_VVB discrete_AJ0 excited_AJ0 states_NN2 that_CJT decay_VVB with_PRP their_DPS own_DT0 distinctive_AJ0 time_NN1 scales_NN2 ._SENT In_PRP thiol-protected_AJ0 Au_NN0 nanoclusters_NN2 ,_PUN a_AT0 sharp_AJ0 transition_NN1 from_PRP excitonic_NN1 to_PRP plasmonic_AJ0 dynamics_NN0 is_VBZ seen_VVN as_PRP the_AT0 size_NN1 increases_VVZ from_PRP Au246_CRD (_PUL SR_NP0 )_PUR 80_CRD to_PRP Au279_CRD (_PUL SR_NP0 )_PUR 84_CRD (_PUL Fig._NN1 3b_CRD )_PUR ._SENT However_AV0 ,_PUN the_AT0 transition_NN1 from_PRP excitonic_NN1 to_PRP plasmonic_AJ0 behavior_NN1 is_VBZ not_XX0 simply_AV0 a_AT0 function_NN1 of_PRF nanocluster_NN1 size_NN1 :_PUN the_AT0 smaller_AJC nanocluster_NN1 Au144_NN1 (_PUL SR_NP0 )_PUR 60_CRD has_VHZ plasmonic_AJ0 pump-power_NN1 dependence_NN1 ._SENT 
4._CRD Quantum_NN1 mechanical_AJ0 view_NN1 of_PRF plasmons_NN2 
Atomistic_AJ0 quantum_NN1 mechanical_AJ0 methods_NN2 can_VM0 practically_AV0 be_VBI applied_VVN to_PRP systems_NN2 on_PRP the_AT0 scale_NN1 of_PRF tens_CRD to_PRP hundreds_CRD of_PRF atoms_NN2 ._SENT Thus_AV0 ,_PUN unlike_PRP metal_NN1 nanoparticles_NN2 with_PRP diameters_NN2 larger_AJC than_CJS 2_CRD –_PUN 3_CRD nm_NN2 ,_PUN many_DT0 atomically_AV0 precise_AJ0 nanoclusters_NN2 are_VBB within_PRP a_AT0 size_NN1 range_NN1 that_CJT can_VM0 be_VBI studied_VVN using_VVG quantum_NN1 mechanical_AJ0 methods_NN2 to_TO0 understand_VVI their_DPS geometries_NN2 ,_PUN optical_AJ0 properties_NN2 ,_PUN and_CJC dynamics_NN0 with_PRP atomistic_AJ0 detail_NN1 ._SENT The_AT0 majority_NN1 of_PRF the_AT0 quantum_NN1 mechanical_AJ0 calculations_NN2 in_PRP the_AT0 field_NN1 have_VHB used_VVN density_NN1 functional_AJ0 theory_NN1 (_PUL DFT_AJ0 )_PUR approaches_NN2 ,_PUN but_CJC other_AJ0 computational_AJ0 methods_NN2 like_PRP INDO97_CRD –_PUN 99_CRD and_CJC density_NN1 functional_AJ0 tight_AJ0 binding_NN1 (_PUL DFTB_NP0 )_PUR 100_CRD –_PUN 103_CRD give_VVB results_NN2 that_CJT are_VBB largely_AV0 consistent_AJ0 with_PRP DFT_NN1 ._SENT 
Early_AJ0 calculations_NN2 using_VVG time-dependent_AJ0 DFT_NN1 (_PUL TD-DFT_NP0 )_PUR showed_VVD that_CJT bare_AJ0 tetrahedral_AJ0 silver_NN1 nanoclusters_NN2 have_VHB relatively_AV0 sharp_AJ0 absorption_NN1 peaks_NN2 similar_AJ0 to_PRP those_DT0 characteristic_NN1 of_PRF plasmonic_AJ0 nanoparticles_NN2 that_DT0 red-shift_NN1 with_PRP increasing_AJ0 size_NN1 ,_PUN and_CJC extrapolation_NN1 of_PRF the_AT0 absorption_NN1 energy_NN1 to_PRP larger_AJC sizes_NN2 yields_VVZ results_NN2 consistent_AJ0 with_PRP electrodynamics_NN2 for_PRP plasmonic_AJ0 systems_NN2 ._SENT Based_VVN on_PRP these_DT0 early_AJ0 observations_NN2 ,_PUN there_EX0 has_VHZ been_VBN great_AJ0 interest_NN1 in_PRP using_VVG quantum_NN1 mechanical_AJ0 calculations_NN2 to_TO0 understand_VVI the_AT0 emergence_NN1 of_PRF plasmonic_AJ0 properties_NN2 and_CJC in_PRP developing_AJ0 techniques_NN2 to_TO0 characterize_VVI whether_CJS nanoclusters_NN2 have_VHB plasmonic_AJ0 or_CJC excitonic_AJ0 properties_NN2 ._SENT These_DT0 different_AJ0 characterization_NN1 methods_NN2 focus_VVB on_PRP various_AJ0 aspects_NN2 of_PRF the_AT0 definition_NN1 of_PRF plasmons_NN2 from_PRP classical_AJ0 electrodynamics_NN2 ,_PUN and_CJC in_PRP some_DT0 cases_NN2 multiple_AJ0 characterization_NN1 approaches_NN2 attempt_VVB to_TO0 quantify_VVI similar_AJ0 aspects_NN2 of_PRF the_AT0 electrodynamics_NN1 definition_NN1 ._SENT Here_AV0 ,_PUN we_PNP summarize_VVB the_AT0 main_AJ0 characterization_NN1 techniques_NN2 and_CJC then_AV0 focus_VVB on_PRP their_DPS application_NN1 to_PRP prototypical_AJ0 linear_AJ0 metal_NN1 nanowires_NN2 ,_PUN which_DTQ are_VBB widely_AV0 used_VVN as_PRP model_NN1 systems_NN2 ._SENT 
We_PNP note_VVB that_CJT the_AT0 characterization_NN1 methods_NN2 described_VVN here_AV0 all_DT0 focus_NN1 on_PRP the_AT0 static_AJ0 excited_AJ0 states_NN2 computed_VVN by_PRP frequency-domain_AJ0 methods_NN2 like_PRP TD-DFT_NN1 or_CJC the_AT0 absorption_NN1 spectra_NN2 obtained_VVN from_PRP time-domain_AJ0 methods_NN2 like_PRP real-time_AJ0 TD-DFT_NN1 (_PUL RT-TDDFT_NP0 )_PUR ._SENT There_EX0 have_VHB been_VBN some_DT0 computational_AJ0 studies_NN2 of_PRF the_AT0 excited-state_AJ0 dynamics_NN0 using_VVG RT-TDDFT_NN1 on_PRP the_AT0 time_NN1 scale_NN1 of_PRF dephasing106_CRD –_PUN 108_CRD and_CJC non-adiabatic_AJ0 molecular_AJ0 dynamics_NN0 (_PUL NAMD_NP0 )_PUR on_PRP the_AT0 time_NN1 scale_NN1 of_PRF relaxation_NN1 ._SENT However_AV0 ,_PUN criteria_NN2 to_TO0 distinguish_VVI between_PRP excitonic_AJ0 and_CJC plasmonic_AJ0 states_NN2 based_VVN on_PRP the_AT0 dynamics_NN0 are_VBB much_AV0 less_AV0 developed_VVN at_PRP this_DT0 point_NN1 ._SENT 
4.1_CRD ._SENT Oscillatory_AJ0 behavior_NN1 
As_CJS discussed_VVN earlier_AV0 ,_PUN the_AT0 electrodynamics_NN1 description_NN1 of_PRF plasmons_NN2 involves_VVZ an_AT0 oscillation_NN1 of_PRF the_AT0 electron_NN1 density_NN1 ._SENT However_AV0 ,_PUN when_CJS excited_AJ0 states_NN2 are_VBB computed_VVN using_VVG frequency-domain_AJ0 quantum_NN1 mechanical_AJ0 methods_NN2 ,_PUN the_AT0 states_NN2 that_CJT are_VBB obtained_VVN are_VBB stationary_AJ0 states_NN2 ,_PUN meaning_VVG that_CJT the_AT0 electron_NN1 density_NN1 is_VBZ constant_AJ0 over_PRP time_NN1 ._SENT At_PRP a_AT0 first_ORD glance_NN1 ,_PUN it_PNP may_VM0 appear_VVI that_DT0 quantum_NN1 mechanical_AJ0 excited_AJ0 states_NN2 could_VM0 never_AV0 represent_VVI the_AT0 oscillatory_AJ0 behavior_NN1 inherent_AJ0 to_PRP plasmons_NN2 ._SENT However_AV0 ,_PUN this_DT0 apparent_AJ0 contradiction_NN1 is_VBZ straightforward_AJ0 to_TO0 resolve_VVI by_PRP instead_AV0 considering_VVG time-domain_AJ0 quantum_NN1 mechanical_AJ0 methods_NN2 ._SENT Since_CJS the_AT0 electrodynamics_NN1 derivation_NN1 of_PRF plasmonic_AJ0 behavior_NN1 involves_VVZ a_AT0 time-dependent_AJ0 electric_AJ0 field_NN1 ,_PUN a_AT0 time-dependent_AJ0 quantum_NN1 mechanical_AJ0 method_NN1 involving_VVG an_AT0 electric_AJ0 field_NN1 with_PRP explicit_AJ0 time_NN1 dependence_NN1 allows_VVZ for_PRP a_AT0 more_AV0 direct_AJ0 comparison_NN1 ._SENT 
Frequency-domain_AJ0 excited-state_NN1 methods_NN2 like_PRP linear-response_AJ0 TD-DFT_NN2 compute_VVB a_AT0 list_NN1 of_PRF excited_AJ0 eigenstates_NN2 ψk_NN1 ,_PUN along_AVP with_PRP their_DPS corresponding_AJ0 energy_NN1 eigenvalues_NN2 Ek_NP0 and_CJC transition_NN1 dipole_NN1 moments_NN2 equation_NN1 ._SENT The_AT0 absorption_NN1 intensity_NN1 from_PRP the_AT0 ground_NN1 state_NN1 ψg_NN1 to_PRP excited_AJ0 state_NN1 ψk_NN1 is_VBZ proportional_AJ0 to_PRP equation_NN1 ._SENT This_DT0 yields_VVZ a_AT0 "_PUQ stick_NN1 spectrum_NN1 "_PUQ where_CJS each_DT0 excited_AJ0 state_NN1 is_VBZ represented_VVN by_PRP a_AT0 stick_NN1 with_PRP a_AT0 height_NN1 corresponding_VVG to_PRP the_AT0 absorption_NN1 intensity_NN1 ._SENT To_TO0 obtain_VVI an_AT0 absorption_NN1 spectrum_NN1 that_CJT more_DT0 closely_AV0 resembles_VVZ an_AT0 experimental_AJ0 spectrum_NN1 ,_PUN each_DT0 stick_NN1 is_VBZ broadened_VVN using_VVG a_AT0 Lorentzian_AJ0 or_CJC Gaussian_AJ0 function_NN1 ,_PUN and_CJC the_AT0 intensities_NN2 are_VBB summed_VVN to_TO0 give_VVI one_CRD total_AJ0 absorption_NN1 spectrum_NN1 ._SENT 
Time-domain_NN1 quantum_NN1 mechanical_AJ0 methods_NN2 apply_VVB an_AT0 electric_AJ0 field_NN1 as_PRP a_AT0 time-dependent_AJ0 perturbation_NN1 to_PRP the_AT0 system_NN1 and_CJC compute_VVB the_AT0 evolution_NN1 of_PRF the_AT0 wavefunction_NN1 over_PRP time_NN1 ._SENT The_AT0 time-dependent_AJ0 electric_AJ0 field_NN1 may_VM0 be_VBI a_AT0 wavepacket_NN1 with_PRP a_AT0 sinusoidal_AJ0 shape_NN1 over_PRP a_AT0 finite_AJ0 time_NN1 ;_PUN it_PNP may_VM0 also_AV0 be_VBI a_AT0 delta_NN1 function_NN1 where_AVQ an_AT0 electric_AJ0 field_NN1 is_VBZ applied_VVN for_PRP only_AV0 a_AT0 single_AJ0 time_NN1 step_NN1 that_CJT ,_PUN via_PRP a_AT0 Fourier_NP0 transform_NN1 ,_PUN is_VBZ equivalent_AJ0 to_PRP exciting_VVG the_AT0 system_NN1 with_PRP a_AT0 broad_AJ0 distribution_NN1 of_PRF frequencies_NN2 ._SENT We_PNP will_VM0 focus_VVI here_AV0 on_PRP excitation_NN1 with_PRP a_AT0 sinusoidal_AJ0 wavepacket_NN1 with_PRP a_AT0 small_AJ0 enough_DT0 intensity_NN1 that_CJT the_AT0 system_NN1 remains_VVZ mostly_AV0 in_PRP the_AT0 ground_NN1 state_NN1 ._SENT In_PRP the_AT0 time_NN1 domain_NN1 ,_PUN absorption_NN1 can_VM0 be_VBI described_VVN using_VVG first-order_AJ0 time-dependent_AJ0 perturbation_NN1 theory_NN1 ,_PUN which_DTQ we_PNP describe_VVB briefly_AV0 here_AV0 ;_PUN the_AT0 full_AJ0 derivation_NN1 can_VM0 be_VBI found_VVN in_PRP many_DT0 quantum_NN1 mechanics_NN2 textbooks_NN2 ._SENT Within_PRP this_DT0 framework_NN1 ,_PUN the_AT0 Hamiltonian_AJ0 is_VBZ :_PUN equation_NN1 where_CJS Ĥ_NP0 (_PUL 0_CRD )_PUR is_VBZ the_AT0 Hamiltonian_AJ0 of_PRF the_AT0 unperturbed_AJ0 system_NN1 ,_PUN Ĥ′_NP0 (_PUL t_ZZ0 )_PUR is_VBZ the_AT0 time-dependent_AJ0 perturbation_NN1 ,_PUN F0_NP0 is_VBZ the_AT0 maximum_AJ0 intensity_NN1 of_PRF the_AT0 electric_AJ0 field_NN1 of_PRF light_NN1 ,_PUN and_CJC [_PUL small_AJ0 mu_NN1 ,_PUN Greek_AJ0 ,_PUN circumflex_NN1 ]_PUR ;_PUN is_VBZ the_AT0 dipole_NN1 operator_NN1 ._SENT The_AT0 time-dependent_AJ0 wavefunction_NN1 can_VM0 be_VBI written_VVN as_PRP a_AT0 linear_AJ0 combination_NN1 of_PRF the_AT0 eigenfunctions_NN2 ψ_NN1 (_PUL 0_CRD )_PUR k_ZZ0 of_PRF the_AT0 unperturbed_AJ0 system_NN1 :_PUN euqation_NN1 with_PRP coefficients_NN2 ck_NN0 (_PUL t_ZZ0 )_PUR and_CJC energies_NN2 E_ZZ0 (_PUL 0_CRD )_PUR k_ZZ0 =_NP0 ℏωk_NN1 ._SENT If_CJS the_AT0 system_NN1 starts_VVZ in_PRP the_AT0 ground_NN1 stateΨ_NN1 (_PUL 0_CRD )_PUR g_ZZ0 (_PUL 0_CRD )_PUR and_CJC the_AT0 perturbation_NN1 is_VBZ turned_VVN on_AVP from_PRP time_NN1 t_ZZ0 =_NN1 0_CRD until_PRP t_ZZ0 =_NP0 t′_NN1 ,_PUN the_AT0 wavefunction_NN1 at_PRP time_NN1 t′_NN1 has_VHZ the_AT0 coefficients_NN2 equation_NN1 where_AVQ ωkg_NN1 =_NP0 ωk_NP0 −_NP0 ωg_NP0 ._SENT If_CJS ω_NP0 is_VBZ nearly_AV0 resonant_AJ0 with_PRP a_AT0 transition_NN1 (_PUL such_DT0 that_CJT the_AT0 denominator_NN1 ωkg_NN1 −_NP0 ω_NP0 is_VBZ nearly_AV0 zero_CRD )_PUR that_DT0 has_VHZ a_AT0 non-zero_AJ0 transition_NN1 dipole_NN1 moment_NN1 equation_NN1 ,_PUN the_AT0 coefficient_NN1 ck_NN0 (_PUL t′_NN0 )_PUR will_VM0 be_VBI non-zero_AJ0 ,_PUN indicating_VVG that_CJT the_AT0 system_NN1 has_VHZ absorbed_VVN light_NN1 to_PRP transition_NN1 from_PRP Ψ_NP0 (_PUL 0_CRD )_PUR g_NN0 to_PRP Ψ_NP0 (_PUL 0_CRD )_PUR k_ZZ0 ._SENT The_AT0 probability_NN1 of_PRF a_AT0 transition_NN1 from_PRP the_AT0 ground_NN1 state_NN1 to_PRP state_NN1 ψk_NN1 is_VBZ proportional_AJ0 to_PRP |_NN1 ck_NN0 (_PUL t′_NN0 )_PUR |_NN1 2_CRD and_CJC thus_AV0 is_VBZ also_AV0 proportional_AJ0 to_PRP equation_NN1 ._SENT If_CJS there_EX0 are_VBB no_AT0 decay_NN1 processes_NN2 ,_PUN the_AT0 coefficients_NN2 ck_NN0 (_PUL t′_NN0 )_PUR remain_VVB constant_AJ0 in_PRP magnitude_NN1 after_PRP the_AT0 electric_AJ0 field_NN1 is_VBZ turned_VVN off_AVP ._SENT If_CJS ω_NN1 is_VBZ not_XX0 close_AJ0 to_PRP resonance_NN1 with_PRP the_AT0 transition_NN1 from_PRP Ψ_NP0 (_PUL 0_CRD )_PUR g_NN0 to_PRP Ψ_NP0 (_PUL 0_CRD )_PUR k_ZZ0 ,_PUN the_AT0 coefficient_NN1 ck_NN0 (_PUL t′_NN0 )_PUR remains_VVZ small_AJ0 ._SENT 
The_AT0 resulting_AJ0 time-dependent_AJ0 wavefunction_NN1 is_VBZ a_AT0 superposition_NN1 of_PRF the_AT0 ground-state_AJ0 wavefunction_NN1 with_PRP a_AT0 small_AJ0 coefficient_NN1 for_PRP the_AT0 resonant_AJ0 excited-state_NN1 wavefunction_NN1 Ψ_NN1 (_PUL 0_CRD )_PUR k_ZZ0 :_PUN equation_NN1 
The_AT0 time-dependent_AJ0 dipole_NN1 moment_NN1 of_PRF the_AT0 system_NN1 is_VBZ :_PUN equation_NN1 
Thus_AV0 ,_PUN in_PRP a_AT0 time-dependent_AJ0 framework_NN1 ,_PUN absorption_NN1 of_PRF light_NN1 produces_VVZ an_AT0 oscillating_AJ0 dipole_NN1 moment_NN1 ,_PUN and_CJC the_AT0 magnitude_NN1 of_PRF the_AT0 oscillations_NN2 is_VBZ directly_AV0 proportional_AJ0 to_PRP the_AT0 transition_NN1 dipole_NN1 moment_NN1 ._SENT If_CJS the_AT0 system_NN1 is_VBZ excited_VVN using_VVG an_AT0 electric_AJ0 field_NN1 in_PRP the_AT0 shape_NN1 of_PRF a_AT0 delta_NN1 function_NN1 ,_PUN the_AT0 absorption_NN1 spectrum_NN1 over_PRP a_AT0 wide_AJ0 energy_NN1 range_NN1 can_VM0 be_VBI computed_VVN based_VVN on_PRP a_AT0 Fourier_NP0 transform_NN1 of_PRF the_AT0 time-dependent_AJ0 dipole_NN1 moment_NN1 ,_PUN and_CJC the_AT0 spectra_NN2 are_VBB typically_AV0 consistent_AJ0 with_PRP the_AT0 results_NN2 of_PRF frequency-domain_AJ0 calculations_NN2 at_PRP the_AT0 same_DT0 level_NN1 of_PRF theory_NN1 ._SENT 
The_AT0 crucial_AJ0 result_NN1 is_VBZ that_CJT any_DT0 strongly_AV0 absorbing_AJ0 state_NN1 ,_PUN whether_CJS plasmonic_AJ0 or_CJC excitonic_AJ0 ,_PUN has_VHZ a_AT0 large_AJ0 transition_NN1 dipole_NN1 moment_NN1 ,_PUN leading_VVG to_PRP large_AJ0 oscillations_NN2 of_PRF the_AT0 instantaneous_AJ0 dipole_NN1 moment_NN1 in_PRP the_AT0 time_NN1 domain_NN1 that_CJT continue_VVB until_PRP a_AT0 decay_NN1 process_NN1 occurs_VVZ ._SENT An_AT0 example_NN1 of_PRF these_DT0 dipole_NN1 oscillations_NN2 for_PRP the_AT0 icosahedral_AJ0 Ag55_NN1 nanocluster_NN1 is_VBZ shown_VVN in_PRP Fig._NN1 4_CRD ;_PUN in_PRP this_DT0 case_NN1 ,_PUN the_AT0 electric_AJ0 field_NN1 is_VBZ on_AVP for_PRP approximately_AV0 the_AT0 first_ORD 10_CRD fs_NN2 ,_PUN and_CJC decay_NN1 processes_NN2 lead_VVB to_PRP significant_AJ0 damping_NN1 of_PRF the_AT0 oscillations_NN2 between_PRP 20_CRD and_CJC 25_CRD fs_NN2 ._SENT A_AT0 large_AJ0 transition_NN1 dipole_NN1 moment_NN1 is_VBZ necessary_AJ0 for_PRP an_AT0 excited_AJ0 state_NN1 to_TO0 yield_VVI the_AT0 large_AJ0 time-dependent_AJ0 charge_NN1 oscillations_NN2 characteristic_NN1 of_PRF plasmons_NN2 ._SENT However_AV0 ,_PUN large_AJ0 charge_NN1 oscillations_NN2 cannot_NN1 be_VBI the_AT0 only_AJ0 characteristic_NN1 used_VVN to_TO0 determine_VVI whether_CJS an_AT0 excited_AJ0 state_NN1 is_VBZ plasmonic_AJ0 or_CJC excitonic_AJ0 ,_PUN since_CJS every_AT0 strongly_AV0 absorbing_AJ0 state_NN1 will_VM0 induce_VVI large_AJ0 charge_NN1 oscillations_NN2 in_PRP the_AT0 time_NN1 domain_NN1 ._SENT Thus_AV0 ,_PUN more_DT0 criteria_NN2 are_VBB needed_VVN to_TO0 distinguish_VVI strongly_AV0 absorbing_AJ0 plasmonic_AJ0 excited_AJ0 states_NN2 from_PRP strongly_AV0 absorbing_VVG excitonic_AJ0 excited_AJ0 states_NN2 ._SENT 
