Ab initio calculations of optical properties of silver clusters: cross-over from molecular to nanoscale behavior

Electronic and optical properties of silver clusters were calculated using two different ab initio approaches: (1) based on all-electron full-potential linearized-augmented plane-wave method and (2) local basis function pseudopotential approach. Agreement is found between the two methods for small and intermediate sized clusters for which the former method is limited due to its all-electron formulation. The latter, due to non-periodic boundary conditions, is the more natural approach to simulate small clusters. The effect of cluster size is then explored using the local basis function approach. We find that as the cluster size increases, the electronic structure undergoes a transition from molecular behavior to nanoparticle behavior at a cluster size of 140 atoms (diameter ~1.7 nm). Above this cluster size the step-like electronic structure, evident as several features in the imaginary part of the polarizability of all clusters smaller than Ag₁₄₇, gives way to a dominant plasmon peak localized at wavelengths 350 nm ≤ λ ≤ 600 nm. It is, thus, at this length-scale that the conduction electrons’ collective oscillations that are responsible for plasmonic resonances begin to dominate the opto-electronic properties of silver nanoclusters.     

Be^+离子和Li原子极化率和超极化率的理论研究

利用相对论模型势方法计算了Be^+离子和Li原子的波函数、能级和振子强度,进一步得到了基态的电偶极极化率和超极化率,并详细地分析了不同中间态对基态超极化率的贡献.对于Be^+离子,电偶极极化率和超极化率与已有的理论结果符合得非常好.对于Li原子,电偶极极化率与已有的理论结果符合得很好,但是不同理论方法计算给出的超极化率差别非常大,最大的差别超过了一个数量级.通过分析不同中间态对Li原子基态超极化率的贡献,解释了不同理论结果之间有较大差异的原因.     

Ab Initio/有限场方法计算尿素分子的非线性光学极化率

用有限场（ＦＦ）方法在４－３１Ｇ＋２ｐ２ｄ水平上研究了外加电场强度对尿素分子的偶极矩,极化率,一阶超极化率,二阶超极化率的影响。计算发现,要获得上述性质的稳定计算结果,电场强度需确定在０．００１－０．００４ａ．ｕ．范围内。在此电强度范围内,与耦合微扰Ｈａｒｔｒｅｅ－Ｆｏｒｋ（ＣＰＨＦ）法的计算结果符合较好,且可有效地利用二级微扰方法（ＭＰ２）进行电子相关计算。     

Nonlinear optical properties of stilbene and azobenzene derivatives containing azaphosphane groups

We have studied the nonlinear optical (NLO) properties of some donor–acceptor molecules with stilbene and azobenzene molecules as backbone. We have used the nitro group as the acceptor and azaphosphane (R₃P=N–) as the donor group. To study the effect of variation of NLO properties, we have replaced the substituents (Rs) connected to the phosphorus atom by methyl, amine and phenyl groups. We find that both first-order polarizability and hyperpolarizabilities are larger for stilbene derivatives and is maximum for the phenyl substitution. Second-order polarizability is higher for methyl substitution. We have also obtained the two-photon absorption cross-section for these molecules. We find that both one-photon and two-photon absorption cross-sections are maximum for the same excited state (first excited state in the case of stilbene and second excited state in the case of azobenzene derivatives).     

Structure of nano-objects through polarizability and dipole measurements

The electric polarizability and the electric permanent dipole are important quantities for understanding the electronic properties of a cluster. Experimental techniques, the simulations necessary to interpret the experimental results, and a review of measurements on atomic and mixed clusters are presented. For atomic clusters, the polarizability is related to the type of bonding. In simple metal clusters such as alkali clusters, the results are well interpreted by the electron delocalization characteristic of the metallic bonding. In other metal clusters, the polarizability reflects the difficulty of establishing a clear and regular picture of the size evolution of electronic properties. The size evolution observed for covalent and semiconductor clusters is different from the evolution for metal clusters, and the influence of the geometry is preponderant, as demonstrated in the case of fullerenes. For mixed clusters, the measurements of the electric dipole allows one to deduce the charge transfers and the geometric arrangement. This is illustrated in the case of the metal-fullerene system and alkali halide clusters. To cite this article: M. Broyer et al., C. R. Physique 3 (2002) 301–317.     

Relative stability and optical nonlinearity of multiple conformers of 1,1′-substituted ferrocenes

The relative stability and the first and second hyperpolarizabilities of various conformers of four 1,1′-diarylethenylferrocenes have been evaluated at the MP2 computational level. Relative stability on the basis of the minimum polarizability principle is in complete agreement with the conclusion from the minimum energy criterion at the higher computational levels. Since the pi–pi interaction is an attractive force, the conformer with the intramolecular pi–pi interactions belongs to the lowest energy structure and is most likely to be populated. The calculated second hyperpolarizability is in excellent agreement with the experimental data available. There appear two low-energy absorption bands in electronic absorption spectra, where the lower-energy band shifts to the red and is enhanced by molecular distortion. This band is responsible for the largest linear polarizability and second hyperpolarizability of the conformer with inversion symmetry and the magnitude of the latter is dominated by one-photon transition.     

Tailoring the chemical reactivity and optical properties of clusters by size, structures and lasers

We present results of theoretical investigations in three areas. I. Reactivity of anionic noble metal oxide clusters (Ag, Au) relevant for catalyst design: It will be shown that the cooperative effects are needed to activate clusters in order to invoke strongly size selective reactions with O₂ and CO. These results obtained with DFT method elucidated fully experimental findings. II. Stationary optical properties of silver clusters: ab initio results on absorption spectra of small silver clusters and on geometric relaxation of their excited states leading to the observed fluorescence are presented and compared with experimental data. III. Real-time investigation of ultrafast processes and their control by tailored laser fields: nonstoichiometric Na_nF_n-1 clusters are suitable prototypes to study dynamics in excited electronic states. For this purpose we use our combination of the Wigner distribution method and MD “on the fly” allowing to treat all degrees of freedom. Analysis of simulated pump-probe signals will be shown for Na₂F for which experimental data are available. Pump-dump control of the photoisomerization in Na₃F₂ avoiding conical intersection will be presented using our new strategy for obtaining tailored laser fields based on the intermediate target in excited state which (if available) guarantees the controllability in the complex systems.     

Silver atoms and clusters in molecular sieves and clays

Electron spin resonance (ESR) and electron spin echo modulation (ESEM) studies on small paramagnetic silver clusters generated radiolytically in molecular sieves and clays are reviewed. Special attention is paid to the role of framework structure with respect to cluster nuclearity and stability. In general, geometrical size constraints play a crucial role and molecular sieves with cage-like structures with small openings between the cages such as A and rho zeolites stabilize cationic silver clusters more efficiently than channel-like zeolite structures. In addition, other factors like total cation capacity, type of cocation and/or molecular adsorbate in the cages can affect the silver agglomeration process to a great extent. The mechanism of silver agglomeration in irradiated molecular sieves and clays based on the ESR results is described as well as the reactivity of tetrameric and hexameric silver clusters with various molecular adsorbates.     

Thermal expansion in small metal clusters and its impact on the electric polarizability

The thermal expansion coefficients of Na(N) clusters with 8相似文献   

Trends in the electronic and vibrational contributions to the dipole moment,polarizabilities, and first and second hyperpolarizabilities of the hydrides of Li,Na and K

The dipole moments μ, polarizabilities α, and first and second hyperpolarizabilities, β and γ of LiH, NaH and KH (MeH) have been computed using Hartree-Fock, MP2 and CCSD(T) theories. The static electronic and vibrational contributions to these properties are presented. The vibrational properties have been analysed into contributions due to zero-point vibrational averaging and pure vibrational terms. An alternative dissection of the vibrational properties into nuclear relaxation and curvature terms has also been considered. KH has been selected as a model system to study how the number of electrons, which are correlated (2, 10 and 20) affect both electronic and vibrational properties. The 10 electron approximation gives results that are practically the same as those computed by taking into account all 20 electrons of KH. The double-harmonic approximation has been shown to give satisfactory results for the pure vibrational contributions to the polarizability and the first hyperpolarizability, while this approximation is useful for demonstrating, qualitatively, the significance of the pure vibrational contributions to the second hyperpolarizability. In many cases the vibrational contributions are rather small percentages of the corresponding electronic contribution. However, several exceptions to the above observation have been noted. In all the cases considered the vibrational properties should be computed if reasonably accurate property values are sought. Electron correlation is important for both electronic and vibrational contributions to the electrical properties of the hydrides considered. The results are in satisfactory agreement with most of the best theoretical and experimental data concerning bond lengths, vibrational frequencies and electrical properties.     

Static dipole polarizabilities of Scn （n ≤15） clusters

The static dipole polarizabilities of scandium clusters with up to 15 atoms are determined by using the numerically finite field method in the framework of density functional theory. The electronic effects on the polarizabilities are investigated for the scandium clusters. We examine a large highest occupied molecular orbital --- the lowest occupied molecular orbital (HOMO--LUMO) gap of a scandium cluster usually corresponds to a large dipole moment. The static polarizability per atom decreases slowly and exhibits local minimum with increasing cluster size. The polarizability anisotropy and the ratio of mean static polarizability to the HOMO--LUMO gap can also reflect the cluster stability. The polarizability of the scandium cluster is partially related to the HOMO--LUMO gap and is also dependent on geometrical characteristics. A strong correlation between the polarizability and ionization energy is observed.     

Application of polynomial functions in calculations of optical susceptibilities of atoms and molecules by the Floquet method

The role of polynomial terms included in trial many-electron wave functions for variational calculations of the dynamic polarizabilities and hyperpolarizabilities of atoms and molecules in the Floquet theory is examined. The role of these terms is found to be very significant, and, in particular, polynomials of the first order are important in calculating the linear polarizability. To obtain more reliable results in calculating the hyperpolarizabilites, it is necessary to include polynomials of higher orders.     

Silver cluster induced absorption enhancement and conformation control of peptides

We present a theoretical study of the structural and optical properties of isolated silver cluster-tripeptide hybrid systems. We show that small silver clusters induce enhancement of the optical absorption of peptides. Moreover, silver clusters bound to peptides can reduce the conformational flexibility and invoke changes of the secondary structure. Thus, they might serve as local optical probes in biolabelling applications.     

Linear and non-linear response of embedded Na clusters

We investigate Na clusters embedded in Ar matrices. The surrounding Ar atoms are modeled in terms of their dynamical polarizability and the strong electron repulsion. The calibration of the model is discussed. First results for the non-linear optical response of the Na clusters are presented for the test case of Na₈ embedded in Ar ensembles of different sizes. It is shown that blue shift through core repulsion and red shift through dipole polarizability counterweight each other to the end that very little global shift is seen in the spectra. This feature persists to all excitation strengths considered. There are, however, detailed effects, such as for example the Landau fragmentation of the Mie plasmon peak. PACS 36.40.Gk; 36.40.Vz; 31.15.Ew     

Pt_nNi_m(n+m=6,n、m≠0)团簇结构与性质的理论研究

采用密度泛函理论(DFT)中的杂化密度泛函B3LYP方法在Lanl2dz基组水平上对Pt_nNi_m(n+m=6,n、m≠0)团簇的各种可能构型进行了几何结构优化,得出了它们的基态构型,并对其能量、热力学性质、核独立化学位移、光谱和极化率进行了理论研究.研究结果表明,PtNi_5、Pt_2Ni_4和Pt_3Ni_3团簇的基态结构都为四角双锥结构,Pt_4Ni_2和Pt_5Ni团簇的基态结构分别是戴帽三角双锥和三角锥戴四边形结构;Pt_nNi_m团簇的生成焓都为负值,表明团簇在热力学上是稳定的;由核独立化学位移值可得,PtNi_5团簇具有反芳香性,Pt_2Ni_4和Pt_5Ni团簇具有芳香性;从光谱分析来看,Pt_3Ni_3团簇的IR较强吸收峰的个数最多,PtNi_5团簇IR和Raman、Pt_2Ni_4团簇的IR、Pt_3Ni_3和Pt_4Ni_2团簇的Raman只有一个强吸收峰值,Pt_5Ni团簇的峰值只出现在频率较大的位置,频率小的位置几乎为零.     

Vibrational corrections to electric properties of weakly bound systems

The pure electronic and vibrational contributions to electric dipole moments, dipole polarizabilities, and first hyperpolarizabilities have been evaluated for the HF and H₂O dimers. The zero-point vibrational average corrections to dipole moments and dipole polarizabilities turn out to be relatively small. However, the corresponding contributions to the first hyperpolarizability are found to be of the same magnitude as the pure electronic values. The so-called pure vibrational corrections to the dipole polarizability and first hyperpolarizability of hydrogen bonded dimers are exceptionally large and indicate that the perturbation theory method used for their evaluation fails to account properly for the high mechanical and electric anharmonicities present in these systems. The analysis of different harmonic and anharmonic contributions to the pure vibrational correction to the first hyperpolarizability shows explicitly the importance of the low frequency intermolecular modes.     

Inclusion of non-orthogonality on the valence bond charge-transfer model for nonlinear optical properties of push—pull molecules

In models based on valence bond theory for predicting nonlinear optical properties of push-pull molecules, the wave functions representing resonance structures are assumed to be orthogonal. We have extended the two-state valence bond charge-transfer model to include non-zero overlap integrals. The resulting model leads to analytic formulae for the polarizability and hyperpolarizabilities, which are related to the overlap and other molecular parameters. In particular we report, as a function of the overlap: (i) relatively weak dependence of the first-order polarizability; (ii) significant variations in both the magnitude and the shape of the response curves corresponding to the second- and third-order polarizabilities. This result may be of relevance in the context of optical switching effects induced by chemical changes (related to the overlap) rather than the more conventional field-induced effect.     

Chiral asymmetry of anti-symmetric coordinates studied by the Raman differential bond polarizability of S-phenylethylamine

<正>The Raman optical activity(ROA) study on 5-phenylethylamine is presented by the intensity analyses via bond polarizability and differential bond polarizability.Ample information concerning the physical picture of this chiral system is obtained,and its ROA mechanism is constructed.Especially,we propose that the asymmetric modes and/or the off-diagonal elements of the electronic polarizability tensor are the potential keys to the exploration of ROA.     

Hyperpolarizabilities of Chiral Molecules Based on Three-Coupled-Oscillator Model

A chiral molecular model of three coupled oscillators is established. A set of coupling equations and hyperpolarizabilities for the chiral molecules with the tripod structure are presented. The expression of second-order nonlinear susceptibility is derived for an isotropic molecular system. The calculated hyperpolarizabilities o[ NPAN and NPP chiral molecules are consistent with the experimental results and the applicability of this model is validated.     

Processes involved in the formation of silver clusters on silicon surface

We analyze scanning electron microscopy measurements for structures formed in the deposition of solid silver clusters onto a silicon(100) substrate and consider theoretical models of cluster evolution onto a surface as a result of diffusion and formation of aggregates of merged clusters. Scanning electron microscopy (SEM) data are presented in addition to energy dispersive X-ray spectrometry (EDX) measurements of the these films. Solid silver clusters are produced by a DC magnetron sputtering source with a quadrupole filter for selection of cluster sizes (4.1 and 5.6 nm or 1900 and 5000 atoms per cluster in this experiment); the energy of cluster deposition is 0.7 eV/atom. Rapid thermal annealing of the grown films allows analysis of their behavior at high temperatures. The results exhibit formation of cluster aggregates via the diffusion of deposited solid clusters along the surface; an aggregate consists of up to hundreds of individual clusters. This process is essentially described by the diffusion-limited aggregation (DLA) model, and thus a grown porous film consists of cluster aggregates joined by bridges. Subsequent annealing of this film leads to its melting at temperatures lower than to the melting point of bulk silver. Analysis of evaporation of this film at higher temperatures gives a binding energy in bulk silver of ɛ₀= (2.74 ± 0.03) eV/atom. The text was submitted by the authors in English.