Structure and analysis of atomic vibrations in clusters of Cu n (n ≤ 20)

The binding energy, equilibrium geometry, and vibration frequencies of free clusters Cu _n (2 ≤ n ≤ 20) are calculated using the potentials of interatomic interactions found using the tight-binding approximation. The nonmonotonic dependence of the clusters’ minimum vibration frequency on their sizes and the extreme values for the number of atoms in a cluster n = 4, 6, 13, and 19 is demonstrated. It is noted that this result agrees with the theoretical and experimental data on stable structures of small and medium metallic clusters.     

Theoretical and experimental study of IR spectra of large phenol-acetylene clusters,Ph(Ac)n for 8 ≤ n ≤ 12

This work reports a combined theoretical and experimental study on large phenol-acetylene clusters, Ph(Ac)_n, 8 ​≤ ​n ​≤ ​12, extending our earlier work on the smaller clusters [Singh, G.; Nandi, A.; Gadre, S. R.; Chiba, T.; Fujii, A. J. Chem. Phys. 2017, 146, 154303]. Several trial cluster geometries are generated using the molecular electrostatic potential (MESP) for placing additional acetylene moieties, followed by geometry optimization at B97D/aug-cc-pVDZ level theory. The infrared spectra of energetically low-lying (within 0.5 ​mH window) isomers of the clusters are calculated and averaged. The O–H stretching band shows two peaks due to the presence of energetically close isomers differing in the arrangement of acetylenes around the O–H group. The acetylenic C–H stretching band appears around 3260 ​cm⁻¹. The C–H band shows a red shift of about 3 ​cm⁻¹ on going from n ​= ​8 to 12. Moderately size-selected IR spectra of Ph(Ac)_n (n ​= ​~10 and ~13) prepared by a supersonic jet expansion are measured for the acetylenic C–H region by infrared-ultraviolet double resonance spectroscopy combined with time-of-flight mass spectrometry. The observed spectral features are in agreement with the trends of the frequency shift and asymmetric line shape of the C–H stretch band predicted by the theoretical calculations.     

Fragmentation Behavior and Ionization Potentials of Aluminum Clusters Al_n(n≤40)

Al2-Al40 clusters were studied by means of the all-electron DFT method.The properties of the aluminum clusters including binding energy,the second difference in energy,HOMO-LUMO gap,especially fragmentation energies and ionization potentials,were analyzed.The main products from the dissociations of aluminum cluster ions are shown to be Al+Al+n-1 for the larger clusters,and Al++Aln-1 for the smaller ones.And,the calculated ionization potentials are consistent with the experiment data.     

Fragmentation Behavior and Ionization Potentials of Lead Clusters Pb_n(n≤30)

The properties of Pbn(n=2―30) clusters including binding energies,second differences in energy,and HOMO-LUMO gaps,especially fragmentation energies and ionization potentials,have been studied by ab initio calculation.The main fragmentation products of Pbn+ are shown to be Pb+Pbn-1+ for n≤14 and two small cluster fragments for larger ones with n14.The Pb13+ appears frequently as the products in the fragmentations of large clusters.Also,the calculated ionization potentials of the clusters are consistent with the experiment data.     

Study of Structures and Electronic Properties of Pdn-1Pb and Pdn(n≤8) Clusters

Geometric and electronic properties of Pdn-1Pb and Pdn(n≤8) clusters have been studied by using density functional theory with effective core potentials, focusing on the differences between mono- and bimetallic clusters. The average bond length of Pdn-1Pb (n≤8) bimetallic clusters is longer than that of pure palladium clusters except for n = 2 and 3. The most stable structure of Pdn-1Pb (n≤7) is the singlet where there is at least a Pd or Pb atom on its excited state. The energy gaps of Pd-Pb binary clusters are narrower than those of Pdn clusters, and then the chemical activity is strengthened when Pdn clusters are doped with Pb.     

Photoelectron imaging of tetrahydrofuran cluster anions (THF)(n) (-) (1≤n≤100)

Anionic tetrahydrofuran clusters (THF)(n) (-) (1≤n≤100) are studied with photoelectron imaging as gas-phase precursors for electrons solvated in THF. Photoelectron spectra of clusters up to n=5 show two peaks, one of which is attributed to a solvated open chain radical anion and the other to the closed THF ring. At n=6, the spectra change shape abruptly, which become more characteristic of (THF)(n) (-) clusters containing solvated electrons. From n=6-100, the vertical detachment energies (VDEs) of these solvated electron clusters increase from 1.96 to 2.71 eV, scaling linearly with n(-1/3). For fully deuterated (THF-d8)(n) (-) clusters, the apparent transition to a solvated electron cluster is delayed to n=11. Extrapolation of the VDEs to infinite cluster size yields a value of 3.10 eV for the bulk photoelectric threshold. The relatively large VDEs at onset and small stabilization with increasing cluster size compared to other solvated electron clusters may reflect the tendency of the bulk solvent to form preexisting voids that can readily solvate a free electron.     

Structure of carbon fluorochlorides CF n Cl m (n,m ≤ 3) and their singly charged negative ions

The electronic and geometrical structures of carbon fluorochlorides with low coordination numbers (n 3) and their singly charged anions are calculated using the functional density method. The results of the calculations are used to evaluate the electron affinities (EA) of the neutral compounds and the first ionization potentials of the anions as well as the energies of fragmentation through different decay channels of both series. The adiabatic EA of carbon fluorochloride CF _k Cl _3–k is shown to be determined mainly by the presence of a CX₂ unit in these compounds. There are no monotonic changes in stability of either the neutral compounds withn = 3 or the anions withn = 2 or 3 upon successive substitution of one halogen by another.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1044–1049, June, 1993.     

Study of Structures and Electronic Properties of Pdn–1Pb and Pdn （n≤8） Clusters

Geometric and electronic properties of Pdn–1Pb and Pdn (n≤8) clusters have been studied by using density functional theory with effective core potentials, focusing on the differences between mono- and bimetallic clusters. The average bond length of Pdn–1Pb (n≤8) bimetallic clusters is longer than that of pure palladium clusters except for n = 2 and 3. The most stable structure of Pdn–1Pb (n≤7) is the singlet where there is at least a Pd or Pb atom on its excited state. The energy gaps of Pd–Pb binary clusters are narrower than those of Pdn clusters, and then the chemical activity is strengthened when Pdn clusters are doped with Pb.     

Structures and IR/UV spectra of neutral and ionic phenol-Ar(n) cluster isomers (n ≤ 4): competition between hydrogen bonding and stacking

The structures, binding energies, and vibrational and electronic spectra of various isomers of neutral and ionic phenol-Ar(n) clusters with n ≤ 4, PhOH((+))-Ar(n), are characterized by quantum chemical calculations. The properties in the neutral and ionic ground electronic states (S(0), D(0)) are determined at the M06-2X/aug-cc-pVTZ level, whereas the S(1) excited state of the neutral species is investigated at the CC2/aug-cc-pVDZ level. The Ar complexation shifts calculated for the S(1) origin and the adiabatic ionisation potential, ΔS(1) and ΔIP, sensitively depend on the Ar positions and thus the sequence of filling the first Ar solvation shell. The calculated shifts confirm empirical additivity rules for ΔS(1) established recently from experimental spectra and enable thus a firm assignment of various S(1) origins to their respective isomers. A similar additivity model is newly developed for ΔIP using the M06-2X data. The isomer assignment is further confirmed by Franck-Condon simulations of the intermolecular vibrational structure of the S(1) ← S(0) transitions. In neutral PhOH-Ar(n), dispersion dominates the attraction and π-bonding is more stable than H-bonding. The solvation sequence of the most stable isomers is derived as (10), (11), (30), and (31) for n ≤ 4, where (km) denotes isomers with k and m Ar ligands binding above and below the aromatic plane, respectively. The π interaction is somewhat stronger in the S(1) state due to enhanced dispersion forces. Similarly, the H-bond strength increases in S(1) due to the enhanced acidity of the OH proton. In the PhOH(+)-Ar(n) cations, H-bonds are significantly stronger than π-bonds due to additional induction forces. Consequently, one favourable solvation sequence is derived as (H00), (H10), (H20), and (H30) for n ≤ 4, where (Hkm) denotes isomers with one H-bound ligand and k and m π-bonded Ar ligands above and below the aromatic plane, respectively. Another low-energy solvation motif for n = 2 is denoted (11)(H) and involves nonlinear bifurcated H-bonding to both equivalent Ar atoms in a C(2v) structure in which the OH group points toward the midpoint of an Ar(2) dimer in a T-shaped fashion. This dimer core can also be further solvated by π-bonded ligands leading to the solvation sequence (H00), (11)(H), (21)(H), and (22) for n ≤ 4. The implications of the ionisation-induced π → H switch in the preferred interaction motif on the isomerisation and fragmentation processes of PhOH((+))-Ar(n) are discussed in the light of the new structural and energetic cluster parameters.     

Dynamics of electron solvation in I(-)(CH3OH)n clusters (4 ≤ n ≤ 11)

The dynamics of electron solvation following excitation of the charge-transfer-to-solvent precursor state in iodide-doped methanol clusters, I(-)(CH(3)OH)(n = 4-11), are studied with time-resolved photoelectron imaging. This excitation produces a I···(CH(3)OH)(n)(-) cluster that is unstable with respect to electron autodetachment and whose autodetachment lifetime increases monotonically from ~800 fs to 85 ps as n increases from 4 to 11. The vertical detachment energy (VDE) and width of the excited state feature in the photoelectron spectrum show complex time dependence during the lifetime of this state. The VDE decreases over the first 100-400 fs, then rises exponentially to a maximum with a ~1 ps time constant, and finally decreases by as much as 180 meV with timescales of 3-20 ps. The early dynamics are associated with electron transfer from the iodide to the methanol cluster, while the longer-time changes in VDE are attributed to solvent reordering, possibly in conjunction with ejection of neutral iodine from the cluster. Changes in the observed width of the spectrum largely follow those of the VDEs; the dynamics of both are attributed to the major rearrangement of the solvent cluster during relaxation. The relaxation dynamics are interpreted as a reorientation of at least one methanol molecule and the disruption and formation of the solvent network in order to accommodate the excess charge.     

Cn,CnH and their anions: Quest for linearity with n≤8 even versus odd,and beyond

Using the concept of quasi-molecule (“tile”) and the database of quasi-molecules embedded on a parent molecule, it is discussed whether the latter can attain linear form or otherwise. Besides anew accurate optimization of all tiles (quasi-triatomics) at various levels of ab initio theory and basis-sets, the nature of the predicted stationary points for the title parent molecules is probed through a priori calculations here too reported. Also discussed is the common rule that even- $n$ ${\text{C}}_n{\text{H}}^{-}$ anions are linear while odd-numbered ones tend to have nonlinear isomers. The reported quasi-molecule approach is general, and allow the prediction of linearity or otherwise of the parent systems prior to calculations on them. When based on an extension of the bisection method (Varandas, Int. J. Quantum Chem. 2023 , 123, e27036.), it is easy to use even for large parent molecules, as illustrated for neutral and anionic carbon clusters with $n\ge 9$.     

Ion induced dipole clusters H(n)- (3 ≤ n-odd ≤ 13): density functional theory calculations of structure and energy

We investigate anew the possible equilibrium geometries of ion induced dipole clusters of hydrogen molecular ions, of molecular formula H(n)(-) (3 ≤ n-odd ≤ 13). Our previous publications [Sapse, A. M.; et al. Nature 1979, 278, 332; Rayez, J. C.; et al., J. Chem. Phys. 1981, 75, 5393] indicated these molecules would have a shallow minimum and adopt symmetrical geometries that accord with the valence shell electron pair repulsion (VSEPR) rules for geometries defined by electron pairs surrounding a central point of attraction. These earlier calculations were all based upon Hartree-Fock (HF) calculations with a fairly small basis of atomic functions, except for the H3(-) ion for which configuration interaction (CI) calculations were carried out. A related paper [Hirao, K.; et al., Chem. Phys. 1983, 80, 237] carried out similar calculations on the same clusters, finding geometries similar to our earlier calculations. However, although that paper argued that the stabilization energy of negative ion clusters H(n)(-) is small, vibration frequencies for the whole set of clusters was not reported, and so a definitive assertion of a true equilibrium was not present. In this paper we recalculate the energetics of the ion induced dipole clusters using density function theory (DFT) B3LYP method calculations in a basis of functions (6-311++G(d,p)). By calculating the vibration frequencies of the VSEPR geometries, we prove that in general they are not true minima because not all the resulting frequencies correspond to real values. By searching the energy surface of the B3LYP calculations, we find the true minimum geometries, which are surprising configurations and are perhaps counterintuitive. We calculate the total energy and binding energy of the new geometries. We also calculate the bond paths associated with the quantum theory of atoms in molecules (QTAIM). The B3LYP/6-311++G(d,p) results, for each molecule, deliver bond paths that radiate between each polarized H2 molecule and the polarizing H(-) ion.     

HNO与(HF)1≤n≤3分子间的蓝移与红移氢键

运用量子化学从头算方法研究了HNO与分子簇(HF)1≤n≤移氢键, 重极化与重杂化和分子内超共轭导致了氢键的蓝移; 所有的X…H—F(X=O, N, F)氢键都是红移的, 分子间超共轭导致了氢键的红移. 在多分子体系形成的氢键链中, 分子间超共轭作用呈现规律性递变, 它导致了氢键强度与频率位移的规律性变化, 电子密度拓扑分析结果反映和支持了这种规律性变化.     

(BN)n(n≤12)团簇的结构及成键性质

利用遗传算法和Gastreich提出的经验势函数研究了(BN)_n(n≤12)团簇的可能稳定结构, 并对能量较低的异构体在HF/6-31G(d)水平进行优化, 得到了(BN)_n(n≤12)团簇的线状、蒲扇形、单环、双环、三环和笼状结构, 讨论了各种结构的特征及相对稳定性. 分析了BN团簇中原子的成键性质, 在单环结构中, N原子以sp2杂化成键, B原子以sp杂化成键, 而在节点处B原子以sp2杂化成键. (BN)6是唯一没有张力的单环结构.     

HNO与（HF）1≤n≤3分子间的蓝移与红移氢键

运用量子化学从头算方法研究了HNO与分子簇(HF)1≤n≤3形成的蓝移与红移氢键.在这些体系中,F…H-N都是蓝移氢键,重极化与重杂化和分子内超共轭导敛了氰键的蓝移;所有的X…H-F(X=O,N,F)氢键都是红移的,分子问超共轭导致了氢键的红移.在多分子体系形成的氢键链中,分子问超共轭作用呈现规律性递变,它导致了氢键强度与频率位移的规律性变化,电子密度拓扑分析结果反映和支持了这种规律性变化.     

A theoretical investigation on optimal structures of ethane clusters (C2H6)n with n ≤ 25 and their building-up principle

Geometry optimization of ethane clusters (C(2)H(6))(n) in the range of n ≤ 25 is carried out with a Morse potential. A heuristic method based on perturbations of geometries is used to locate global minima of the clusters. The following perturbations are carried out: (1) the molecule or group with the highest energy is moved to the interior of a cluster, (2) it is moved to stable positions on the surface of a cluster, and (3) orientations of one and two molecules are randomly modified. The geometry obtained after each perturbation is optimized by a quasi-Newton method. The global minimum of the dimer is consistent with that previously reported. The putative global minima of the clusters with 3 ≤ n ≤ 25 are first proposed and their building-up principle is discussed.     

Probing the electronic structure and property of neutral and charged arsenic clusters (As(n)(+1,0,-1), n≤8) using Gaussian-3 theory

The structures and energies of As(n) (n = 2-8) neutrals, anions, and cations have been systematically investigated by means of the G3 schemes. The electron affinities, ionization potentials, binding energies, and several dissociation energies have been calculated and compared with limited experimental values. The results revealed that the potential surfaces of neutral As(n) clusters are very shallow, and two types of structural patterns compete with each other for the ground-state structure of As(n) with n ≥ 6. One type is derived from the benzvalene form of As(6), and another is derived from the trigonal prism of As(6). The previous photoelectron spectrum (taken from J. Chem. Phys. 1998 , 109 , 10727 ) for As(3) has been reassigned in light of the G3 results. The experimental electron affinities of As(3) were measured to be 1.81 eV, not 1.45 eV. We inferred from the conclusion of G3 and density functional theory that the experimental electron affinities of 1.7 and 3.51 eV for As(5) are unreliable. The reliable electron affinities were predicted to be 0.83 eV for As(2), 1.80 eV for As(3), 0.54 eV for As(4), 3.01 eV for As(5), 2.08 eV for As(6), 2.93 eV for As(7), and 2.02 eV for As(8). The G3 ionization potentials were calculated to be 9.87 eV for As(2), 7.33 eV for As(3), 8.65 eV for As(4), 6.68 eV for As(5), 7.97 eV for As(6), 6.58 eV for As(7), and 7.65 eV for As(8). The binding energies per atom were evaluated to be 1.99 eV for As(2), 2.01 eV for As(3), 2.61 eV for As(4), 2.39 eV for As(5), 2.51 eV for As(6), 2.55 eV for As(7), and 2.67 eV for As(8). These theoretical values of As(2), As(3), and As(4) are in excellent agreement with those of experimental results. Several dissociation energies were carried out to examine relative stabilities. This characterized the even-numbered clusters as more stable than the odd-numbered species.     

Spectral signatures of four-coordinated sites in water clusters: infrared spectroscopy of phenol-(H2O)n (∼20 ≤ n ≤ ∼50)

We report infrared spectra of phenol-(H(2)O)(n) (～20 ≤ n ≤ ～50) in the OH stretching vibrational region. Phenol-(H(2)O)(n) forms essentially the same hydrogen bond (H-bond) network as that of the neat water cluster, (H(2)O)(n+1). The phenyl group enables us to apply the scheme of infrared-ultraviolet double resonance spectroscopy combined with mass spectrometry, achieving the moderate size selectivity (0 ≤ Δn ≤ ～6). The observed spectra show clear decrease of the free OH stretch band intensity relative to that of the H-bonded OH band with increasing cluster size n. This indicates increase of the relative weight of four-coordinated water sites, which have no free OH. Corresponding to the suppression of the free OH band, the absorption peak of the H-bonded OH stretch band rises at ～3350 cm(-1). This spectral change is interpreted in terms of a signature of four-coordinated water sites in the clusters.     

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments: test calculations for Au, AuF, and Sn(n) cluster (n ≤ 20)

The response of the electronic wavefunction to an external electric or magnetic field is widely considered to be a typical valence property and should, therefore, be adequately described by accurately adjusted pseudopotentials, especially if a small-core definition is used within this approximation. In this paper we show for atomic Au and Au(+), as well as for the molecule AuF and tin clusters, that in contrast to the case of the static electric dipole polarizability or the electric dipole moment, core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation. This error increases with increasing size of the core chosen. For tin clusters, which are of interest in ongoing molecular beam experiments currently carried out by the Darmstadt group, the diamagnetic and paramagnetic isotropic components of the magnetizability tensor almost cancel out and large-core pseudopotentials do not even predict the correct sign for this property due to erroneous results in both the diamagnetic and (more importantly) the paramagnetic terms. Hence, all-electron calculations or pseudopotentials with very small cores are required to adequately predict magnetizabilities for atoms, molecules and the solid state, making it computationally more difficult to obtain this quantity for future investigations in heavy atom containing molecules or clusters. We also demonstrate for this property that all-electron density functional calculations are quite robust and give results close to wavefunction based methods for the atoms and molecules studied here.     

Electronic Structure and Chemical Bonding in Monoclinic and Cubic Li2-xHxTiO3 (0≤ x ≤ 2)

The linear muffintin orbitals method in a tight binding approximation and extended Huckel theory are used to study the electronic structure and chemical bonding of lithium titanate (Li₂TiO₃) and its protonated analogs (Li_1.75H_0.25TiO₃ and H₂TiO₃). The effect of protons on electron spectrum characteristics and bond strength are investigated for the monoclinic and cubic phases of lithium titanate. Phase stability is evaluated by cohesion energy calculations.