AN SCF-CI STUDY OF HIGHLY EXCITED VIBRATIONAL STATES OF BENT TRIATOMIC MOLECULES AND ITS APPLICATION TO O_(3)

A self-consistent-field—configuration interaction(SCF-CI)procedure of studying highly excited vibrational states of bent triatomic molecules is suggested and its application to O_3 is investigated.

Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

It is widely believed that Shor＇s factoring algorithm provides a driving force to boost the quantum computing research.However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor＇s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory（OCT） is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor＇s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.

Theoretical study of highly vibrational states of nonlinear triatomic molecules using Lie algebraic approach

The vibrational excitations of bent triatomic molecules are studied by using Lie algebra. The RMS error of fitting 30 spectroscopic data is 1.66 cm-1 for SO2. The results show that the expansion of a molecular algebraic Hamiltonian can well describe the experimental data. And the total vibrational levels can be calculated using this Hamiltonian. At the same time, the potential energy surface can also be obtained with the algebraic Hamiltonian.

Density of excess modes below the first phonon mode in four-dimensional glasses

Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law scaling:D(ω)~ω~γ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finitesize glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)~ω^(3.5) could be generalized to 4D glasses.Here,we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses.It is found that the system size dependence of D(ω) below the first phonon-like mode varies with spatial dimensions:D(ω) increases in2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω^(3.5)scaling,rather than the ω~4 scaling,works in the lowest-frequency regime accessed in 4D glasses,regardless of interaction potentials and system sizes examined.Therefore,our findings in 4D glasses,combined with previous results in 2D and 3D glasses,suggest a common low-frequency scaling of D(ω)~ ω^3.5) below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.

Molecular Dynamics Simulations of Silica Nanotube： Structural and Vibrational Properties Under Different Temperatures

Four-, six-, and eight-membered ring silica nanotubes at temperatures from 300 K to 1600 K are relaxed by classical molecular dynamics simulations with three potential models. The simulation results indicate that the stability of the end rings of the three silica nanotubes gradually decreases with increase in temperature. The validity of the vibrational features of silica nanotubes is shown by the vibrational density of states. Infrared spectra on the silica nanotubes under different temperatures are investigated. A detailed assignment of each spectral peak to the corresponding vibrational mode of the three nanotubes has been addressed. The results are in good agreement with the other theoretical and experimental

Steering Vibrational Population Transfer via Double-∑-Type Laser Scheme

The vibrational state-selected population transfer from a highly vibrationally excited level to the ground level is of great importance in the preparation of ultra-cold molecules. By using the time-dependent quantum-wave-packet method, the population transfer dynamics is investigated theoretically for the HF molecule. A double-E-type laser scheme is proposed to transfer the population from the ｜v=16〉 level to the ground vibrational level ｜v=0〉 on the ground electronic state. The scheme consists of two steps： The first step is to transfer the population from ｜v=16〉 to ｜v=7〉 via an intermediate level ｜v=11〉, and the second one is to transfer the population from ｜v=7〉 to ｜v=0〉 via ｜v=3〉. In each step, three vibrational levels form a E-type population transfer path under the action of two temporally overlapped laser pulses. The maximal population-transfer efficiency is obtained by optimizing the laser inten- sities, frequencies, and relative delays. Cases for the pulses in intuitive and counterintuitive sequences are both calculated and compared. It is found that for both cases the population can be efficiently （over 90%） transferred from the ｜v=-16〉 level to the ｜v=0〉 level.

Rotational Population Measurement of Ultracold 85Rb^133Cs Molecules in the Lowest Vibrational Ground State

We measure the rotational populations of ultracold SS Rbla3 Cs molecules in the lowest vibrational ground state by a depletion spectroscopy and quantify the molecular production rate based on the measurement of single ion signal area. The SSRb133Cs molecules in the X1∑＋（v = 0） are formed from the short-range （2）^3П0＋（V = 10, J = 0） molecular state. A home-made external-cavity diode laser is used as the depletion laser to measure the rotational populations of the formed molecules. Based on the determination of single ion signal, the production rates of molecules in the J=0 and J = 2 rotational levels are derived to be 4800mole/s and 7200mole/s, respectively. The resolution and quantification of molecules in rotational states are facilitative for the manipulation of rotational quantum state of ultracold molecules.

Study of highly excited vibrational dynamics of HCP integrable system with dynamic potential methods

Highly excited vibrational dynamics of phosphaethyne(HCP)integrable system are investigated based on its dynamic potentials.Taking into consideration the 2:1 Fermi resonance between H–C–P bending vibrational mode and C–P stretching vibrational mode,it is found that the effects of H–C stretching vibrational mode on vibrational dynamic features of the HCP integrable system are significant and regularly vary with Polyad numbers(P number).The geometrical profiles of the dynamic potentials and the corresponding fixed points are sensitive to the variation of H–C stretching vibrational strength when P numbers are small,but are not sensitive when P numbers become larger and the corresponding threshold values become lower.The phase space trajectories of different energy levels in a designated dynamic potential(P=28)were studied and the results indicated that the dynamic potentials govern the various dynamic environments in which the vibrational states lie.Furthermore,action integrals of the energy levels contained in dynamic potential(P=28)were quantitatively analyzed and elucidated.It was determined that the dynamic environments could be identified by the numerical values of the action integrals of trajectories of phase space,which is equivalent with dynamic potentials.

Generation of Arbitrary Pure States for Three-dimensional Motion of a Trapped Ion

In this paper, we propose a scheme for generating an arbitrary three-dimensional pure state of vibrational motion of a trapped ion. Our scheme is based on a sequence of laser pulses, which are tuned to the appropriate vibrational sidebands with respect to the appropriate electronic transition.

Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit–phonon hybrid system

Counter-rotating-wave terms(CRWTs)are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation.Here by exemplifying in a nonequilibrium qubit–phonon hybrid model,we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation.By using extended coherent phonon states,we obtain the quantum master equation with heat exchange rates contributed by rotating-waveterms(RWTs)and CRWTs,respectively.We find that including only RWTs,the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias,whereas they are strongly enhanced by considering CRWTs in addition.Furthermore,for the phonon statistics,the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs,whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition.Therefore,CRWTs in quantum heat transfer system should be treated carefully.

A polaron theory of quantum thermal transistor in nonequilibrium three-level systems

We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polarontransformed Redfield equation combined with full counting statistics.The steady state heat currents are obtained via this unified approach over a wide region of system–bath coupling,and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits,respectively.A giant heat amplification phenomenon emerges in the strong system–bath coupling limit,where transitions mediated by the middle thermal bath are found to be crucial to unravel the underlying mechanism.Moreover,the heat amplification is also exhibited with moderate coupling strength,which can be properly explained within the polaron framework.

Imaging Photodissociation Dynamics of MgO at 193 nm

In this work,we used time-sliced ion velocity imaging to study the photodissociation dynamics of Mg O at 193 nm.Three dissociation pathways are found through the speed and angular distributions of magnesium.One pathway is the one-photon excitation of Mg O(X^(1)∑^(+))to Mg O(G^(1)Π)followed by spin-orbit coupling between the G^(1)Π,3^(3)Πand ^(1^(5))Πstates,and finally dissociated to the Mg(^(3)Pu)+O(^(3)Pg)along the 1^(5)Πsurface.The other two pathways are one-photon absorption of Mg O(A^(1)Π)state to Mg O(G^(1)Π)and Mg O(4^(1)Π)state to dissociate into Mg(^(3)P_(u))+O(^(3)P_(g))and Mg(^(1)S_(g))+O(^(1)S_(g)),respectively.The anisotropy parameters of the dissociation pathways are related to the lifetime of the vibrational energy levels and the coupling of rotational and vibronic spin-orbit states.The total kinetic energy analysis gives D0(Mg-O)=21645±50 cm^(-1).

Ab initio calculations on the α^3∑u^＋ state properties of dimer ^7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometry of the α^3∑u^＋ state for ^7Li2 is made at numerous basis sets such as 6-311＋＋G（2df）, cc-PVTZ, 6-311＋＋G（2df, p）, 6-311G（3df,3pd）, 6-311＋＋G（2df,2pd）, D95（3df,3pd）, 6-311＋＋G, DGDZVP, 6-311＋＋G（3df,2pd）, 6-311G（2df,2pd）, D95V＋＋, CEP-121G, 6-311＋＋G（d,p）, 6-311＋＋G（2df, pd） and 6-311＋＋G（3df,3pd） in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction （SAC/SAC=CI） method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at those sets over a wide internuclear distance range from about 3.0α0 to 37.0α0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at ccopVTZ, the spectroscopic data （Te, De, D0, ωe,ωeХe, αe and Be） are computed and they are 1.006 eV, 338.71 cm^-1, 307.12 cm^-1, 64.88 cm^-1, 3.41 cm^-1, 0.0187 cm^-1 and 0.279 cm^-1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant （By） and six centrifugal distortion constants （Dr Hv, Lv, My, Nv, and Ov） are calculated. The scattering length is calculated to be -27.138α0, which is in good accord with the experimental data.

Vacuum Ultraviolet Photodissociation Dynamics of N_(2)O+hν→N_(2)(X^(1)Σg+)+O(^(1)S0) in the Short Wavelength Tail of D^(1)Σ+Band

Vacuum ultraviolet photodissociation dynamics of N2O+hν→N2(X^(1)Σg+)+O(^(1)S0)in the short wavelength tail of D^(1)Σ+band has been investigated using the time-sliced velocity-mapped ion imaging technique by probing the images of the O(^(1)S0)photoproducts at a set of photolysis wavelengths including 121.47 nm,122.17 nm,123.25 nm and 123.95 nm.The product total kinetic energy release distributions,vibrational state distributions of the N2(X^(1)Σg+)photofragments and angular anisotropy parameters have been obtained by analyzing the raw O(^(1)S0)images.It is noted that additional vibrationally excited photoproducts(3≤v≤8)with a Boltzmann-like feature start to appear except the non-statistical component as the photolysis wavelength decreases to 123.25 nm,and the corresponding populations become more pronounced with decreasing of the photolysis wavelength.Furthermore,the vibrational state specific anisotropy parameterβat each photolysis wavelength exhibits a drastic fluctuation nearβ=1.75 at v<8,and decreases to a minimum as the vibrational quantum number further increases.While the overall anisotropy parameterβfor the N2(X^(1)Σg+)+O(^(1)S0)channel presents a roughly monotonical increase from 1.63 at 121.47 nm to 1.95 at 123.95 nm.The experimental observations suggest that there is at least one fast nonadiabatic pathway from initially prepared D^(1)Σ+state to the dissociative state with bent geometry dominating to generate the additional vibrational structures at high photoexcitation energies.

Photodissociation Dynamics of AlO at 193 nm using Time-Sliced Ion Velocity Imaging

The photodissociation dynamics of Al O at 193 nm is studied using time-sliced ion velocity mapping.Two dissociation channels are found through the speed and angular distributions of aluminum ions:one is one-photon dissociation of the neutral AlO to generate Al(2 Pu)+O(3 Pg),and the other is two-photon ionization and then dissociation of AlO^+to generate Al^+(1 Sg)+O(3 Pg).Each dissociation channel includes the contribution of AlO in the vibrational states v=0-2.The anisotropy parameter of the neutral dissociation channel is more dependent on the vibration state of AlO than the ion dissociation channel.

Investigation of electron localization in harmonic emission from asymmetric molecular ion

We theoretically investigate the electron localization around two nuclei in harmonic emission from asymmetric molecular ion. The results show that the ionization process of electron localized around one nucleus competes with its transfer process to the other nucleus. By increasing the initial vibrational level, more electrons localized around the nucleus D＋ tend to transfer to the nucleus He2＋ so that the ionizations of electrons localized around the nucleus He2＋ increase. In this case, the difference in harmonic efficiency between Hell2＋ and HeD2＋ decreases while the difference in harmonic spectral structure increases. The evident minimum can be observed the spectral structure of HeD2＋, which is due to the strong in the harmonic spectrum of Hell2＋ compared with that in interference of multiple recombination channels originating from two nuclei. Time-dependent nuclear probability density, electron-nuclear probability density, double-well model, and time-frequency maps are presented to explain the underlying mechanisms.

Theoretical Study on the Potential Energy Curve and Vibration-rotation Spectra of BeF Radical

The potential energy curve （PEC） of BeF（X2Σ＋） radical is investigated by using the complete active space self-consistent field （CASSCF） method followed by the highly accurate valence internally contracted multireference configuration interaction （MRCI） approach over the internuclear separation range from 0.0522 to 2.0472 nm. The PEC is fitted to the analytic Murrell-Sorbie function, which is employed to accurately determine the spectroscopic parameters. The present D0, De, Re, ωe, ωeχe, αe and Be are 6.14 eV, 6.22 eV, 0.1372 nm, 1236.12 cm-1, 9.11 cm-1, 0.0175 cm-1 and 1.4651 cm-1, respectively. These parameters have been compared with those of previous investigations reported in the literature. With PEC determined at the present level of theory, a total of 75 vibrational states have been predicted for the first time by numerically solving the radial Schrdinger equation of nuclear motion using the Numerov method. For each vibrational state, the complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined for the first time. Comparing with the available experiments and other theories, we find that the present spectroscopic parameter and molecular constant results are more accurate and complete than the previous theoretical investigations.

The v-v energy transfer of highly vibrationally excited states (I)──Vibrational quenching of CO(v) by CO_2

The relaxation of the highly vibrationally excited CO (v=1-8) by CO\-2 is studied by time_resolved Fourier transform infrared emission spectroscopy (TR FTIR). 193 nm laser photolysis of the mixture of CHBr\-3 with O\-2 generates the highly vibrationally excited CO(v) molecules. TR FTIR records the intense infrared emission of CO(v→v-1). The vibrational populations of each level of CO(v) have been determined by the method of spectral simulation. Based on the evolution of the time resolved populations and the differential method, 8 energy transfer rate constants of CO(v=1-8) to CO 2 molecules are obtained: (5.7±0.1), (5.9±0.1), (5.2±0.2), (3.4±0.2), (2.4±0.3), (2.2±0.4), (2.0±0.4) and (1.8±0.6) (10 -14 cm 3·molecule -1·s -1), respectively. A two_channel energy transfer model can explain the feature of the quenching of CO(v) by CO 2. For the lower vibrational states of CO, the vibrational energy transfers preferentially to the υ\-3 mode of CO 2. For the higher levels, the major quenching channel changes to the vibrational energy exchange between CO(v→v-1) and the υ\-1 mode of CO 2.

A study on the bonding structure of CaO-SiO_2 slag by means of molecular dynamics simulation

The investigation results of the bonding structure of CaO-SiO2 slag by means of molecular dynamics simulation are presented. The characteristics of partial radial distribution function gij(r) are in good agreement with the measurement of X-ray diffraction, and the variation of Qn with different SiO4 tetrahedra following the change of Xcao is consistent with the results of Raman spectroscopy, The partial vibrational density of states Fsi(ω) shows that two bands appear in the range of 636-737 cm-1 and 800? 200 cm-1 respectively which are also consistent with Raman spectroscopy.

High-resolution photofragment translational spectro- scopy for the UV photodissociation of C_2H_5I

The photodissociation of ethyl iodide at 279.71, 281.73, 304.02 and 304.67 nm has been studied on our new mini-photofragment translational spectrometer with a total flight path of only 5 cm. Some vibra-tional peaks are firstly resolved in the TOF spectra of I*(2P1/2) and I(2P3/2) channels. These vibrational peaks are assigned to the excitation states (ν2 = 0, 1, 2,…) of the umbrella mode (ν2, 540 cm-1) of the photofragment C2H5, and the distribution of the vibrational states is obtained. The dissociation energy has been determined to be D0(C-I)=2.314 ± 0.03 eV. The energy partitioning of the available energy (Eavl=ET+Eint=ET+EV,R) calculated from our experimental data E int /E avl= 22.1% at 281.73 nm, 22.4% at 304.02 nm for the I* channel, and E int /E avl= 25.2% at 279.71 nm, 25.9% at 304.67 nm for the I channel, seem to be more reliable.