Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the 1 ＋ X^1∑g^＋ state of sodium dimer

The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the dissociation energy De and the harmonic frequency We for the XIEg＋ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and We results can be attained at the QCISD/6-311G（3df,3pd） level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell-Sorbie function. The spectroscopic parameters De, DO, Re, ωe, ωe Xe, αe and Be are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm^-1, 0.7288 cm^-1, 0.000729 cm^-1 and 0.1449 cm^-1, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G（3df,3pd） level of theory, a total of 63 vibrational states is found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants （Dr Hv, Lv, Mv, Nv and Ov） are reported for the first time for the first 31 vibrational states when J = 0.

Analytical Potential Energy Function,Spectroscopic Constants and Vibrational Levels for A^1E_u^+ State of Dimer ~7Li_2

The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.

Ab initio calculations on the spectroscopic constants, vibrational levels and classical turning points for the 2^1Пu state of dimer ^7Li2

The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

Distribution of Vibrational Energy Levels of Protein Molecular Chains

The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.

An ab initio potential energy surface and vibrational energy levels of HXeBr

A three-dimensional global potential energy surface for the electronic ground state of HXeBr molecule is constructed from more than 4200 ab initio points. These points are generated using an internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q） and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces. The three-body dissociation channel is found to be the dominate dissociation channel for HXeBr. Based on the obtained potentials, low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm is found to be in good agreement with the available experimental band origins.

Theoretical Studies on the Potential Energy Surface and Vibrational Energy Levels of HXeBr

The potential energy surface for the electronic ground state of the HXeBr molecule is constructed from more than 4200 ab initio points calculated using the internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q）. The stabilities and dissociation barriers are identified from the potential energy surface. The three-body dissociation channel is found to be the dominant dissociation channel for HXeBr. Low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins.

Vibrational Spectra of Nonrigid Molecule HCP in an Algebraic Model

An algebraic Harniltonian for the two coupled nonlinear vibrations of highly excited nonrigid molecule HCP was presented. The Hamiltonian reduces to the conventional one in a limit which was expressed in terms of harmonic oscillator operators. It showed that the algebraic model can better reproduce the data than the conventional model by fitting the observed data of HCP.

A Strategy for Magnifying Vibration in High-Energy Orbits of a Bistable Oscillator at Low Excitation Levels

This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is vMidated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM.

Investigations on analytic potential energy function, spectroscopic parameters and vibrational manifolds (J = 0) of the SD + (X^3 Σ^- ) ion

This paper investigates the spectroscopic properties of the SD^＋（X^3∑^-） ion by employing the coupled-cluster singles-doubles-approximate-triples [CCSD（T）] theory combining with the quintuple correlation-consistent basis set augmented with diffuse functions （aug-cc-pV5Z） of Dunning and co-workers. The accurate adiabatic potential energy function is obtained by the least-squares fitting method with the 100 ab initio points, which are calculated at the unrestricted CCSD（T）/aug-cc-pV5Z level of theory over the internuclear separation range from 0.09 to 2.46 nm. Using the potential, it accurately determines the spectroscopic parameters （De, ωeХe, αe and Be）. The present De, Re, We, ωeХe, αe and Be results are of 3.69119 eV, 0.13644 nm, 1834.949 cm^-1, 25.6208 cm^-1, 0.1068 cm^-1 and 4.7778 cm^-1, respectively, which are in remarkably good agreement with the experimental findings. A total of 29 vibrational states has been predicted by numerically solving the radial Schrodinger equation of nuclear motion when the rotational quantum number J equals zero. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reported when J = 0 for the first time, which are in good accord with the measurements wherever available.

Production and Detection of Ultracold Ground State 85Rb133Cs Molecules in the Lowest Vibrational Level by Short-Range Photoassociation

We investigate the production of ultracold ground state x^1∑7＋（u = 0） RbCs molecules in the lowest vibrational level via short-range photoassociation followed by spontaneous emission. The starting point is the laser cooled 85Rb and laa cs atoms in a dual species, forced dark magneto-optical trap. The special intermediate level （5）O＋ （u = 10） correlated to the （2）311 electric state is achieved by the photoassociation process. The formed ground state X1∑＋ （u = 0） molecule is resonantly excited to the 2111 intermediate state by a 651 nm pulse laser and is ionized by a 532nm pulse laser and then detected by the time-of-flight mass spectrum. Saturation of the photoionization spectroscopy at large ionization laser energy is observed and the ionization efficiency is obtained from the fitting. The production of ultracold ground state 85Rblaacs molecules is facilitative for the further research about the manipulation of ultracold molecules in the rovibrational ground state.

Vibrations induced by tunnel boring machine in urban areas: In situ measurements and methodology of analysis

Excavation with tunnel boring machine(TBM)can generate vibrations,causing damages to neighbouring buildings and disturbing the residents or the equipment.This problem is particularly challenging in urban areas,where TBMs are increasingly large in diameter and shallow in depth.In response to this problem,four experimental campaigns were carried out in different geotechnical contexts in France.The vibration measurements were acquired on the surface and inside the TBMs.These measurements are also complemented by few data in the literature.An original methodology of signal processing is pro-posed to characterize the amplitude of the particle velocities,as well as the frequency content of the signals to highlight the most energetic bands.The levels of vibrations are also compared with the thresholds existing in various European regulations concerning the impact on neighbouring structures and the disturbance to local residents.

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves （PECs） of the ground state （^3∏） and three low-lying excited states （^1∑, ^3∑,^1∏） of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel-Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schrodinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the ^3∏ state, of which the dissociation asymptote is Cd（^1S） ＋ Se（^3p）, is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39eV. However, the first excited state is only 1132.49cm^-1 above the ground state and the ^3∑ state is the highest in the four calculated states.

Accurate ab initio-based analytical potential energy function for S_2(~1△_g) via extrapolation to the complete basis set limit

The potential energy curves（PECs） of the first electronic excited state of S2（a^1△g） are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning： aug-cc-p VX Z（X = T, Q, 5, 6）. In order to obtain PECs with high accuracy, PECs calculated with aug-cc-p V（Q, 5）Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function（APEF） using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6 Z and the extrapolated AV（Q, 5）Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.

Low-lying electronic states of CuN calculated by MRCI method

The high accuracy ab initio calculation method of multi-reference configuration interaction（MRCI） is used to compute the low-lying eight electronic states of CuN.The potential energy curves（PECs） of the X;∑;,1;Π,2;∑;,1;△,1;△,1;∑;,1;Π,and;∑;in a range of R=0.1 nm-0.5 nm are obtained and they are goodly asymptotes to the Cu（;S;） + N（;S;） and Cu（;S;）+N（;D;） dissociation limits.All the possible vibrational levels,rotational constants,and spectral constants for the six bound states of X;∑;,1;Π,2;∑;,1;△,1;∑;,and 1;Π are obtained by solving the radial Schrdinger equation of nuclear motion with the Le Roy provided Level 8.0 program.Also the transition dipole moments from the ground state X;∑;to the excited states 1;Π and 2;∑;are calculated and the result indicates that the 2;∑-X;∑ transition has a much higher transition dipole moment than the 1;Π-X;∑;transition even though the l;Π state is much lower in energy than the 2;∑;state.

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves （PECs） for the ground state （X2∑＋） and the four excited electronic states （A2∏, B2∏, C2∑＋, 4∏） of a Bell molecule are calculated using the multi-configuration reference single and double excited configuration interaction （MRCI） approach in combination with the aug-cc-pVTZ basis sets. The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm, and the equilibrium bond length Re and the vertical excited energy Te are determined directly. It is evident that the X2∑＋, A2∏, B2∏, C2∑＋ states are bound and 4∏ is a repulsive excited state. With the potentials, all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero （J = 0） by numerically solving the radial SchrSdinger equation of nuclear motion. Then the spectroscopic data are obtained including the rotation coupling constant w e, the anharmonic constant WeXe, the equilibrium rotation constant Be, and the vibration-rotation coupling constant ae. These values are compared with the theoretical and experimental results currently available, showing that they are in agreement with each other.

Safety of engineered structures against blast vibrations： A case study

Blasting used for rock excavation is associated with ground vibrations having potential damage to surrounding structures.The extent of damage produced in a structure depends largely on ground motion characteristics,dynamic characteristics of structure and the type of geological strata on which it is founded.The safety of surrounding structures against blast vibrations is a cause of concern.However,use of a systematic approach to rock blasting helps to complete the excavation safely in time without endangering the safety of surrounding structures.Various steps are commonly adopted at construction sites to ensure safety of engineered structures against blast vibrations,e.g.adopting a suitable safe vibration level,developing site-specific attenuation relation,estimating safe charges for different distances,designing blasting pattern,and monitoring vibrations during actual blasting.The paper describes the details of studies conducted for ensuring safety of an 85 years old masonry dam and green concrete of varying ages during excavation of about 30,000 m;of hard rock in Maharashtra,India.The studies helped to complete the rock excavation safely in time and the safety of the dam was ensured by monitoring blast vibrations during actual rock excavation.

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction(MRCI) approach in combination with the aug-cc-pVTZ basis sets.The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm,and the equilibrium bond length R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π is a repulsive excited state.With the potentials,all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero(J = 0) by numerically solving the radial Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.