Transition Moment Integrals Research Articles

Multipole oscillator strength and polarizability for confined hydrogen-like atoms under high pressure

Multipole oscillator strength (f (k)) acts as a foundation in estimating multipole polarizability in a quantum system. Moreover, a knowledge of f (k) as well as under extreme pressure may be treated as the benchmark in high pressure spectroscopy. Further, an investigation of rate of change of these quantities and transition moment integral as a function of confinement radius (R) may offer many hitherto unexplained features. Here, we derive several such relations for confined H-like atom as a test case. In this regard, a virial theorem is utilized. The versatility of these derived relations in the context of atom is also discussed. Apart from that, we report numerically calculated results of α (k), f (k) for a confined H-like atom trapped inside a spherical cavity of radius R. A detailed and systematic analysis of these are undertaken in case of k ranging from 1–4, with special emphasis on 1s, 2s, 2p, 3d states. Their behavior is found to be significantly different from their respective free counterparts.

Electronic states of MgO: Spectroscopy, predissociation, and cold atomic Mg and O production

We used multiconfigurational methods and a large basis set to compute the potential energy curves of the valence and valence-Rydberg electronic states of MgO molecule. New bound electronic states are found. Using these highly correlated wave functions, we evaluated their mutual spin-orbit couplings and transition moment integrals. For the bound electronic states of MgO, we deduced an accurate set of spectroscopic constants that agree remarkably well with experimental results. Moreover, our potentials, transition moments, and spin-orbit coupling evolutions are incorporated into Fermi golden rule calculations to deduce the radiative lifetimes of MgO(B (1)Σ(+)) rovibrational levels and the natural lifetimes of MgO(A (1)Π) vibrational levels, where a good agreement is found with experimental values. Finally, we suggest new routes for the production of cold Mg and O atoms and cold MgO molecules.

ChemInform Abstract: The Electronic Structure and Second-Order Nonlinear Optical Properties of Donor-Acceptor Acetylenes: A Detailed Investigation of Structure- Property Relationships

A series of donor-acceptor acetylene compounds was synthesized in which systematic changes in both the conjugation length and the donor-acceptor strength were made. The effect of these structural changes on the spectroscopic and electronic properties of the molecules and, ultimately, on the measured second-order molecular hyperpolarizabilities (beta) was investigated. It was found that increases in the donor-acceptor strength resulted in increases in the magnitude of beta. For this class of molecules, the increase is dominated by the energy of the intramolecular charge-transfer transition, while factors such as the ground to excited-state dipole moment change and the transition-moment integral are much less important. Increasing the conjugation length from one to two acetylene linkers did not result in an increase in the value of beta; however, beta increased sharply in going from two acetylenes to three. This increase is attributed to the superposition of several nearly isoenergetic excited states.

Ab initio vibrational spectrum of [formula omitted

The vibrational spectrum and structure of ( 2 Σ + ) He – MgH 2 + has been investigated using relativistically-corrected UCCSD(T). Vibrational wave functions for low-lying l = 0 states were obtained numerically using a w co-ordinate Eckart–Watson vibrational Hamiltonian, in conjunction with an embedded analytical UCCSD(T) potential. For the ground vibrational state, vibration-averaged Mg–H and Mg–He bond lengths differ by −33 and 53 m a 0 from those corresponding to the ab initio potential surface minimum. Vibration transition moment integrals and associated radiative properties of ( 2 Σ + ) He – MgH 2 + have been calculated using an adapted quadrature scheme, in conjunction with an embedded analytical UCCSD(T) dipole moment function.

Enhanced Intensity Distribution Analysis of the Rotational–Vibrational Spectrum of HCl

Data are presented that indicates the best fit of intensity of the HCl vibrational�rotational FTIR spectrum, which includes a Boltzmann population profile, is accomplished by accounting for factors from the full transition moment integral and by relaxing the rigid-rotor approximation. Mathcad is used to generate intensity distributions. A typical HCl FTIR spectrum is shown and two methods are discussed for presenting the spectrum together with a calculated intensity distribution. The two methods are the use of transparencies or projection using PowerPoint to manipulate the images so that they overlay. A direct visual comparison can then be made by students in the classroom as to the quality of the fit. Information describing the HCl spectrum and the quality of these data, a description of intensity distributions using Boltzmann population profiles and how they are displayed, and techniques for employing both visualization methods in the classroom are presented in the Supplemental Material. Also available in the Supplemental Material is the HCl spectrum saved as an Excel file and the Mathcad file used to generate the intensity distributions.

Theory of Monte Carlo simulations of the magnetic circular dichroism spectra of alkali metal/rare gas systems

AbstractThe history of magnetic circular dichroism (MCD) spectroscopy in the study of alkali metal/rare gas (M/Rg) cryogenic systems is reviewed in the context of developing a better understanding of alkali metal/hydrogen systems of current interest to the U.S. Air Force as enhanced‐performance cryogenic rocket propellants. A new theory for simulating the MCD spectra of M/Rg systems is presented together with a careful discussion of the theory's implicit and explicit approximations and their implications. This theory uses a classical Monte Carlo (MC) simulation scheme to model the perturbing effects of the Rg environment on the 2S → 2P MCD‐active transition of the M atom. The theory sets up the MC–MCD simulation as a 6 × 6 matrix eigenvalue/eigenvector problem in the 2P manifold in which are included the effects of M–Rg interactions, metal atom spin‐orbit coupling in the 2P manifold, magnetic Zeeman perturbations of the 2S and 2P manifolds, Boltzmann temperature factors, and electric dipole transition moment integrals for left circularly polarized (LCP) and right circularly polarized (RCP) light. The theory may be applied to any type of trapping site of the host M in the guest Rg matrix; a single atom substitutional metal atom trapping site (one host Rg atom is replaced by one guest M atom) is modeled in this study for M = Na and Rg = Ar. Two temperature factors are used in these simulations; a lattice temperature to model the mobility of the Rg lattice and a magnetic temperature to model Boltzmann factors in the 2S ground manifold. The 6 × 6 eigenvalue/eigenvector problem is solved for a number of randomly generated and suitably averaged Rg configurations to yield the simulated MC‐MCD spectrum for the single substitutional Na/Ar system. The MC–MCD simulations of Na/Ar give the characteristic triplet MCD spectrum with the correct Boltzmann temperature dependence. The simulated MC–MCD spectrum correctly inverts when the direction of the applied magnetic field is reversed. Addition of the LCP and RCP absorbances gives rise to a characteristic 2S → 2P triplet absorption feature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Relationship between the Dipole Strength of Ligand Pre-Edge Transitions and Metal-Ligand Covalency.

The electric dipole contributions to the observed pre-edge intensities in ligand K-edge X-ray absorption (XAS) spectra are analyzed in terms of covalent-bonding contributions between the metal and ligand for a prototype system with one hole in the d shell. One- and two-center contributions to the intensity are identified. By direct evaluation of the integrals involved in the intensity expression, the two-center terms are shown to be at least 1 order of magnitude smaller than the one-center terms and can be ignored to a reasonable approximation. The one-center terms reflect the amount of ligand character in the partially occupied metal-based MOs and are proportional to the intrinsic transition moment of a ligand-centered 1s --> np transition. The final intensity does not contain terms proportional to the square of the metal-ligand distance as might have been expected on the basis of the analogy between ligand K-edge and ligand-to-metal charge transfer (LMCT) transitions that both formally lead to transfer of electron density from the ligand to the metal. This is due to the fact that the transition density is completely localized on the ligand in the case of a ligand K-edge transition but is delocalized over the metal and the ligand in the case of a LMCT transition. The effective nuclear charge dependence of the one-center transition moment integral was studied by Hartree-Fock level calculations and was found to be small. Electronic relaxation effects were considered and found to be small from a Hartree-Fock calculation on a cupric chloride model.

A restricted active space SCF study of the lifetime of the A3Π state of SH+

Restricted active space (RAS) SCF calculations have been performed on the potential curves for the X3Σ- and A3Π states of the SH+ ion and on the lifetime of the v′ = 0,1 vibrational levels of the A state. The convergence of the transition moment integral as a function of the size of the active orbital space was used to select the active orbitals. The calculated value of the v′ = 0 lifetime is 1·1 µs. An estimate of the errors remaining in the calculation leads to a final theoretical value of 1·07 ± 0·13 µs. Computed bond distances and bond energies are 1·367 (1·364) Å and 3·46 (3·70)eV, respectively, for the X state, and 1·502 (1·501) Å and 1·64 (1·78)eV, respectively, for the A state (experimental values within parentheses).

The electronic structure and second-order nonlinear optical properties of donor-acceptor acetylenes: a detailed investigation of structure-property relationships

A series of donor-acceptor acetylene compounds was synthesized in which systematic changes in both the conjugation length and the donor-acceptor strength were made. The effect of these structural changes on the spectroscopic and electronic properties of the molecules and, ultimately, on the measured second-order molecular hyperpolarizabilities (beta) was investigated. It was found that increases in the donor-acceptor strength resulted in increases in the magnitude of beta. For this class of molecules, the increase is dominated by the energy of the intramolecular charge-transfer transition, while factors such as the ground to excited-state dipole moment change and the transition-moment integral are much less important. Increasing the conjugation length from one to two acetylene linkers did not result in an increase in the value of beta; however, beta increased sharply in going from two acetylenes to three. This increase is attributed to the superposition of several nearly isoenergetic excited states.

A restricted active space (RAS) SCF study of the lifetime of theA 3? state of OH+

Restricted Active Space (RAS) SCF calculations have been performed of the potential curves for theX3Σ− andA3Π states of the OH+ ion and on the lifetime of thev=0−2 vibrational levels of theA state. The convergence of the transition moment integral as a function of the size of the active orbital space was used to select the active orbitals. The calculated value of thev=0 lifetime is 2.4 µs. An estimate of the errors remaining in the calculation leads to a final theoretical value of 2.7±0.1 µs. Computed bond distances and bond energies are 1.031 (1.029) A and 5.05 (5.01) eV, respectively, for theX state, and 1.137 (1.135) A and 1.57 eV, respectively, for theA state (experimental values within parenthesis).

Control and diagnostics of reactive plasma by photochemical and photoionization techniques

Abstract

A method for the calculation of transition moments between electronic states of molecules using a different one‐electron basis set for each state

AbstractA state‐specific approach to the calculation of transition moments between molecular electronic states requires that the wavefunction for each state is expanded in its optimum one‐electron basis and that nonorthonormal basis techniques are used for the calculation of the transition moment integrals. A method has been developed for carrying out such nonorthonormal basis calculations, based on the corresponding orbitals transformation and appropriately defined density matrices, which may be used with configuration interaction (CI) wavefunctions. Further improvements of the method have resulted in a decrease in the time required for the calculations and thus allow its application with moderately large CI expansions for each state. Nonorthonormal basis calculations on transition moments in H2O have been carried out using the above method. The results are in agreement with those of large MRD‐CI calculations.

Infrared band intensities: a comparative study of the transition moment matrix elements for the fundamental and overtones: Part II . Application to CO, HCl and OH

The various expressions considered in Part I for the transition moment matrix elements of fundamental and first two overtones are applied to carbon monoxide. The coefficients a ij in the expressions R io = Σ a ij p j (where R io is the transition moment integral for the O → i vibrational transition and p j is the dipole moment derivative ∂ j P /∂XXX j , XXX = ( r — r e)/ r e, r e is equilibrium bond distance) are reported for i, j = 1, 2, 3. It is found that these coefficients do not vary by more than 5% when compared for the same i, j values in various expressions irrespective of the most exhaustive treatments used in deriving the original expressions. On the basis of the values of the coefficients obtained for CO, generalisations have been suggested on the effects of inclusion of mechanical and electrical anharmonicity to the intensities of fundamental and first two overtones. It is generally observed that the contribution of p' 1, is about 100 fold more than the contribution of p' 2, for R 10. On the other hand the contributions of p' 1, and p, for R 20 and R 30 are of nearly equal magnitude but opposite in sign. The contribution of p' 1 to R 10 is much higher than its contribution to R 20 and R 20. The various observations lead us to conclude that, whereas the effect of inclusion of mechanical anharmonicity on the intensity of the fundamental band is negligible, this effect is almost comparable to the effect of inclusion of electrical anharmonicity for the first two overtones. Simple forms of the a ij expressions are applied to HC1 and OH to demonstrate the effect of variation of molecular constants on the a ij values. On the basis of the observed trend in the values of these coefficients for CO, HCl and OH general remarks on the effects of hydrogen bonding on IR band intensities are given.

Electrical anharmonicity for the OH stretching vibration of methanol and its hydrogen bonded complexes

We have calculated the first and second dipole moment derivatives for a number of hydrogen bonded systems involving methanol and a variety of organic bases. Herman and Shuler's [1] expressions for the intensities of fundamental and first overtone are employed for the calculations. Both ++ and +− combinations of experimental values of transition moment integrals R 1 0 and R 2 0 are considered. Given below are the typical values of μ 1 and μ 2 for the two sign combinations in the case of dilute solutions of CH 3OH in CCl 4 representing free OH and CD 3OH in DMSO-d 6 as well as self associated CD 3OH in CD 3OD. It is found that for all the systems considered both for ++ and +− combinations μ 1 as well as μ 2 increase on hydrogen bonding. Often a reference is made in the literature that the intensity of the first overtone band of XH stretching vibration decreases on hydrogen bonding whereas that of the fundamental increases. On the basis of these observations a decrease in the overtone intensity Methanol in ++ comb. +−comb. μ 1 × 10 20 μ 2 × 10 20 μ 1 × 10 20 μ 2 × 10 21 CCl 4 4.567 1.017 4.770 8.094 DMSO-d 6 20.443 1.641 20.750 3.943 CD 3OD 23.545 2.033 23.952 4.936 can be explained on the basis of the fact that the negative contribution to the overtone intensity from an increase in the first derivative of the dipole moment supersedes the positive contribution from the increase in the second derivative of the dipole moment. This explanation is quite justified as it can be noticed from the above values that whereas μ 1 increases about 4 to 5 times on hydrogen bonding in the cases considered in these studies, μ 2 only increases by 50 to 10%. This observation is similar to the prediction made by Di Paolo, Bourderon and Sandorfy [2] on the basis of their theoretical model calculations on the influence of Electrical Anharmonicity on infrared intensities in hydrogen bonded systems. However, contrary to their predictions it is rather clear from these studies that the decreasing intensities of first overtones on hydrogen bonding can be explained by taking +− combinations as nicely as from ++ combinations of transition moment values.

Transition moment integrals and the hypervirial theorem. I

For pt. I see abstr. A41484 of 1972. Hypervirial theorems for the operator W=exp(itx) for one-dimensional systems described by potentials involving only positive powers of x have been shown to lead to a recurrence relation in the transition moment integrals Tn=(A,xnB) where A and B are eigenstates of the system in question. This recurrence relation is also directly derived from other hypervirial theorems. Transition moments calculated in this way compare favourably with those obtained by direct computation.

Theoretical Electronic Transition Probabilities in Diatomic Molecules. I. Hydrides

Hartree–Fock (HF) electronic transition moments calculated in both the position and momentum representations are presented as a function of the internuclear separation R for the BeH, MgH, OH, and SH (A–X) systems. The vibrational averages of these quantities are obtained and the results are used to calculate some absorption band oscillator strengths. For the OH (A–X) system several independent experimental determinations of the 0–0 band oscillator strength have been reported in the literature. Our theoretical value of 20.6 × 10−4 differs from experiment by a factor of 2.5. Active electron and virtual orbital approximations to the HF transition moment integrals are given. Consideration of the united and separated atom limits and the region of the equilibrium internuclear separation for the states involved leads to an abbreviated discussion of the effect of correlation on the HF transition moments. HF transition moment calculations at a single value of R are also reported for the BH+, AlH+, HF+, and HCl+ (A–X) systems.

π-SCF and INDO calculations and the absorption, polarized excitation and circular dichroism spectra of [4]-helicenes

The absorption and circular dichroism spectra of (-)d-1,12-dimethyl-benzo[c]phenanthrene-5-acetic acid are reported, together with the polarized excitation and fluorescence spectra of the parent hydrocarbon, [4]-helicene. The transition energies of 1,12-dimethyl-[4]-helicene calculated in the π-SCF approximation, and the corresponding dipole and rotational strengths obtained by the dipole-velocity method, show that the optical isomer studied has the M-configuration with the stereochemical form of a segment of a left-handed helix. Analogous calculations in the INDO approximation using both the dipole-velocity and the dipole-length procedure with separate consideration of the one-centre and the two-centre transition moment integrals, indicate that the more satisfactory dipole and rotational strengths are obtained in the two-centre dipole-velocity formulation. The appearance of σ → π* transitions at higher energies limits the application of the π-SCF procedure, but the INDO method is found to place these tra...

Computations for Two-center Transition Moments Concerning Slater Orbitals with Non-integer Principal Quantum Numbers

The precision of the parabolic interpolation technique which have been usually applied for the computations bf the two-center transition moment integrals with Slater Orbitals of non-integer effective principal quantum numbers is ascertained tolerable by comparing with the results of the McLaurin series expansion technique.

Electronic Transition Moment Integrals for First Ionization of CO and the A - X Transition in CO+. Some Limitations on the use of the r-Centroid Approximation.

Integrals necessary for the determination of transition moment matrix elements from experimental data have been evaluated numerically by use of vibrational wave functions derived from RKR potentials. A power series expansion for the electronic transition moment has been assumed. The significant quantities which can be related to an arbitrary center of expansion are vibrational overlap integrals and quantities of the form ʃψ v' r n ψ v″ dr. Experimental band intensities and relative populations for vibrational levels of the initial electronic state are needed to determine the expansion coefficients. Transition moment integrals have been calculated for first ionization from the ground electronic state of CO and for the A 2Π i - X 2Σ+ transition of CO+. Comparison of these integrals with previous calculations based on Morse functions has shown them to be rather sensitive to the wave-functions [potentials] used. Characteristics generally attributed to the r-centroid and related integrals are examined, and some limitations on the use of the r-centroid approximation are discussed, following a review of assumptions made in the use of that approximation.