Diabatization Method Research Articles

Towards the ab initio determination of strictly diabatic states, study for (NaRb)+

A generalization of the effective metric approach is proposed and applied both for the calculation of radial couplings and for the determination of diabatic states along a single coordinate using the formalism of variational effective Hamiltonian theory. The application to the ionic molecule NaRb+ shows that strictly diabatic states are obtained even for very short distances where a huge number of crossings are observed. Polarization and electronic delocalization effects are estimated. A comparison with various diabatization methods is performed. The proposed method brings a significant improvement with respect to the existing ones.

Photodissociation of ozone in the Chappuis band. I. Electronic structure calculations

Potential-energy surfaces of the 1 1A′, 1 1A′′, and 2 1A′′ states of ozone and corresponding transition-dipole-moment surfaces have been computed as a function of the two bond distances and the bond angle. The calculations are based on the complete-active-space self-consistent field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) electronic-structure models. For the calculations of the A″1 surfaces, which exhibit a conical intersection, a diabatic representation has been constructed, employing a direct diabatization method implemented at the CASSCF level. The slow variation of the diabatic potentials and transition dipole moments with nuclear geometry allows us to perform the ab initio calculations on a widely spaced grid. The complete potential-energy and transition-dipole-moment surfaces are then efficiently obtained by interpolation. This procedure leads to very significant savings of computing time compared to the mapping of the rapidly varying potentials and derivative couplings in the conventional adiabatic representation. Diabatic potentials at the CASPT2 level have been obtained by applying the adiabatic-to-diabatic transformation constructed at the CASSCF level to the adiabatic CASPT2 potentials. The properties of the resulting adiabatic and diabatic A″1 potential-energy surfaces are discussed, with emphasis on the 1 1A′′–2 1A′′ conical intersection, which is of relevance for the photodissociation dynamics of ozone in the Chappuis band. The computation of the photoabsorption cross section and the comparison between theory and experiment are discussed in the accompanying paper.

Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case

A two-by-two diabatic propagation method is developed to deal with general one-dimensional multi-channel curve crossing problems. Each crossing is treated within the newly completed two-state semiclassical theory in the diabatic representation and is represented by a nonadiabatic transition matrix (I-matrix). A product of all the I-matrices yields the reduced scattering matrix for the entire system. This theory can handle the multi-channel curve crossing problems as simply as a two-state problem. An analysis of the complex crossing points in the momentum space can provide a comprehensive illustrative criterion of this method. A detailed severe numerical test is made by taking a seven-state system with 6 and 12 nonzero diabatic couplings. It is demonstrated that dominant processes among the state-to-state transitions are well reproduced by the present semiclassical theory.

Improvement of Spin-up of Precipitation Calculation with Use of Observed Rainfall in the Initialization Scheme

ABSTRACT A new approach is proposed for the initialization of the primitive equations model (hereafter, NWP model), taking account of the effect of non-adiabatic heating due to release of the latent heat into humidity and divergent wind fields. In the present paper, an operational model of the Japan Meteorological Agency (JMA), the Japanese Spectral Model (JSM) is taken up as the NWP model. For the purpose of the present study, rainfall amount is estimated, with a resolution of about 5-km mesh, from radar-AMeDAS composite precipitation data (hereafter, R-A data), where AMeDAS stands for the Automated Meteorological Data Acquisition System which is a network of automated surface observation stations including raingauge measurements. The observed rainfall is considered to represent the mesoscale precipitation field. The total heating rate calculated from the R-A data is assumed to be partitioned parabolically in the vertical between the lifting condensation level (LCL) and the cloud top (TBB CT) estimated by the GMS (Japanese geostationary meteorological satellite), where TBB means the black body temperature. The diabatic initialization method proposed here consists of two steps. The first step is a physical initialization of the water vapour field, where the relative humidity field is changed to be more moist over the area of rainfall (>1 mm hr−1). The moistening is performed in such a way that, if the air is not moist enough over the area of rainfall, the lapse rate at each model layer from the LCL to the TBB CT becomes a critical value presumably required by the moist convective adjustment scheme used in the NWP model concerned. On the other hand, over the area where no rainfall is observed, the relative humidity is left untouched. The second step is a nonlinear normal mode initialization (NNMI) which includes the non-adiabatic heating rate obtained from the R-A data among other factors. The first four vertical modes with the period less than 6 hours are adopted. It should be remarked that the divergent component of wind field which is necessary to continuously maintain the condensation due to mesoscale rainfall is also initialized at the stage of NNMI with the large-scale condensation and the moist convective adjustment. Improvement in the operational performance of the NWP model with the use of the proposed diabatic initialization method is demonstrated for a case study and statistical verification. The forecasts with and without the present diabatic initialization are compared. Particularly, amelioration of the spin-up of mesoscale precipitation calculation for the first 6 hours after the start is clearly seen. The initialization method shows stable execution and seems to be useful for the prediction of the mesoscale phenomena, particularly in the tropics where meteoroligical data are relatively sparse.

Periodic transonic flow without and with condensation in a 2-D plane channel

Steady 2-D adiabatic viscous flow and diabatic inviscid flow with energy supply by homogeneous condensation in a channel with a wavy wall have been numerically simulated. The methods used are an analytical-numerical combination procedure for the shock/boundary layer interaction and a diabatic finite volume method to solve the time dependent Euler equations, being linked with the classical nucleation theory and a droplet growth law. The influences of viscous effects and heat addition on the flow field with more than one local supersonic region as well as the choking state have been investigated. The aim is to achieve an adiabatic periodic flow field with imbedded shock waves and a diabatic periodical one including condensation and evaporation phenomena. In the case of adiabatic flow the calculated velocity distribution is compared with experimental and analytical results.

Evaluation of stability corrections in wind speed profiles over the North Sea

An improved meteorological method for estimating the wind speed profile over sea is developed. In the proposed “diabatic” method, the Monin-Obukhov similarity theory, which takes into account the stability of the planetary boundary layer, is applied. By choosing parameterization of several components, the over-sea profile parameters ( u ∗, θ ∗, q ∗, z 0 and L ) can be expressed in terms of routine weather data only (wind speed, sea water temperature and air temperature). With these parameters the wind speed as a function of height can be calculated. The diabatic method has been tested using a 4-month data-set consisting of wind speeds measured at heights of 18 and 70 m and temperatures of the air and the sea water. The mean wind speed measured at a height of 70 m over this period was 9.6 m s −1. Using the diabatic method the estimated mean wind speed at the same height was 9.3 m s −1, with an r.m.s. difference of 1.1 m s −1. The estimated mean wind speed using the logarithmic profile (only neutral stratification) was 8.7 m s −1 with an r.m.s. difference of 1.4 m s −1. This shows that the proposed diabatic method gives a better estimate of the mean wind speed than does the logarithmic method. The diabatic method also yields a more accurate estimate of the frequency distribution of the wind speed as characterized by the Weibull shape and scale parameters and of the average diurnal variation in the wind speed. If the two methods are applied to a 4-year period, it is found that the mean wind speed estimated by each method is almost the same. However, the diabatic method gives a much better simulation of the mean seasonal wind speed.

The diabatic surface method: A model for chemical reactivity

The diabatic surface model is formulated in terms of an effective hamiltonian which can be parametrized in terms of the coulomb and exchange intergrals of Heitler-London Valence Bond Theory. The synchronous and asynchronous concerted pathways for the 2 s + 2 s cycloaddition of two ethylene molecules are used as a numerical example to illustrate the utility of the method.

Scanning calorimetry with adiabatic or controlled diabatic surroundings

Controlled diabatic (non-adiabatic) scanning calorimetry as a counterpart to the adiabatic method is described in this article. It is shown that two main advantages result from this technique: a) cooling experiments without lack of accuracy in comparison to heating runs can be performed and b) accurate and most reliable c p -values result from this method because influences of changing calorimetric surroundings are compensated by a selfcontrolling system. Examples of c p -curves are given in order to elucidate the adiabatic and diabatic method as well.

Use of molecular properties in the one‐dimensional model of nonadiabatic transitions

AbstractA systematic analysis of a diabatization method proposed in a recent publication is presented for the one‐dimensional linear model of nonadiabatic transitions, and the method is extended to the exponential model. The asymptotic behavior of molecular properties is studied, and the usefulness of simple properties like the kinetic energy and multipole moments is examined in detail. The method is easy to use, and provides a reliable a posteriori procedure to deal with the existence of strong radial couplings between adiabatic states, when a program to calculate the radial couplings exactly is not available.

Nutrient Loading of Southern Lake Michigan by Dry Deposition of Atmospheric Aerosol

Aerosol samples and micrometeorological data were collected at 87°00’W 42°00’N in the mid southern Lake Michigan basin from May through September, 1977, to determine total phosphorus and nitrate-nitrite nitrogen particulate (TP + N) loadings. Hi-volume samplers with cellulose fiber filters and a meterological data collection system were operated on board the USEPA's R/V Roger R. Simons. A diabatic drag coefficient method was used to estimate aerosol deposition velocity (V d), which had a mean value of 0.65 cm/s. TP + N concentration and V d were determined for 42 distinct sampling periods of at least three to four hours each. A climatological data base was used to compute weighted average loading rates for TP + N. Dry deposition loading for the southern basin was found to be 0.15 to 0.18 × 10 6 kg/year for P; N loading was 3.5 to 5.1 × 10 6 kg/year. TP + N inputs via dry deposition account for 15% or more of all atmospheric nutrient inputs, and are significant nutrient sources to midlake waters.

Trace element loading of southern Lake Michigan by dry deposition of atmospheric aerosol

Aerosol samples and meteorological data were collected at a mid-southern Lake Michigan site (87° 00′ W, 42° 00′ N) from May through September 1977. Hi-volume samplers with cellulose fiber filters and a digital meteorological data recording system were operated on board the U.S. EPA's R/VRoger R. Simons during four intensive sampling periods. Aerosol samples were analyzed by atomic absorption spectroscopy for seventeen trace elements. A diabatic drag coefficient method was used to determine aerosol deposition velocity (vd) overlake. A meanvd of 0.5 cm s−1 was found for the 0.1<diameter<2.0 μm aerosol. By relating the observed trace element concentrations andvd to a long-term climatological record, annual dry deposition loadings to the southern basin for nine elements were estimated. For four elements, Fe, Mn, Pb, and Zn, dry deposition loadings to the southern basin alone of at least 500, 30, 250, and 100 (×103 kg yr−1) were found. For Fe and Mn, these loadings represent about 15% of the total of all inputs to Lake Michigan. for Zn and Pb, about one-third to one-half of the annual loading from all sources is from dry deposition of atmospheric aerosol.