Larkin method

Electro chemists first investigated the Saul yev method in 1988 and 1989 [381,382], including GEM, and the incorporation of implicit boundary values was added later [144]. The result of these studies is broadly that the last of Larkin s options above, averaging LR and RL, is the best. This has about the same accuracy as Crank-Nicolson, and could be considered to be easier to program. The third option, alternating LR with RL, produces oscillations. 

X-ray emission rates in simple molecules have been extensively studied by Larkins and his group [10,11]. Larkins and Rowlands [12] made the MO calculations with the complete-neglect-of-differential-overlap (CNDO/2) method and pointed out that there are significant contributions of interatomic transitions to the C K x-ray emission rates in CO, HCN, and CO2 molecules, but relative intensities are less sensitive to inclusion of crossover transitions. Applying the ab initio MO method to CO, they also examined [13] various factors influencing the molecular x-ray emission rate, such as choice of basis set, choice of length and velocity forms, electronic relaxation effect, and interatomic contributions. Phillips and Larkins extended their calculations to other simple molecules [14,15]. 

In the calculations of x-ray emission rates in molecules with the DV-Xq method, we have used various approximations and numerical techniques. We examine several factors which influence the theoretical calculations of molecular x-ray emission rates, i.e. the accuracy of the DV integration, the electronic relaxation effect, and the contributions from the interatomic transitions. The examination of other factors, such as the choice of dipole operators, basis-set dependence, and the vibrational eflfect, has been reported by Larkins [10,11] with the ab initio method. 

Recently, Larkin et al. (2000) have encountered (in a study of the spin-ladder system Sr(Cui xZnj )203, which falls outside this review, but see sect. 8.3.4) muon spin relaxation functions with too shallow and too broad minima of polarization to be reproduced by Kubo-Toyabe functions. Again, longitudinal field data showed the spin system to be static. These authors used an approach (called Kubo golden rule, KGR), which was originally derived by Kubo (see Kubo 1981 and Yamazaki 1997) to describe their findings. For details we refer to the original papers. The KGR method allows the calculation of the muon spin relaxation function for arbitrary field distributions (if they can be described by arithmetic function). In the spin-ladder compound an exponential field distribution reproduced the data. The approach of Noakes and Kalvius (1997) can be reproduced using KGR. 

Hamaker, B. R., A. A. Mohamed, J. E. Habben, C. P. Huang, and B. A. Larkins. 1995. Efficient procedures for extracting maize and sorghum kernel proteins reveals higher prolamin contents than the conventional method. Cereal Chemistry 72 583-588. 

Calculations by the renormalization group method in the tricritical point vicinity (Larkin and Khmel nilski, 1969 Riedel and Wegner, 1972) have led to values of the tricritical indices, coinciding with those in the meam field approximation for 3D space d = 3. 

If the parameters Aij, aij and Eij are all known, the initial concentrations and a temperature profile are given, the rate equations would predict the behaviour of the reaction. For very large systems a program LARKIN that integrates the, in general stiff, system of equations [27]. The initial value problems may be solved by routines like METANl [29] or SODEX [30, 31]. Both methods are based on a semi-implicit midpoint rule. 

Brightman AO. Barr R. Crane FL. Morre DJ (1988) Plant Physiol 86 1264 Barr R. Crane FL (1988) Plant Physiol 88 suppl 79 Marre E. Lado P. Ferroni A. Ballarin-Denti A (1974) Plant Sci Lett 2 257 Parsons A. Blackford S. Sanders D (1989) Planta 178 215 Miller CO (1963) Mod Methods Plant Anal 6 194 32. Horgan R (1987) In Hoad G V. Lenton JR. Jackson MB, Atkin RK (eds) Hormone action in plant development — a critical appraisal. Butterworth, London, p 119 Larkin PJ, Scowcroft WR (1981) Theor Appl Genet 60 197 Connett RJA. Hanke DE (1987) Planta 170 161 Sekar MC, Hokin LE (1986) J Membr Biol 89 193... 

Clarke, F. J. J., and Larkin, J. A. (1985). Emissivity determined from hemispherical reflectance and transmittance throughout the thermal infrared spectrum. High Temperatures-High Pressures 17, 89. Description of new method of mid-IR diffuse measurements leading to mid-IR diffuse standards. 

The low-pressure static method has been developed to a high degree of sophistication by the NPL Division of Chemical Standards group [Pemberton (11) Larkin and Pemberton ( 7) ]. In their work on the ethanol-water system between 30(°C) and 90(°C), they claim an accuracy in measured vapor pressures of +0.02% or +2.6(Pa),... 

Woodcock HL, Miller BT, Hodoscek M, Okur A, Larkin JD, Pond JW, Brooks BR (2011) MSCALE a general utility for multiscale modeling. J Chem Theory Comput 7 1208-1219 Chung LW, Hirao H, Li X, Morokuma K (2012) The ONIOM method its foundation and applications to metalloenzymes and phombiology. Wiley Interdiscip Rev Comput Mol Sci 2 327-350... 

T. N. Chiesl, R. E. Forster, B. E, Root, M. Larkin, and A. E. Barron. Stochastic single-molecule videomicroscopy methods to measure electrophoretic DNA migration modalities in polymer solutions above and below entanglement. Anal. Chem., 79 (2007), 7740-7747. 

Bearpark MJ, Larkin SM, Vreven T (2008) Searching for conical intersections of potential energy surfaces with the ONIOM method application to previtamin D. J Phys Chem A 112 7286-7295... 

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