Douglas gradient

Malkin, L, Malkina, O.L. and Malkin, V.G. (2002) Relativistic calculations of electric field gradients using the Douglas—Kroll method. Chemical Physics Letters, 361, 231-236. 

Bioinorganic systems often contain heavy elements that need to be treated with an explicit relativistic method. It is now possible to carry out an explicit relativistic electronic structure calculation on the fly (152). The scalar-relativistic Douglas - Kroll - Hess method was implemented by us recently in the BOMD simulation framework (152). To use the relativistic densities in a non-relativistic gradient calculations turned out to be a valid approximation of relativistic gradients. An excellent agreement between optimized structures and geometries obtained from numerical gradients was observed with an error smaller than 0.02 pm. 

Smith, A.M.O. and Gamberoni, N. (1956). Transition, pressure gradient and stability theory. Douglas Aircraft Kept. No. ES-26338. 

Slower-growing Douglas fir in the Pacific Northwest has an advantage compared to most pines in that it displays a more rapid improvement in MFA up the stem, i.e. the juvenile-corewood zone appears to be no more than two metres tall and the radial extent of very low stiffness is reduced. Further up the stem the corewood-outerwood gradient in MFA is similar to that found in pines. 

Heavy fuel deposits were expected in boiling systems, and therefore the initial studies of deposition and activity transport for power reactors concentrated on the CANDU-BLW concept until the fields at Douglas Point became a concern. The deposit thickness was proportional to iron concentration in the coolant and to the square of the heat flux (69) deposition was reversible and quickly reached a steady value set by the local conditions. The corrosion products initially deposit by hydrodynamic and electrostatic effects then boiling accelerates deposition by drawing water and its contained iron into the deposit to replace the steam that leaves. Local alkalinity gradients within the deposit determine whether iron crystallizes to cement the deposit or dissolves to weaken it, and erosion processes then define the equilibrium thickness (70), This model works well in explaining deposition under boiling conditions. 

F. Neese, A. Wolf, T. Fleig, M. Reiher, B. A. Hess. Calculation of electric-field gradients based on higher-order generalized Douglas-KroU transformations. /. Chem. Phys., 122 (2005) 204107. 

V. A. Nasluzov, N. Rosch. Density functional based structure optimization for molecules containing heavy elements analytical energy gradients for the Douglas-KroU-Hess scalar relativistic approach to the LCGTO-DF method. Chem. Phys., 210 (1996) 413 25. 

M. Pempointner, M. Seth, P. Schwerdt-feger. A point-charge model for the nuclear quadrupole moment Coupled-cluster, Dirac-Fock, Douglas-KroU, and nonrelativistic Hartree-Eock calculations for the Cu and F electric field gradients in CuF. /. Chem. Phys., 108(16) (1998) 6722-6738. 

Douglas-Kroll Energy and Gradients in NWChem Estimating Scalar Relativistic Effects Using Douglas-Kroll Contracted Basis Sets. 

Mastalerz R, Barone G, Lindh R and Reiher M 2007 Analytic high-order douglas-kroU-hess electric field gradients. J. Chem. Phys. 127(7), 074105. 

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