A general multi-configuration Hartree-Fock program

The Coupling program, which is important not only for the Grasp2018 package but for the atom theory in general, is presented in this paper. This program is designed as a part of the Grasp2018 package. The Coupling performs the transformation of atomic state functions (ASFs) from a $LSJ$-coupled CSF basis into several other configuration state function (CSF) bases such as $jj$, $LK$, $JK$, $JJ$, and many others. It allows identification of the energy structure of practically any element in different coupling schemes and also allows selection of the most suitable one. In addition, examples of how to use the Coupling program are given in additional file Example_Calculation.pdf listed in source directory grasp2018/src/appl/Coupling/Sample_Runs.

Program Title: Coupling

Program Files doi: http://dx.doi.org/10.17632/7tv9n8g24w.1

Licensing provisions: MIT license

Programming language: Fortran 95.

External routines/libraries used: Grasp2018 modules: jj2lsj_data_1_C, jj2lsj_data_2_C, jj2lsj_data_3_C and Atsp2K module: sqlsf.f.

Nature of problem: The Coupling program is designed as a part of the Grasp2018 package for the computation of atomic state function transitions and for identification atomic properties in different coupling schemes.

Solution method: Spin-angular coupling transformation of multiconfiguration expansions obtained in $LS$ and $jj$ coupling schemes.

Additional comments including restrictions and unusual features: The transformations of the configuration state functions is supported for one, two, and three open shell structures including open $s$, $p$, $d$, and $f$-shells. For shells with $l>3$ (i.e. beyond the $f$-shells), however, a proper transformation of the antisymmetrized shell states can be carried out only for the case of one or two equivalent electrons. The $jj⟷LS$ transformation matrices, which are applied internally by the program, are consistent with the previously published definitions of the reduced coefficients of fractional parentage and $jj⟷LS$ transformation matrices. The transformation from $LSJ$-coupling to all main coupling schemes is performed by the program Coupling. The number and types of coupling schemes depend on the number of coupled shells in $LS$-coupling.

We develop a simple and effective method for solving the Schrödinger equation of a hydrogen atom in a constant magnetic field with arbitrary strength. Energies are obtained not only for the ground and low-lying states but also for highly excited states with precision from 12 up to 20 decimal digits. The calculations are performed for an entire range of magnetic field intensity up to $9.4\times 10^8$ Tesla, the strongest field ever observed. The strong point of the development of the method is the construction of an anharmonic oscillator model for a hydrogen atom in a constant magnetic field via the Kustaanheimo–Stiefel transformation. This model allows the use of purely algebraic calculations and the Feranchuk–Komarov (FK) operator method for effectively solving the Schrödinger equation. The advantages of the basis set in this work are also discussed to extend its application to other problems, such as multi-electron atoms in a constant magnetic field. We also provide a program written by FORTRAN for the solutions mentioned above.

Program Title: CHAMF

Program Files doi: http://dx.doi.org/10.17632/s5shscgfcj.1

Licensing provisions: BSD 3-clause

Programming language: FORTRAN77

Nature of problem: The Schrödinger equation for a hydrogen atom in a magnetic field is rewritten into that of a four-dimensional anharmonic oscillator by using the Kustaanheimo–Stiefel transformation. The later has a structure more convenient for applying the algebraic method based on annihilation and creation operators. Therefore, the FK operator method [1] can be applied for obtaining high-accuracy numerical solutions which means the obtained energies converge to a given precision (up to twenty decimal digits in this work). The method is developed for an entire range of magnetic field intensity up to $9.4\times 10^8$ Tesla and for not only ground state but also highly excited states.

Solution method: The FK operator method is modified and used for the high-accuracy numerical solutions. This method combines with the algebraic technique which is useful for calculating all the needed matrix elements. Thus, the Schrödinger equation becomes the symmetric generalized eigenvalue problem which can be solved by the subroutine dsygvx.f of the LAPACK library [2]. For the better accuracy with quadruple precision, we modify this subroutine and its dependence with using the real*16 number instead of the real*8. Moreover, a free parameter introduced by the FK operator method can be used for increasing the speed of convergence. The optimal choice of this free parameter is implemented in the program.

Additional comments including restrictions and unusual features: Operating system: Linux. RAM: at least 1 GByte per core. The gfortran compiler is recommended for this program. The running time is from a centisecond to a few minutes depending on the required precision. However, for the super-strong magnetic fields ($\gamma \ge 200$), the running time may reach to two hours for the precision of twelve decimal digits, and RAM is needed to be at least 60 GB.

[1] I. Feranchuk, A. Ivanov, Van-Hoang Le, A. Ulyanenkov, Non-perturbative Description of Quantum Systems, Springer, Switzerland, 2015. doi:10.1007/978-3-319-13006-4.

[2] Netlib.org. LAPACK: Linear Algebra PACKage, Subroutine dsygvx.f. URL http://www.netlib.org/lapack/lapack-3.1.1/html/dsygvx.f.html

Prescription drug abuse can lead to serious medical negligence, so there is an urgent need to address its screening problem. Gliclazide is widely used as an antihypertensive drug for lowering blood sugar, but its excessive intake can cause serious harm to human body. Here we take gliclazide as an example to provide a method to realize the screening of drug abuse. Flower-like silver nanoparticles were prepared as surface enhanced Raman scattering (SERS) substrate, which can quantitatively and accurately detect the concentration of gliclazide. To understanding the enhanced activity of flower-like silver substrates, the Finite-Difference Time-Domain (FDTD) simulation model was established, and the simulation results showed that flower-like silver had high SERS substrate activity as well as enhanced hot spots at the rough particle surface and the adjacent particles. The experimental results indicated that the flower-shaped silver had an excellent Raman enhancement effect using R6G as detection molecules. When the gliclazide solutions with different concentration gradients were tested, the molecular vibrational modes were also obtained using Gaussian calculations. The rapid and accurate detection of gliclazide concentration was processed by Principal Component Analysis, which were consistent with the experiment, suggesting the importance of the combination of experiment and calculation. Finally, SERS substrate test was performed on the daily medication gliclazide tablets (II), which proved that the flower-like silver still has great Raman enhancement effect on the detection of actual samples.

The adiabatic approximation in time-dependent density functional theory (TDDFT) yields reliable excitation spectra with great efficiency in many cases, but fundamentally fails for states of double-excitation character. We discuss how double-excitations are at the root of some of the most challenging problems for TDDFT today. We then present new results for (i) the calculation of autoionizing resonances in the helium atom, (ii) understanding the nature of the double excitations appearing in the quadratic response function, and (iii) retrieving double-excitations through a real-time semiclassical approach to correlation in a model quantum dot.