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* doc : update for VdW correction * doc : fix bug in index.rst * doc : add another layer in example/vdw * doc : add link for vdw example * doc : add part for XC functionals * docs : update deeph and out_mat_XX * docs : update session for converging SCF * docs : update part on structure optimization * docs : update pp_orb * docs : add examples * docs : update typo * docs : update interface list(only 1 layer) Co-authored-by: wenfei-li <liwenfei@gmail.com>
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| # Geometry Optimization | ||
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| ## Methods | ||
| ### BFGS | ||
| ### CG | ||
| By setting `calculation` to be `relax` or `cell-relax`, ABACUS supports structural relaxation and variable-cell relaxation. | ||
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| ## Constrained Optimization | ||
| Current implementation of variable-cell relaxation in ABACUS now follows a nested procedure: fixed cell structural relaxation will be performed, followed by an update of the cell parameters, and the process is repeated until convergence is achieved. | ||
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| An example of the variable cell relaxation can be found in our [repository](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/relax/pw_al), which is provided with the reference output file log.ref. Note that in log.ref, each ionic step is labelled in the following manner: | ||
| ``` | ||
| ------------------------------------------- | ||
| RELAX CELL : 3 | ||
| RELAX IONS : 1 (in total: 15) | ||
| ------------------------------------------- | ||
| ``` | ||
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| indicating that this is the first ionic step of the 3rd cell configuration, and it is the 15-th ionic step in total. | ||
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| ## Optimization Algorithms | ||
| In the nested procedure mentioned above, we used CG method to perform cell relaxation, while offering four different algorithms for doing fixed-cell structural relaxation: BFGS, SD(steepest descent), CG(conjugate gradient), as well as a mixed CG-BFGS method. The optimziation algorithm can be selected using keyword [relax_method](./input_files/input-main.md#relaxmethod). We also provide a [list of keywords](./input_files/input-main.md#geometry-relaxation) for controlling the relaxation process. | ||
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| ### BFGS method | ||
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| The [BFGS method](https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm) is a quasi-Newton method for solving nonlinear optimization problem. It belongs to the class of quasi-Newton method where the Hessian matrix is approximated during the optimization process. If the initial point is not far from the extrema, BFGS tends to work better than gradient-based methods. | ||
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| In ABACUS, we implemented the BFGS method for doing fixed-cell structural relaxation. | ||
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| ### SD method | ||
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| The [SD (steepest descent) method](https://en.wikipedia.org/wiki/Gradient_descent) is one of the simplest first-order optimization methods, where in each step the motion is along the direction of the gradient, where the function descents the fastest. | ||
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| In practice, SD method may take many iterations to converge, and is generally not used. | ||
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| ### CG method | ||
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| The [CG (conjugate gradient) method](https://en.wikipedia.org/wiki/Conjugate_gradient_method) is one of the most widely used methods for solving optimization problems. | ||
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| In ABACUS, we implemented the CG method for doing fixed-cell structural relaxation as well as the optimization of cell parameters. | ||
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| ## Constrained Optimization | ||
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| Apart from conventional optimization where all degrees of freedom are allowed to move, we also offer the option of doing constrained optimization in ABACUS. | ||
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| ### Fixing Atomic Positions | ||
| Users may note that in the above-mentioned [example](), the atomic positions in STRU file are given along with three integers: | ||
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| ``` | ||
| Al | ||
| 0.0 | ||
| 4 | ||
| 0.00 0.00 0.00 1 1 1 | ||
| 0.53 0.50 0.00 1 1 1 | ||
| 0.50 0.00 0.52 1 1 1 | ||
| 0.00 0.50 0.50 1 1 1 | ||
| ``` | ||
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| For relaxation calculations, the three integers denote whether the corresponding degree of freedom is allowed to move. For example, if we replace the STRU file by: | ||
| ``` | ||
| Al | ||
| 0.0 | ||
| 4 | ||
| 0.00 0.00 0.00 1 1 0 | ||
| 0.53 0.50 0.00 1 1 1 | ||
| 0.50 0.00 0.52 1 1 1 | ||
| 0.00 0.50 0.50 1 1 1 | ||
| ``` | ||
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| then the first Al atom will not be allowed to move in z direction. | ||
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| Fixing atomic position is sometimes helpful during relaxation of isolated molecule/cluster, to prevent the system from drifting in space. | ||
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| ### Fixing Cell Parameters | ||
| Sometimes we want to do variable-cell relaxation with some of the cell degrees of freedom fixed. This is achieved by the [fixed_axes](./input_files/input-main.md#fixedaxes) keyword. We offer the options of fixing certain axis(axes), or fixing the volume. |
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| # Basis set and Pseudopotentials | ||
| # Basis Set and Pseudopotentials | ||
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| ## Basis Set | ||
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| ABACUS supports both pw and lcao XXXXX | ||
| ABACUS supports both PW and LCAO basis set, controlled by keyword [basis_type](./input_files/input-main.md#basistype) in INPUT file. | ||
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| ## Generating atomic orbital bases | ||
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| In ABACUS, the atomic orbital bases are generated using a scheme developed in the [paper](https://iopscience.iop.org/article/10.1088/0953-8984/22/44/445501). We provide a script named “generate_orbital.sh” under the directory tools/ to generate the atomic orbitals bases. In order to run this script, an ORBITAL_INPUT file is required. | ||
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| An example of this ORBITAL_INPUT file can be found in $ABACUS/tools/SIAB/SimulatedAnnealing/example_N: | ||
| ``` | ||
| #1.exe_dir | ||
| #---------------------------------------------------------------------------- | ||
| EXE_pw bin/ABACUS.fp_mpi.x | ||
| EXE_orbital bin/SIA_s.exe | ||
| #---------------------------------------------------------------------------- | ||
| #( In this part, the direction of the two used exe is provided ) | ||
| #2.electronic calculatation | ||
| #---------------------------------------------------------------------------- | ||
| targets 07_N # element | ||
| ref_bands 5 # reference bands | ||
| nbands 8 # num of bands for calculate ( > reference bands) | ||
| Ecut 50 # cutoff energy (in Ry) | ||
| Rcut 6 # cutoff radius (in a.u.) | ||
| Pseudo_dir ./ | ||
| Pseudo N.LDA.UPF | ||
| smearing_sigma 0.01 # energy range for gauss smearing (in Ry) | ||
| #---------------------------------------------------------------------------- | ||
| #( In this part , some parameters of calculating are given ) | ||
| #3.structure information | ||
| #---------------------------------------------------------------------------- | ||
| Dis 1.0 1.1 1.5 2.0 3.0 | ||
| #---------------------------------------------------------------------------- | ||
| #( In this part , it gives us the bond length of the reference system( in | ||
| #angstrom) ) | ||
| #4.orbital calculatation | ||
| #---------------------------------------------------------------------------- | ||
| maxL 2 # the max angular momentum (L<=2) | ||
| Level 2 # num of levels to generate orbitals(<=5) | ||
| #(num) (the max ang) (num of S) (num of P) (num of D) | ||
| level1 1 1 1 | ||
| level2 2 1 1 1 | ||
| #---------------------------------------------------------------------------- | ||
| #( In this part, some information of orbital is given ) | ||
| #5.Metropolis parameters (in most cases do not need to change) | ||
| #---------------------------------------------------------------------------- | ||
| Start_tem_S 1.0e-4 # start temperature for optimize Spillage(default 1.0e-4) | ||
| Start_tem_K 1.0e-2 # start temperature for optimize Kinetic (default 1.0e-2) | ||
| Step_S 20 # num of steps for optimize Spillage (default 20) | ||
| Step_K 15 # num of steps for optimize Kinetic (default 15) | ||
| Delta_kappa 0.01 # delta kappa (default 0.01) | ||
| #---------------------------------------------------------------------------- | ||
| #(In this part, some parameters of Metropolis is given. In most cases, they | ||
| #do not need to be changed , only when you run into a situation , that the | ||
| #Kinnetic energy is larger than the maximum value allowed , you can enlarge | ||
| #the start temperature appropritely, or you can enlarge the delta_kappa, e.g. | ||
| #start_tem_k 1.0e-2 to 5.0e-1, delta_kappa 0.01 to 0.02. more steps can make | ||
| #the orbitals better , too) | ||
| ``` | ||
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| The ORBITAL_INPUT file contains 5 parts : | ||
| 1. exe_dir | ||
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| The paths of two executable files: | ||
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| - EXE_pw: executable file of ABACUS | ||
| - EXE_orbital: executable file of orbital generation | ||
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| We can get the exe file of orbital generation as below: | ||
| ``` | ||
| cd tools/SIAB/1_Source/ | ||
| make s | ||
| ``` | ||
| 2. electronic calculation | ||
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| Parameters for electronic calculations: | ||
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| - targets | ||
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| the element type of which orbitals are to be generated. Its value has form of ‘element.id_element’, for example 07_N. | ||
| - ref_bands | ||
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| the number of reference bands for orbital generation. We usually take the number of occupied bands of the system. For the N element, we take its “dimers” as the reference systems, so the number of ref_bands should be 5 (valence electrons of this element)\*2(number of the atoms of the system)/2 (1 band contain 2 electrons)=5. While for Na element, we take trimer as reference systems, and the number of the ref_bands should be 1\*3/2=1.5 for 1.5 is not a integer, here we use 2 for its ref_bands. Most elements use dimer as reference systems, except for Li, Na, K, Ca, which use trimer instead. | ||
| - nbands | ||
| The default value of basis_type is pw. The size of pw basis set is controlled by imposing an upper bound for the [kinetic energy cutoff](./input_files/input-main.md#ecutwfc) of the plane wave. | ||
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| the number of bands to be calculated in electronic calculation. Here, we use the gaussian smearing for the electronic structure calculation, so the value of this parameter can not be smaller than the value of ref_bands | ||
| - Ecut | ||
| When choosing lcao basis set, users need to prepare a set of atomic orbitals. Such files may be downloaded from the [official website](http://abacus.ustc.edu.cn/pseudo/list.htm). For more information, also check the `NUMERICAL_ORBITAL` section in the specification of the [STRU file](./input_files/stru.md). | ||
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| the Energy cutoff (in Ry) | ||
| - Rcut | ||
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| the radius cutoff of atomic orbital (in a.u) | ||
| - Pseudo_dir | ||
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| the path to the directory where the pseudopotential file is. | ||
| - Pseudo | ||
| ## Generating atomic orbital bases | ||
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| the file name of pseudopotential | ||
| - smearing_sigma | ||
| Users may also choose to generate their own atomic obitals. In ABACUS, the atomic orbital bases are generated using a scheme developed in the [paper](https://iopscience.iop.org/article/10.1088/0953-8984/22/44/445501). A detailed description of the procedure for generating orbitals will be provided later. | ||
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| the gaussian smearing (in Ry) for scf calculations. The default vaule is 0.01. In case that the scf iterations don’t converage (which could happen, e.g., for transition metal dimers), the user may increase this parameter, say, to 0.05. | ||
| 3. structure information | ||
| ## BSSE Correction | ||
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| This part gives the bond lengths of the reference systems (dimer or trimer). Generally, the bond lengths are chosen to distribute on both sides of the equilibrium value. For example, for N dimer we use (in Å): | ||
| - Dis 1.0 1.1 1.5 2.0 3.0 | ||
| For treating BSSE(Basis Set Superposition Error), we allow for the inclusion of "empty" or "ghost" atoms in the calculation. Namely, when expanding the Hamiltonian, basis sets on the atoms are used, while the ionic potentials on those atoms are not included when constructing the Hamiltonian. | ||
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| It means we take 5 reference systems (dimer), and the bond lengths are 1.0 1.1 1.5 2.0 3.0 angstrom, respectively. Every element has reference systems with different bond lengths, which could be found in file $ABACUS/tools/SIAB/DIS.txt. | ||
| 4. orbital generation | ||
| An empty atom is defined in the `STRU` file when an element name contains the "empty" suffix, such as "H_empty", "O_empty" and so on. Here we provide an [example]() of calculating the molecular formation energy of $H_2O$ with BSSE correction. | ||
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| The main parameters for orbital generation | ||
| In the example, we provide four STRU files: | ||
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| - maxL | ||
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| the max angular momentum for orbitals to be generated | ||
| - level | ||
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| number of levels to generate orbitals. In the main part of this section, level1, level2... provide the information of each layer, the max angular momentum and the number of s, p, d orbitals. | ||
| - STRU_0 : used along with ntype = 2;normal calculation of water molecule ($E(\text{H}_2\text{O})$) | ||
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| For example, if we want to use 2 steps to generate DZP basis for N, we can set this part like this: | ||
| ``` | ||
| maxL 2 # the max angular momentum (L<=2) | ||
| level 2 # num of levels to generate orbitals(<=5) | ||
| (num) (the max ang) (num of S) (num of P) (num of D) | ||
| level1 1 1 1 | ||
| level2 2 1 1 1 | ||
| ``` | ||
| Because of the property of symmetry, taking dimer or trimer as reference systems can not generate the f orbitals very well. And test results show that f orbital has little effect on improving the results. It means we generate one s orbital and one p orbital in first step (level1), and generate one s, p, d orbital in the second step (level2). | ||
| 5. Metropolis parameters | ||
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| The main parameters for Metropolis optimization. | ||
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| - Start_tem_S | ||
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| start temperature for spillage optimization | ||
| - Start_tem_K | ||
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| start temperature for kinetic energy optimization | ||
| - Step_S | ||
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| number of steps for spillage optimization | ||
| - Step_K | ||
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| number of steps for kinetic energy optimization | ||
| - Delta_kappa | ||
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| the accept rise of spillage when optimizing the kinetic energy | ||
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| After preparing the ORBITAL_INPUT file, one just needs to run the script "$PATH_TO/generate_orbital.sh ORBITAL_INPUT" and wait for the results. The results will be written into several output files under the directory $element.id_element/$Rcut/, for example 07_N/6/. | ||
| obtained total energy of -466.4838149140513 eV | ||
| - STRU_1 : used along with ntype = 2;calculation of single O atom ($E_O$) | ||
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| obtained total energy of -427.9084406198214 eV | ||
| - STRU_2 : used along with ntype = 3;calculation of 1st H atom ($E_{H1}$) | ||
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| obtained total energy of -12.59853381731160 eV | ||
| - STRU_3 : used along with ntype = 3;calculation of 2nd H atom ($E_{H2}$) | ||
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| Some output files listed here are useful. | ||
| - ORBITAL_RESULTS.txt | ||
| obtained total energy of -12.59853378720844 eV | ||
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| this file shows some important information of the orbital, we can see the spillage of the orbital to judge whether the orbital is good enough for us to use. | ||
| - running_1.txt | ||
| the details of generating orbitals | ||
| - ORBITAL_PLOTU.dat | ||
| you can open it by using any drawing softwares to visualize the shape of the orbital | ||
| - ORBITAL_7U.dat | ||
| the general type is ORBITAL_($element.id)U.dat . This is the orbital file we will use in the calculation. And you can rename it as anything you want. We usually use the covention “element_xc_rcut_ecut_XsY pZd”, e.g., N_lda_6.0au_50Ry_2s2p1d, which tells the key parameters for the basis set construction. | ||
| > Note : Remember to adjust the parameter `ntype` in INPUT file | ||
| For some elements, you can download the reference ORBITAL_INPUT files and pseudopotentials from our [website](http://abacus.ustc.edu.cn/pseudo.html). | ||
| Thus, the formation energy is given by: | ||
| $$ | ||
| \Delta E(\text{H}_2\text{O}) = E(\text{H}_2\text{O}) - E(\text{O}) - E(\text{H}^1) - E(\text{H}^2) \approx -13.38 eV | ||
| $$ | ||
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| A file README is also given and you can decide the parameters with it as a reference. | ||
| In most cases, you just need to modify the parameters in Section 1, 2. Section 4 may be | ||
| partially modified if you need higher precision orbitals. The users are not encouraged to change | ||
| the settings in sections 5, unless you are very familiar with the code generating algorithms. | ||
| ## Pseudopotentials | ||
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| ## BSSE | ||
| In ABACUS, we only supports norm-conserving pseudopotentials. We support four different formats of the pseudopotential files: UPF, UPF2, VWR, and BLPS. For more information, check the `ATOMIC_SPECIES` section in the specification of the [STRU file](./input_files/stru.md). | ||
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| ## Pseudopotentials | ||
| Here we list some common sources of the pseudopotential files: | ||
| 1. [Quantum ESPRESSO](http://www.quantum-espresso.org/pseudopotentials/). | ||
| 2. [SG15-ONCV](http://quantum-simulation.org/potentials/sg15_oncv/upf/). | ||
| 3. [DOJO](http://www.pseudo-dojo.org/). |
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