CASINO manual - Theory of Condensed Matter

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to prevent this file getting too large). The vmc.hist file contains all the raw VMC data, which should be subjected to a statistical analysis. Note that the data in here is averaged over processors, so in the example above vmc.hist will contain 8334 lines, and each line contains energy data averaged over 12 cores. The error bar in VMC and DMC energies is affected by serial correlation (caused by the sampling points not being truly independent of each other). There are two ways of removing this. One is the correlation-time method—see Sec. 24.2—which is automatically used by the ve utility (for VMC data only) using the data in the main output file. The other is the reblocking method (see Sec. 24.1). Reblocking is done to a limited extent 3 by casino ‘on-the-fly’ and the reblocked error bar is printed at the end of the output file. It may also be performed by using the reblock utility to analyse the data in vmc.hist or the equivalent DMC file dmc.hist. (The utility also applies the correlation-time method to give a second measure of the effect of serial correlation and of course both methods should agree.) Under normal circumstances, however, it is not necessary to post-process the data since the on-the-fly reblocking and the reblock utility should give the same answers. Circumstances where you might want to do this include VMC runs which have been ‘continued’ from a previous run, explicit statistical studies of QMC, and the accumulation of ill-behaved expectation values like forces. Or indeed when learning how the reblocking method works. So let’s see how the reblocking method works. Type reblock in the directory containing the vmc.hist file. It will first ask you what units you want. Then it will print out a reblocking analysis (see Sec. 24.1): it will calculate an estimate of the standard error in the mean energy as a function of the length of blocks into which the data are gathered. The error bar will generally be too small for low values of the block length, and then should go up to a roughly constant value for larger block lengths. For very large block lengths the estimated error bar will oscillate as the error bar on the error bar becomes large. The constant value in the middle is the accurate error bar you want. Note that, in general, VMC calculations will reach this plateau more quickly than DMC calculations since they use a much larger time step and there is therefore less serial correlation in the data. In fact, for many VMC calculations, the standard error in the mean energy reaches its plateau at a block length of 1, so that one does not see the standard error rising significantly as the block length is increased. A file called reblock.plot is normally produced as part of the output of the reblock procedure. If you have the program xmgrace (or gnuplot) set up on your system, then you can visualize the results of reblock by typing plot reblock—you should be able to see a ‘plateau’ in the standard-errorversus-block-length curve, like the one shown in the figure below. (The block length is given by 2 raised to the power of the ‘reblocking transformation number’.) In the example shown below, the standard error in the mean energy is 0.00035 a.u. Note that xmgrace is a very useful thing to have, and it is used by various casino utilities. If you don’t have it set up on your system then you can download it for free from the following website: plasma-gate.weizmann.ac.il/Grace/ (it is also present in most modern Linux repositories, though not generally installed by default). 3 The on-the-fly reblocking only does energies (it should do all expectation values whether in the .hist files or expval.data) plus there is currently no system for loading previous on-the-fly reblocking data when continuing a run or any utilities for extracting the on-the-fly reblocking data from a calculation. This will be improved in a future release of casino. 16
Std. err. in the mean DMC energy (a.u.) 0.0005 0.0004 0.0003 0.0002 0.0001 0 0 5 10 15 20 Reblocking transformation number The file config.out contains the final positions of the electrons and the current state of the random number generator so that the VMC run can be continued if desired. To do this, set the input keyword newrun to F and rename the config.out file to config.in (in fact the runqmc script will normally ask if it can do this for you), then run the calculation for another vmc nstep steps. All the extra data will be put onto the end of vmc.hist and the error bar from the reblocking analysis will be smaller (in principle the error bar can be made as small as desired). As I already mentioned, you need to use the reblock utility for continued runs since the on-the-fly reblocking will no longer work. Finally, go and find a system with more than one electron and a Jastrow factor, such as the beryllium dimer in ~/CASINO/examples/molecule/be2/. Experiment with switching use jastrow between F (HFVMC) and T (VMC with a Jastrow factor), and see the energy- and error-bar-lowering effect of the Jastrow factor (results shown below for 12 cores). Without Jastrow: E = -29.107(8) ; var = 6.6(6) Total CASINO CPU time ::: 4.0744 seconds With Jastrow: E = -29.215(2) ; var = 0.303(2) Total CASINO CPU time ::: 6.0221 seconds After any casino calculation, you can delete all the output that casino produces and restore the directory to the state it was in at the start of the calculation by typing clearup. 6.3 Wave function optimization The values for the parameters in the Jastrow factor used in the last part of the previous section (and other adjustable parameters such as the coefficients in a multideterminant expansion, or backflow parameters) generally need to be optimized so that we have best possible trial wave function of the given functional form. There are various methods for doing this, including minimization of the variance(‘varmin’), minimization of the energy (‘emin’), and minimization of the mean absolute deviation of the local energies from the median (‘madmin’). Wave-function optimization is probably the most difficult part of QMC for beginners, and perseverance will help. The user might first like to take a look at Sec. 25.1, which contains a detailed summary of the theory and best practice. Here we simply summarize. 17
Page 1 and 2: CASINO User’s Guide Version 2.13
Page 3 and 4: 8.6 GAUSSIAN94/98/03/09 . . . . . .
Page 5 and 6: 29.2 Fourier transformation of CASI
Page 7 and 8: 1 Introduction casino is a computer
Page 9 and 10: 3.2 Legal stuff casino is given awa
Page 11 and 12: - Grossman-Mitas DMC-DFT molecular
Page 13 and 14: Your defined setup can then be perm
Page 15 and 16: - : perform compilation (default).
Page 17 and 18: 6 Introductory user’s guide: how
Page 19 and 20: ATOM BASIS TYPE The basis used to r
Page 21: ENVMC v0.60: Script to extract VMC
Page 25 and 26: Jastrow factor from each cycle of t
Page 27 and 28: V(x) Ψ init (x) τ{ t Ψ 0 (x) x T
Page 29 and 30: the energy becomes roughly constant
Page 31 and 32: many cores, time limits etc, which
Page 33 and 34: Set the verbosity level of the mach
Page 35 and 36: 6.7 How to run coupled DFT-DMC mole
Page 37 and 38: unqmcmd --startqmc=M Start the chai
Page 39 and 40: config.out This is the name under w
Page 41 and 42: ‘slater-type’: use Slater-type
Page 43 and 44: CUSTOM SPAIR DEP (Block) This input
Page 45 and 46: initial configurations come from DM
Page 47 and 48: DTDMC (Real) Time step for DMC run
Page 49 and 50: FORCES INFO (Integer) Controls the
Page 51 and 52: nucleus is assumed to lie at the or
Page 53 and 54: MOVIECELLS (Logical) If F then casi
Page 55 and 56: OPT MAXITER (Integer) Largest permi
Page 57 and 58: of G vectors and discards all those
Page 59 and 60: half a million cores, it may be des
Page 61 and 62: VM REWEIGHT (Logical) If vm reweigh
Page 63 and 64: default this is 0 hartree. It shoul
Page 65 and 66: A very detailed specification of th
Page 67 and 68: -1 0 0 1 1 1 1 1 1 1 0 2 1 0 1 2 Pa
Page 69 and 70: cusp conditions; otherwise, only th
Page 71 and 72: Detailed information about each of
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|k| (outermost). Hence one can spec
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large and the wave function is near
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R(i) in atomic units 0.000000000000
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2. The charge-density Fourier coeff
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c_767: [ 996 ] ... Compressed expan
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valence charges for each atom %%%%%
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1988). This can be found online. An
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1.3813695578425E+00 1.3957621401173
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PWSCF Method: DFT DFT Functional: u
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0.125203784849961E-01 0.13042462855
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3.3000000000000E+00 2.0000000000000
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Potential Number of grid points 200
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9. Clearly, the total number of pos
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EBEST (DMC only) Best estimate of t
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Use G-vector set 1 Number of sets 2
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1000.0 rho_a(G)*rho_b(-G) 16.0 4.12
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total weight must always be include
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The exporter does not currently wor
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8.4.2 Generating gwfn.data files wi
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After successfully running properti
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% mv Test.FChk dna.Fchk run gaussia
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• By default, gaussian uses spin
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Routine Purpose qmc write Writes th
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not the case the defaults can be ch
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8.10 TURBOMOLE Website: www.turbomo
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• crysgen06/09, crystaltoqmc: The
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• quickblock: Simple reblocking u
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• In Movie Settings choose Trajec
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the move rejection probability is h
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This leads to the single-electron d
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In the UNR [19] scheme the modified
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13.7 Evaluating expectation values
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Population-control catastrophes sho
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where u k has the periodicity of th
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Although the constraint equations a
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18 Wave-function updating Consider
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19.2 Evaluating the nonlocal pseudo
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of a unit point charge at r j in ev
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19.4.3 1D Coulomb interaction Coulo
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To investigate whether the extrapol
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correlations, such as might be enco
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where n is the order of the expansi
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terms by definition, and it can be
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which is therefore independent of r
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where the local energy, E L , is E
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Another variant of variance minimiz
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The energy minimization method used
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valid. The first problem, which ari
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• Is emin min energy too high? Th
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It may be activated by setting vmc
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that the number of configuration mo
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• It is possible to use blip orbi
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0.5 0.5 0.0 particle 1 det 1 : 9 or
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The clearup twistav script can be u
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In the infinite system limit, the s
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Note that this has the k −2 diver
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• The effective time step, Eq. (3
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1 2 H He 1.00794 4.00260 3 4 5 6 7
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and the Dirac delta function is δ(
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33.2.2 Atomic densities K eywords:
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The spin-density matrix is a two-by
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33.3.3 Homogeneous and isotropic sy
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33.4 Structure factor and spherical
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33.5 One-body density matrix, two-b
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[ where the approximation ρ (1)T
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The figure shows the localization l
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with F HFT mix = − F P mix = −
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The input keyword to activate the c
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To each walker r j , we assign a li
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37 Magnetic fields and the fixed-ph
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38 Analysis of the performance of C
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the orbitals, α = 2 [11]. The use
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39.2 Implementation basics and perf
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• Use ‘endif’ and ‘enddo’
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• Evidence of testing on serial a
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B Appendix 2: Automatic testing of
Page 225 and 226:
• Delete any eepot.data and densi
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* "Generic" CASINO_ARCHs are intend
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- ‘head -n 1 /etc/redhat-release
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for a single job in an ensemble of
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inary executable. CASINO does not r
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otherwise. The following tags are o
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[2] V.R. Saunders, R. Dovesi, C. Ro
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[50] W. Janke, Statistical Analysis
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CASINO manual - Theory of Condensed Matter

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