CASINO manual - Theory of Condensed Matter

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1 START SET 1 Spherical harmonic l,m 0 0 Expansion order N_h 3 Spin dep (0->uu=dd=ud; 1->uu=dd/=ud; 2->uu/=dd/=ud) -1 Cutoff (a.u.) ; Optimizable (0=NO; 1=YES) 0.d0 1 Parameter values ; Optimizable (0=NO; 1=YES) END SET 1 END H TERM where use is made of spin-triplet dependencies as defined in the custom striplet dep input block. Notes: • There are 6 types of term available: u (isotropic electron–electron terms), χ (isotropic electron–nucleus terms), f (isotropic electron–electron–nucleus terms), p (plane-wave expansions in electron–electron separation), q (plane-wave expansions in electron position) and W /H (isotropic, homogeneous three-electron term). All of these terms are optional: e.g., omitting all the lines from ‘START Q TERM’ to ‘END Q TERM’ will give a Jastrow factor with no q terms. In many cases (particularly in the presence of pseudopotentials) only u and χ terms are needed, and this is good since higher-order terms such as f-functions can become very expensive in large systems. • The ‘truncation order’ should be either 2 or 3. If it is of value C then the Jastrow factor is C times differentiable everywhere; it must therefore be at least 2 for the kinetic-energy integrand to be well-defined. If it is 3 then the local energy is continuous in configuration space (assuming the orbitals are smooth). This is not strictly required, and leads to the loss of some variational freedom, but it makes the numerical optimization of cutoff lengths easier. In general, we recommend setting C = 3. • In a future release, the u and χ terms may be made anisotropic; there are place-holders for this in the Jastrow data set. At present, however, both must be isotropic. There should only be one set of u terms, and the spherical harmonic l and m values should therefore be set to 0. • The ‘expansion order’ of u determines the number of parameters. Typically it is given a value between 4 and 8. • The ‘spin-dep params’ line allows the user to specify whether the same u-parameters are to be used for parallel- and antiparallel-spin electron-pairs. If the value is set to 0 then the same parameters are used for parallel and antiparallel pairs (this option should not be used in general); if the value is set to 1 then different parameters are used for parallel and antiparallel pairs; if it is set to 2 then different parameters are used for up-spin, down-spin and opposite-spin pairs: this is useful for spin-polarized systems. 12 • The cutoff length is given a default value if it is set to 0. Note that it is possible to optimize the cutoff length using variance minimization. This can be useful, because the choice of cutoff length has a significant effect on the optimized energy and variance. Unfortunately, optimizing the cutoff length is numerically difficult: variance minimization will take many more iterations to converge if the cutoff is optimizable. Setting the truncation order to 3 can help somewhat. • It is possible to specify exactly which of the expansion coefficients (‘parameter values’) are optimizable and which are not. One does not need to specify all of the expansion coefficients: any that are not listed are assumed to be zero. If all of the parameter values in all of the Jastrow terms are blank, as is the case in the example given above, then the following default behaviour will be used: if one is studying a homogeneous system, or a 3D-periodic system or is using energy minimisation, a simple default for u will be chosen that satisfies the Kato 12 When particles other than electrons are present in the systems, introduced via the particles block input keyword, these definitions change a little. Information on the particle and particle-pair splittings are given near the beginning of the out file. 62
cusp conditions; otherwise, only the Slater wave function will be used for the first configuration generation run when performing wave-function optimization. 13 • Different χ functions are used for different species of ion: the ‘number of sets’ can be chosen to be equal to the number of chemically distinct species. One can optionally specify how the atoms in each set are to be labelled. The ‘labelling’ flag can be set to ‘1’, meaning that each atom is labelled by its number within the simulation cell, or ‘2’, meaning that groups of atoms are labelled by their number within the primitive cell, or ‘3’, meaning that groups of atoms are labelled by their species. • The ions in each set are specified by giving a list of the numbers that label them. If the labelling flag is set to ‘1’ (the default if the labelling flag is absent: see above) then, in the first primitive cell, the atom labels are the same as the labels used in the xwfn.data file that specifies the geometry of the system; the atoms in the subsequent primitive cells are labelled in the same order as the first. If the labelling flag is set to ‘2’ then the atom labels are the same as those used in the xwfn.data file (so the same χ functions are used for translationally equivalent atoms within the supercell). If the labelling flag is set to ‘3’ then the atom labels refer to species (in the order in which the species occur in the xwfn.data file), so that all atoms of the same species have the same χ functions. • It is possible to make the Jastrow factor enforce the electron–nucleus cusp condition. This should only be done if the χ-set contains bare nuclei and the orbitals do not satisfy the cusp condition. With a Gaussian basis set, it is much better to use the in-built cusp correction algorithm activated with the input keyword cusp correction than to use the Jastrow. Likewise, numerical atomic orbitals already satisfy the electron–nucleus cusp conditions. • There are two spin-dependence options for χ: if it is 0 then the same parameters are used for up- and down-spin electrons; if it is 1 then different parameters are used. • Similar comments to those made for u apply to the ‘spherical harmonic’ labels, the cutoff length and the parameter values of χ. 14 • The f function contains terms that approximately duplicate the u and χ terms: additional constraints can be placed on f to remove these terms if desired. Duplication of u and χ should generally be permitted, however. • The number of f-parameters grows very rapidly with the electron–electron and electron–nucleus expansion orders, which should normally be either 2 or 3. Note also that calculating f-functions can be very expensive in large systems, particularly if the cutoffs are allowed to get too big. • The spin-dependence options for f are exactly the same as for u. • The p and q terms can only be present in periodic systems. The p term makes a small but significant improvement to the wave function in most cases, whereas the q term does not appear to help much. It is especially important to use a p term if the finite-size correction to the kinetic energy is to be calculated (see Sec. 29). Note that q should only be used if the origin is a centre of inversion symmetry of the charge density. • The spin-dependence options for p and q are the same as those of u and χ respectively. • For p, a list of simulation-cell G-vectors must be provided. These are specified in terms of the reciprocal-lattice vectors. Only one out of each G and −G should be specified. The same parameter value is used for G-vectors with the same label. Note that the make p stars utility can be used to generate p terms to paste into the correlation.data file. • For q, a list of primitive-cell G-vectors must be provided. Again, G-vectors with the same label have the same parameter value. It is possible to specify a negative relationship between parameter values by using a negative label for the appropriate G-vectors. 13 The u-parameters are listed in the following order for electron systems: coefficients for spin-up pairs; coefficients for antiparallel pairs (if spin-dependence is 1 or 2); coefficients for spin-down pairs (if spin-dependence is 2). For each spin-pair, the number of parameters is equal to the expansion order. 14 For electron systems, the parameter values are given for spin-up electrons, then (if the spin-dependence is 1) for spin-down electrons. For each spin-type, the number of parameters is equal to the expansion order. 63
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CASINO User’s Guide Version 2.13
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8.6 GAUSSIAN94/98/03/09 . . . . . .
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29.2 Fourier transformation of CASI
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1 Introduction casino is a computer
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3.2 Legal stuff casino is given awa
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- Grossman-Mitas DMC-DFT molecular
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Your defined setup can then be perm
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- : 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 and 22: ENVMC v0.60: Script to extract VMC
Page 23 and 24: Std. err. in the mean DMC energy (a
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: -1 0 0 1 1 1 1 1 1 1 0 2 1 0 1 2 Pa
Page 71 and 72: Detailed information about each of
Page 73 and 74: |k| (outermost). Hence one can spec
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Page 77 and 78: R(i) in atomic units 0.000000000000
Page 79 and 80: 2. The charge-density Fourier coeff
Page 81 and 82: c_767: [ 996 ] ... Compressed expan
Page 83 and 84: valence charges for each atom %%%%%
Page 85 and 86: 1988). This can be found online. An
Page 87 and 88: 1.3813695578425E+00 1.3957621401173
Page 89 and 90: PWSCF Method: DFT DFT Functional: u
Page 91 and 92: 0.125203784849961E-01 0.13042462855
Page 93 and 94: 3.3000000000000E+00 2.0000000000000
Page 95 and 96: Potential Number of grid points 200
Page 97 and 98: 9. Clearly, the total number of pos
Page 99 and 100: EBEST (DMC only) Best estimate of t
Page 101 and 102: Use G-vector set 1 Number of sets 2
Page 103 and 104: 1000.0 rho_a(G)*rho_b(-G) 16.0 4.12
Page 105 and 106: total weight must always be include
Page 107 and 108: The exporter does not currently wor
Page 109 and 110: 8.4.2 Generating gwfn.data files wi
Page 111 and 112: After successfully running properti
Page 113 and 114: % mv Test.FChk dna.Fchk run gaussia
Page 115 and 116: • By default, gaussian uses spin
Page 117 and 118: 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
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• 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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