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31 EXPLICITLY CORRELATED METHODS 231 31.2.3 The fixed amplitude ansatz (FIX) The diagonal ansatz is used and the amplitudes of the explicitly correlated configurations are determined by the wavefunction cusp conditions, i.e. T i j,1 i j = 1 2 T i j,−1 i j = 1 4 This ansatz is orbital invariant, size consistent and free of GBSSE. 31.3 RI Approximations Various approximations such as A, B, C, HY1, HY2 exist for the matrix elements of the firstorder Hamiltonian (see I). They differ in the way the RI approximations are made. In the limit of a complete RI basis, approximations B and C are identical and yield the exact result for a given wave function ansatz. We generally recommend approximation C, which is simpler and more efficient than approximation B. Normally, the union of the AO and RI basis sets is used to approximate the resolution of the identity (CABS approach). In the hybrid approximations (HY1, HY2, HX) only the AO basis is used in some less important terms. Together with the recommended approximation C, HY1 or HY2 can be used; HY2 is more accurate, HY1 more efficient. In most cases, approximation 3C(HY1) provides an excellent compromise between accuracy and efficiency. In approximation A, all terms involving exchange operators are neglected. This approximation is used along with local approximations in our low-order scaling LMP2-F12/3*A(loc) method that can be applied to large molecules (cf. section 31.11) If the extended Brillouin condition (EBC, see I) is assumed, the explicitly correlated and conventional amplitude equations decouple and can be solved independently. These approximations are denoted by a star, e.g. 3*C. 31.4 Basis sets In <strong>MOLPRO</strong> the F12 integrals can only be computed using density fitting (DF) approximations. The many electron integrals are approximated by resolutions of the identity (RI) expansions. Thus, F12 calculations require three different basis sets: the orbital (AO) basis, the DF basis, and the RI basis. We recommend as AO basis sets the augmented correlation consistent basis sets (denoted AVnZ) or the specially optimized correlation consistent F12 basis sets (denoted VnZ-F12, cf. K.A. Peterson and H.-J. Werner, J. Chem. Phys. 128, 084102 (2008)). Normally, triples zeta basis sets (AVTZ or VTZ-F12) yield excellent results that are close to the basis set limit. Diffuse basis functions are rather essential both for the HF and MP2-F12 energies, and therefore the standard VTZ sets are not recommended. If the AVnZ or VnZ-F12 orbital basis sets are used, suitable density fitting (DF) basis and resolution of the identity (RI) basis sets are automatically chosen. For the AVnZ orbital basis sets, AVnZ/MP2FIT amd VnZ/JKFIT basis sets are used by default for the DF and RI, respectively. The associated optimized CABS basis set of Peterson et al. can be chosen by specifying RI BASIS=OPTRI. For the VnZ-F12 orbital basis, the associated CABS (OPTRI) basis sets are used by default. Other basis sets can be chosen using the DF BASIS, DF BASIS EXCH and RI BASIS options (cf. section 31.6). See section 15 for more details about density fitting. This is an example for using multiple basis sets for density fitting and resolution of the identity
31 EXPLICITLY CORRELATED METHODS 232 ***,h2o geom={o; h1,o,r; h2,o,r,h1,theta} r=0.97 ang theta=104 basis={ default,avtz set,df default,avtz/mp2fit !density fitting basis set,jk default,avtz/jkfit !density fitting basis for Fock and exchange matrices set,ri default,avtz/optri !ri cabs basis } hf ccsd(t)-f12,df_basis=df,df_basis_exch=jk,ri_basis=ri http://www.molpro.net/info/current/examples/h2o_basissets1.com The following two examples yield identical results: ***,h2o geom={o; h1,o,r; h2,o,r,h1,theta} r=0.97 ang theta=104 basis={ default,avtz set,df,context=mp2fit default,avtz !density fitting basis set,jk,context=jkfit default,avtz !density fitting basis for Fock and exchange matrices set,ri,context=optri default,avtz !ri cabs basis } hf ccsd(t)-f12,df_basis=df,df_basis_exch=jk,ri_basis=ri http://www.molpro.net/info/current/examples/h2o_basissets2.com ***,h2o geom={o; h1,o,r; h2,o,r,h1,theta} r=0.97 ang theta=104 basis=avtz hf ccsd(t)-f12,df_basis=avtz/mp2fit,df_basis_exch=avtz/jkfit,ri_basis=avtz/optri http://www.molpro.net/info/current/examples/h2o_basissets3.com In the latter example the specifications MP2FIT and JKFIT could be omitted, i.e. the input ccsd(t)-f12,df basis=avtz,df basis exch¯vtz,ri basis=optri would be equivalent. In fact, since default density fitting basis sets are used
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MOLPRO Users Manual Version 2010.1
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ii • Møller-Plesset perturbation
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iv 3. Explicitly correlated LMP2-F1
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vi The original reference to uncont
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viii Rangehybrid methods: T. Leinin
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CONTENTS x 4.12 Summary of keywords
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CONTENTS xii 10.4 Geometry Files .
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CONTENTS xiv 16.9.4 Sanity check on
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CONTENTS xvi 19.5.1 Defining the st
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CONTENTS xviii 20.4 Miscellaneous t
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CONTENTS xx 29.6.3 Manually Definin
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CONTENTS xxii 34.1.5 Printing optio
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CONTENTS xxiv 39.10Point group symm
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CONTENTS xxvi 42.2.7 Numerical Hess
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CONTENTS xxviii 53 QM/MM INTERFACES
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CONTENTS xxx A.3.11 Fedora 13 (32-b
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CONTENTS xxxii C.41 THGFL: . . . .
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2 RUNNING MOLPRO 2 of directories o
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2 RUNNING MOLPRO 4 also some parts
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2 RUNNING MOLPRO 6 Note that option
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3 DEFINITION OF MOLPRO INPUT LANGUA
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4 GENERAL PROGRAM STRUCTURE 14 Glob
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4 GENERAL PROGRAM STRUCTURE 16 in d
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4 GENERAL PROGRAM STRUCTURE 18 Tabl
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4 GENERAL PROGRAM STRUCTURE 20 tion
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4 GENERAL PROGRAM STRUCTURE 22 Prog
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4 GENERAL PROGRAM STRUCTURE 24 LCIS
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5 INTRODUCTORY EXAMPLES 26 In the a
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5 INTRODUCTORY EXAMPLES 28 5.7 Proc
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6 PROGRAM CONTROL 30 ***,h2o benchm
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6 PROGRAM CONTROL 32 6.5 Allocating
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6 PROGRAM CONTROL 34 6.7.1 IF state
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6 PROGRAM CONTROL 36 Certain import
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6 PROGRAM CONTROL 38 ZERO ONEINT TW
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6 PROGRAM CONTROL 40 6.13.1 Example
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6 PROGRAM CONTROL 42 Table 5: One-e
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7 FILE HANDLING 44 7.4 DATA The DAT
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8 VARIABLES 46 Numbers: Logicals: S
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8 VARIABLES 48 8.4 System variables
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8 VARIABLES 50 are valid variable d
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8 VARIABLES 52 CM=1.d0/219474.63067
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8 VARIABLES 54 DEL4 ∇ 4 DARWIN Da
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8 VARIABLES 56 CHARGE NELEC SPIN CI
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9 TABLES AND PLOTTING 58 8.11 Readi
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9 TABLES AND PLOTTING 60 plotted; i
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10 MOLECULAR GEOMETRY 62 PLANEXZ z-
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10 MOLECULAR GEOMETRY 64 geometry s
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10 MOLECULAR GEOMETRY 66 ***,H2O ge
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10 MOLECULAR GEOMETRY 68 entries. D
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11 BASIS INPUT 70 resolution in exp
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11 BASIS INPUT 72 • The Binning/C
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11 BASIS INPUT 74 The specification
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11 BASIS INPUT 76 the exponents of
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11 BASIS INPUT 78 ***,h2o geom={o;
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12 EFFECTIVE CORE POTENTIALS 80 is
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13 CORE POLARIZATION POTENTIALS 82
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14 INTEGRATION 84 14.1 Sorted integ
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14 INTEGRATION 86 smaller than this
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14 INTEGRATION 88 THR D3EXT THREST
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14 INTEGRATION 90 THRQ2 LMP2 THRAO
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14 INTEGRATION 92 Table 7: Default
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15 DENSITY FITTING 94 DF-HF,DF_BASI
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15 DENSITY FITTING 96 LOCFIT F12 LO
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16 THE SCF PROGRAM 98 16 THE SCF PR
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16 THE SCF PROGRAM 100 16.1.4 Optio
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16 THE SCF PROGRAM 102 16.3 Saving
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16 THE SCF PROGRAM 104 r1=1.85,r2=1
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16 THE SCF PROGRAM 106 16.9.1 Level
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17 THE DENSITY FUNCTIONAL PROGRAM 1
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18 ORBITAL LOCALIZATION 124 geometr
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18 ORBITAL LOCALIZATION 126 GROUP,3
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18 ORBITAL LOCALIZATION 128 18.9 Op
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19 THE MCSCF PROGRAM MULTI 130 f) c
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19 THE MCSCF PROGRAM MULTI 132 19.3
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19 THE MCSCF PROGRAM MULTI 134 WF,6
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19 THE MCSCF PROGRAM MULTI 138 or C
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19 THE MCSCF PROGRAM MULTI 144 icst
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20 THE CI PROGRAM 148 ***,N2 geomet
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20 THE CI PROGRAM 150 and double ex
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20 THE CI PROGRAM 152 refstat: mxsh
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20 THE CI PROGRAM 154 Default is to
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20 THE CI PROGRAM 156 20.3.8 Restri
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20 THE CI PROGRAM 158 DM and NATORB
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20 THE CI PROGRAM 160 ZERO: THRDLP:
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20 THE CI PROGRAM 162 PAIRS=1: prin
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20 THE CI PROGRAM 164 problem is to
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21 MULTIREFERENCE RAYLEIGH SCHRÖDI
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22 NEVPT2 CALCULATIONS 176 IHINT=0
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23 MØLLER PLESSET PERTURBATION THE
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Page 221 and 222: 25 EXCITED STATES WITH EQUATION-OF-
Page 229 and 230: 27 THE MRCC PROGRAM OF M. KALLAY (M
Page 235 and 236: 28 SMILES 202 This code is not incl
Page 237 and 238: 29 LOCAL CORRELATION TREATMENTS 204
Page 257 and 258: 30 LOCAL METHODS FOR EXCITED STATES
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Page 261 and 262: 31 EXPLICITLY CORRELATED METHODS 22
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Page 277 and 278: 32 THE FULL CI PROGRAM 244 32 THE F
Page 279 and 280: 33 SYMMETRY-ADAPTED INTERMOLECULAR
Page 289 and 290: 34 PROPERTIES AND EXPECTATION VALUE
Page 301 and 302: 35 RELATIVISTIC CORRECTIONS 268 •
Page 303 and 304: 36 DIABATIC ORBITALS 270 This proce
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Page 307 and 308: 38 QUASI-DIABATIZATION 274 This cal
Page 309 and 310: 38 QUASI-DIABATIZATION 276 ***,h2s
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Page 313 and 314: 39 THE VB PROGRAM CASVB 280 39 THE
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39 THE VB PROGRAM CASVB 282 configu
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39 THE VB PROGRAM CASVB 284 be proj
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39 THE VB PROGRAM CASVB 286 The lis
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39 THE VB PROGRAM CASVB 288 This ke
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39 THE VB PROGRAM CASVB 290 to writ
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40 SPIN-ORBIT-COUPLING 292 integral
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40 SPIN-ORBIT-COUPLING 294 40.6.1 P
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40 SPIN-ORBIT-COUPLING 296
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41 ENERGY GRADIENTS 298 41 ENERGY G
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41 ENERGY GRADIENTS 300 state2) and
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41 ENERGY GRADIENTS 302 ZMAT OPT3N
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42 GEOMETRY OPTIMIZATION (OPTG) 304
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43 VIBRATIONAL FREQUENCIES (FREQUEN
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45 MINIMIZATION OF FUNCTIONS 340 45
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45 MINIMIZATION OF FUNCTIONS 342 **
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46 BASIS SET EXTRAPOLATION 344 extr
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46 BASIS SET EXTRAPOLATION 346 ***,
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46 BASIS SET EXTRAPOLATION 348 46.3
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46 BASIS SET EXTRAPOLATION 350 geom
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47 POTENTIAL ENERGY SURFACES (SURF)
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48 POLYNOMIAL REPRESENTATIONS (POLY
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49 THE VSCF PROGRAM (VSCF) 364 THER
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50 THE VCI PROGRAM (VCI) 366 CITHR=
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50 THE VCI PROGRAM (VCI) 368 surf,s
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52 THE COSMO MODEL 370 52 THE COSMO
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52 THE COSMO MODEL 372 or using the
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54 THE TDHF AND TDKS PROGRAMS 374 o
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55 ORBITAL MERGING 376 MOVE command
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55 ORBITAL MERGING 378 55.13 Exampl
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56 MATRIX OPERATIONS 380 ***,NO mer
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56 MATRIX OPERATIONS 382 56.2 Loadi
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56 MATRIX OPERATIONS 384 If NATURAL
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56 MATRIX OPERATIONS 386 56.14 Form
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56 MATRIX OPERATIONS 388 ***,h2o ma
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A INSTALLATION GUIDE 390 the result
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A INSTALLATION GUIDE 392 For IA32 L
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A INSTALLATION GUIDE 394 3. If any
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A INSTALLATION GUIDE 396 -gfortran
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A INSTALLATION GUIDE 398 A.3.7 Test
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A INSTALLATION GUIDE 400 --noverbos
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A INSTALLATION GUIDE 402 A.3.12 ope
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A INSTALLATION GUIDE 404 A.3.14 Ins
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B RECENT CHANGES 406 B.1.4 New basi
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B RECENT CHANGES 408 1) · exp(−9
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B RECENT CHANGES 410 B.4 New featur
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B RECENT CHANGES 412 5. Multipole m
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C DENSITY FUNCTIONAL DESCRIPTIONS 4
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+ 9 8 (1 − ζ ) 4/3 C DENSITY FUN
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D LICENSE INFORMATION 456 D.1 BLAS
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D LICENSE INFORMATION 458 D.3 Boost
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INDEX 460 DFTTHRESH, 109 Difference
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INDEX 462 NOGPRINT, 38 NOGRIDSAVE,
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