5.3 Overview of Available Functionals 5.3.5 Exchange-Correlation Functionals 5.3.7 User-Defined Density Functionals

5.3.6 Specialized Functionals

(February 4, 2022)

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SRC1-R1: TDDFT short-range corrected functional [Eq. (1) in Ref. 102, 1st row atoms]
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SRC1-R2: TDDFT short-range corrected functional [Eq. (1) in Ref. 102, 2nd row atoms]
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SRC2-R1: TDDFT short-range corrected functional [Eq. (2) in Ref. 102, 1st row atoms]
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SRC2-R2: TDDFT short-range corrected functional [Eq. (2) in Ref. 102, 2nd row atoms]
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BR89: Becke-Roussel meta-GGA exchange functional modeled after the hydrogen atom⁷³
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B94: meta-GGA correlation functional by Becke that uses the BR89 exchange functional to compute the Coulomb potential⁷⁹
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B94hyb: modified version of the B94 correlation functional for use with the BR89B94hyb exchange-correlation functional⁷⁹
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BR89B94h: 15.4% HF exchange + 84.6% BR89 meta-GGA exchange + BR89hyb meta-GGA correlation⁷⁹
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BRSC: Exchange component of the original B05 exchange-correlation functional⁷¹
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MB05: Exchange component of the modified B05 (BM05) exchange-correlation functional⁹³⁰
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B05: A full exact-exchange Kohn-Sham scheme of Becke that uses the exact-exchange energy density (RI) and accounts for static correlation^{71, 933, 932}
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BM05 (XC): Modified B05 hyper-GGA scheme that uses MB05 instead of BRSC as the exchange functional⁹³⁰
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PSTS: Hyper-GGA (100% HF exchange) exchange-correlation functional of Perdew, Staroverov, Tao, and Scuseria⁸⁷⁶
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MCY2: Mori-Sánchez-Cohen-Yang adiabatic connection-based hyper-GGA exchange-correlation functional^{791, 215, 699}

This example illustrate the use of the RI-B05 and RI-PSTS functionals. These are presently available only for single-point calculations, and convergence is greatly facilitated by obtaining converged SCF orbitals from, e.g., an LDA or HF calculation first. (LDA is used in the example below but HF can be substituted.) Use of the RI approximation (Section 6.6) requires specification of an auxiliary basis set.

Example 5.1 Q-Chem input of H ${}_{2}$ using RI-B05.

$comment
   H2, example of SP RI-B05.  First do a well-converged LSD, G3LARGE is the
   basis of choice for good accuracy.
$end

$molecule
   0 1
   H   0.  0.   0.0
   H   0.  0.   0.7414
$end

$rem
   METHOD           lda
   BASIS            g3large
   SCF_GUESS        core     ! required
   PURECART         2222     ! required
   THRESH           14
   INCDFT           false
   SYM_IGNORE       true
   SYMMETRY         false
   SCF_CONVERGENCE  9
$end

@@@

$molecule
   read
$end

$rem
   EXCHANGE        b05            ! or set to psts for ri-psts
   BASIS           g3large
   AUX_BASIS       rib05-cc-pvtz  ! the aux basis for both RI-B05 and RI-PSTS
   SCF_GUESS       read
   PURECART        2222           ! required
   THRESH          4
   PRINT_INPUT     true
   INCDFT          false
   SYM_IGNORE      true
   SYMMETRY        false
   MAX_SCF_CYCLES  0              ! required
   DFT_CUTOFFS     0              ! required
$end

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5.3.6 Specialized Functionals