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10.14 Electronic Couplings for Electron- and Energy Transfer

10.14.3 Fragment-Based Methods for Electronic Coupling

(December 20, 2021)

10.14.3.1 Approach based on absolutely localized molecular orbitals

One can use absolutely localized molecular orbitals (ALMOs, see Chapter 12) to construct charge-localized diabatic states directly from DFT calculations. The ALMOs on each fragment are expanded by the AO basis functions belonging to the same fragment alone, whose corresponding MO coefficient matrix is fragment block-diagonal. 564 Khaliullin R. Z., Head-Gordon M., Bell A. T.
J. Chem. Phys.
(2006), 124, pp. 204105.
Link
In energy decomposition analysis methods, 563 Khaliullin R. Z. et al.
J. Phys. Chem. A
(2007), 111, pp. 8753.
Link
, 486 Horn P. R., Mao Y., Head-Gordon M.
Phys. Chem. Chem. Phys.
(2016), 18, pp. 23067.
Link
ALMOs are utilized to separate the effects of polarization and charge transfer in intermolecular binding, because they have the useful property that they do not allow for charge transfer between fragments under the Mulliken definition of charge population. Making use of this property, one can construct charge-localized diabats for hole and electron transfer. For example, considering the initial and final states of a hole transfer process, |D+A and |DA+, the two diabats can be represented in the following form:

|ψa =1(N-1)!det{ϕD1(a),ϕD2(a),,ϕDnD-1(a)ϕA1(a),ϕA2(a),,ϕAnA(a)} (10.128a)
|ψb =1(N-1)!det{ϕD1(b),ϕD2(b),,ϕDnD(b)ϕA1(b),ϕA2(b),,ϕAnA-1(b)} (10.128b)

For systems where the donor and acceptor moieties are well-separated, one can construct the ALMO-based diabats by simply concatenating orbitals obtained from isolated fragment calculations: D+ and A for one diabat, and D and A+ for the other. The energy of each ALMO diabat can then be variationally optimized with respect to orbital rotations on fragment, using the SCFMI technique (see Section 12.4). 1085 Stoll H., Wagenblast G., Preuss H.
Theor. Chem. Acc.
(1980), 57, pp. 169.
Link
, 359 Gianinetti E., Raimondi M., Tornaghi E.
Int. J. Quantum Chem.
(1996), 60, pp. 157.
Link
, 564 Khaliullin R. Z., Head-Gordon M., Bell A. T.
J. Chem. Phys.
(2006), 124, pp. 204105.
Link
These ALMO-based diabatic states are variationally optimized such that the associated nuclear forces can be easily computed. 736 Mao Y., Horn P. R., Head-Gordon M.
Phys. Chem. Chem. Phys.
(2017), 19, pp. 5944.
Link
The mutual polarization of donor and acceptor moieties in the presence of each other is also taken into account.

To calculate the electronic coupling between two ALMO diabats, one should first construct the diabatic Hamiltonian in the ALMO state basis

𝐇=(HaaHabHbaHbb) (10.129)

and then transform that into the Löwdin-orthogonalized basis

𝐇=𝐒-1/2𝐇𝐒-1/2 (10.130)

whose off-diagonal element, Hab, corresponds to the diabatic coupling to be evaluated. In the 2-state case, we have

Hab=11-Sab2|Hab-Haa+Hbb2Sab| (10.131)

which requires the overlap between two ALMO diabats and the diagonal and off-diagonal elements of 𝐇. The interstate overlap is given by

Sab=ψa|ψb=det[(𝐂o(a))𝐒𝐂o(b)]. (10.132)

where 𝐂o(a) and 𝐂o(b) are MO coefficients for the occupied orbitals in diabats |ψa and |ψb, respectively, and 𝐒 is the AO overlap matrix.

The elements of the diabatic Hamiltonian matrix can be evaluated using the multi-state DFT (MSDFT) approach. 179 Cembran A. et al.
J. Chem. Theory Comput.
(2009), 5, pp. 2702.
Link
, 955 Ren H. et al.
J. Phys. Chem. Lett.
(2016), 7, pp. 2286.
Link
, 740 Mao Y., Montoya-Castillo A., Markland T. E.
J. Chem. Phys.
(2019), 151, pp. 164114.
Link
For the diagonal elements, it is straightforward to employ the KS energies of the two diabats:

Haa=EaKS[𝐏(a)],Hbb=EbKS[𝐏(b)] (10.133)

where 𝐏(a) and 𝐏(b) are the one-electron density matrices associated with two ALMO states |ψa and |ψb, respectively. The approximation for the off-diagonal element is theoretically more challenging. In the original MSDFT scheme, 179 Cembran A. et al.
J. Chem. Theory Comput.
(2009), 5, pp. 2702.
Link
, 955 Ren H. et al.
J. Phys. Chem. Lett.
(2016), 7, pp. 2286.
Link

Hab=Sab[Vnn+𝐏ab𝐡+12𝐏ab𝐈𝐈𝐏ab+12(ΔEac+ΔEbc)] (10.134)

where 𝐏ab is the one-particle transition density matrix between two ALMO states

𝐏ab=𝐂o(a)[(𝐂o(b))𝐒𝐂o(a)]-1(𝐂o(b)) (10.135)

The first three terms on the right-hand side of Eq. (10.134) correspond to the contributions from nuclear repulsion, one-electron Hamiltonian (kinetic energy and nuclei-electron attraction), and full two-electron integrals (Coulomb and full HF exchange), which can be derived as in non-orthogonal CI. 1120 Thom A. J. W., Head-Gordon M.
J. Chem. Phys.
(2009), 131, pp. 124113.
Link
The last term accounts for the contribution from exchange-correlation (XC) functional as a correction to the HF coupling, which is given by the average of the difference between the KS and HF energies calculated from the same one-electron density matrix for each diabat:

ΔEac =EaKS[𝐏(a)]-EaHF[𝐏(a)] (10.136a)
ΔEbc =EbKS[𝐏(b)]-EbHF[𝐏(b)]. (10.136b)

This approach was denoted as ALMO(MSDFT) in Ref.  740 Mao Y., Montoya-Castillo A., Markland T. E.
J. Chem. Phys.
(2019), 151, pp. 164114.
Link
and it was found to overestimate the electronic couplings for the tested hole and electron transfer systems. A modified approach, denoted as ALMO(MSDFT2), was proposed in Ref.  740 Mao Y., Montoya-Castillo A., Markland T. E.
J. Chem. Phys.
(2019), 151, pp. 164114.
Link
, which evaluates the XC contribution using the XC energy of the symmetrized transition density matrix

Hab=Sab[Vnn+𝐏ab𝐡+12𝐏ab𝐈𝐈𝐏ab+Exc[𝐏~ab]] (10.137)

where

𝐏~ab=12(𝐏ab+𝐏ba). (10.138)

Note that in Eq. (10.137), 𝐈𝐈 includes only Coulomb integrals and a fraction of exact exchange if hybrid functionals are employed.

According to the benchmark results in Ref.  740 Mao Y., Montoya-Castillo A., Markland T. E.
J. Chem. Phys.
(2019), 151, pp. 164114.
Link
, ALMO(MSDFT2) shows better accuracy than the original MSDFT method for hole and electron transfer, and thus it is implemented as the default approach to compute electronic couplings between ALMO diabats in Q-Chem. We note that the results given by Eq. (10.137) may become inaccurate when the overlap between two states becomes near-singular, as

𝝈ba=(𝐂o(b))𝐒𝐂o(a) (10.139)

is inverted when constructing the transition density [Eq. (10.135)]. To circumvent this numerical issue, one can replace the inverse in Eq. (10.135) with the Penrose pseudo-inverse, which was suggested for a similar objective in Ref.  863 Pavanello M. et al.
J. Chem. Phys.
(2013), 138, pp. 054101.
Link
.

10.14.3.2 Projection operator Diabatization (POD)

Besides ALMO-based diabatization method, other fragment-based diabatization methods are available in Q-Chem. The projection operator diabatization (POD) method 582 Kondov I. et al.
J. Phys. Chem. C
(2007), 111, pp. 11970.
Link
starts from a standard KS-DFT calculation of the system and post-processes the converged Fock matrix. It first transforms the Fock matrix into the Löwdin-orthogonalized AO basis and then partitions that into the donor and acceptor blocks, assuming that these orthogonalized AO basis functions still retain their original fragment tags:

𝐅~=𝐒-1/2𝐅𝐒-1/2=(𝐅~dd𝐅~da𝐅~ad𝐅~aa) (10.140)

One then diagonalizes 𝐅~dd and 𝐅~aa separately

ϵd=𝐃d𝐅~dd𝐃d,ϵa=𝐃a𝐅~aa𝐃a, (10.141)

where the eigenvectors 𝐃d and 𝐃a define the single-particle “diabatic states”:

|φ¯p(d)=μ|χ~μ(d)(Dd)pμ|φ¯p(a)=μ|χ~μ(a)(Da)pμ, (10.142)

and transforms the off-diagonal block of the Fock matrix into this diabatic basis

𝐅¯da=𝐃d𝐅~da𝐃a (10.143)

yielding

𝐅¯=(ϵd𝐅¯da𝐅¯adϵa) (10.144)

The couplings between these single-particle diabatic orbitals can then be directly read off from the elements of 𝐅¯da.

The Q-Chem implementation of the POD method follows the description in Refs.  582 Kondov I. et al.
J. Phys. Chem. C
(2007), 111, pp. 11970.
Link
and 1250 Yang C.-H., Yam C. Y., Wang H.
Phys. Chem. Chem. Phys.
(2018), 20, pp. 2571.
Link
, where a closed-shell reference system is used to generate the Fock matrix to be processed, i.e., 𝐅 in Eq. (10.140). By default, only the D(HOMO) - A(HOMO) coupling is calculated for the hole transfer cases, and the D(LUMO) - A(LUMO) coupling for the electron transfer cases. To calculate the couplings between multiple pairs of donor and acceptor orbitals, the user can set $rem variable POD_MULTI_PAIRS to TRUE and control the number of orbitals pairs through POD_WINDOW. See the instruction in Sec. 10.14.3.4.

Because of the use of globally Löwdin-orthogonalized orbitals in Eq. (10.140), the diabatic orbitals created by POD cannot be strictly localized on fragments. This renders the POD results unstable with the change of employed AO basis sets: when larger basis sets are used, the mixing between AO basis functions on different fragments becomes stronger, and the resulting Hab decreases. To alleviate this problem, a revised POD method, which was named as “POD2”, was proposed by Ghan et al.. 356 Ghan S. et al.
J. Chem. Theory Comput.
(2020), 16, pp. 7431.
Link
It avoids the global Löwdin-orthogonalization of the AO basis; instead, it separately diagonalizes the the donor and acceptor blocks of the Fock matrix (in the original AO basis):

𝐅dd𝐂d=𝐒dd𝐂dϵd,𝐅aa𝐂a=𝐒aa𝐂aϵa (10.145)

The obtained diabatic MO coefficient matrix is fragment-block-diagonal in the AO basis:

𝐂diab=(𝐂d𝟎𝟎𝐂a) (10.146)

Transforming the AO Fock matrix into this diabatic MO basis, the D-D and A-A blocks of the resulting matrix are diagonal matrices:

𝐅¯diab=𝐂diabT𝐅𝐂diab=(ϵd𝐅¯da𝐅¯adϵa) (10.147)

Using the matrix elements in the off-diagonal block (𝐅¯da) directly would yield overestimated couplings since the diabatic MOs 𝐂d and 𝐂a are not orthogonal to each other. Therefore, a final orthogonalization step is required to obtain the diabatic coupling between a pair of orbitals that are located on the donor and acceptor, respectively. Denoting this pair of orbital as ϕd and ϕa, one can construct the 2×2 Hamiltonian and overlap matrices:

𝐇=(ϵdF¯daF¯adϵa),𝐒=(1SdaSad1) (10.148)

Two orthogonalization schemes have been investigated by Ghan et al.. 356 Ghan S. et al.
J. Chem. Theory Comput.
(2020), 16, pp. 7431.
Link
The first approach performs a Löwdin orthgonalization on ϕd and ϕa, which is denoted as POD2L. The resulting coupling between the orthogonalized diabatic orbitals are

Hdaeff=11-Sda2|F¯da-12(ϵd+ϵa)Sda| (10.149)

The second approach employs the Gram-Schmidt orthogonalization, which keeps one of the two orbitals (ϕd or ϕa) intact while ensures that the other is strictly orthogonal to it. This approach is denoted as POD2GS, and it might be better choice for asymmetric cases (e.g. surface and adsorbates) where one can choose to retain the orbital on the less sizable fragment. These two POD2 variants afford significantly improved accuracy over the original POD method, especially in terms of the robustness with regard to the use of extensive basis sets.

10.14.3.3 Fragment Orbital DFT (FODFT)

Fragment orbital DFT (FODFT) 828 Oberhofer H., Blumberger J.
Phys. Chem. Chem. Phys.
(2012), 14, pp. 13846.
Link
, 1018 Senthilkumar K. et al.
J. Chem. Phys.
(2003), 119, pp. 9809.
Link
, 1005 Schober C., Reuter K., Oberhofer H.
J. Chem. Phys.
(2016), 144, pp. 054103.
Link
is an approach to compute the diabatic couplings for hole and electron transfer between fragments. There have been several different flavors of FODFT approaches developed in literature, and here we introduce the most recent variant by Schober et al. 1005 Schober C., Reuter K., Oberhofer H.
J. Chem. Phys.
(2016), 144, pp. 054103.
Link
Considering a hole transfer process D++AD+A+ or an electron transfer process D-+AD+A-, where the donor (D) and acceptor (A) fragments have nD and nA electrons, respectively, the procedure is as follows:

  • Perform KS-DFT calculations for isolated donor and acceptor fragments; collect the converged fragment orbitals:
    {ϕD1,ϕD2,,ϕDnD±1} and {ϕA1,ϕA2,,ϕAnA}

  • Löwdin-orthogonalize the occupied orbitals on two fragments. The reactant diabat (D+A or D-A) can be represented as

    |ψ¯a=1(N-1)!det{ϕ¯D1,ϕ¯D2,,ϕ¯DnD±1ϕ¯A1,ϕ¯A2,,ϕ¯AnA} (10.150)

    where “ϕ¯” denotes Löwdin-orthogonalized orbitals, and N=nD+nA. Note that the lowest unoccupied orbital where the electron is transferring to, ϕDnD in the case of HT or ϕAnA+1 in the case of ET, also needs to be made orthogonal to the space spanned by all occupied orbitals.

  • Construct the product diabat (DA+ or DA-), simply by moving the hole from ϕ¯DnD to ϕ¯AnA (HT), or the excess electron from ϕ¯DnD+1 to ϕ¯AnA+1 (ET)

    |ψ¯b=1(N-1)!det{ϕ¯D1,ϕ¯D2,,ϕ¯DnDϕ¯A1,ϕ¯A2,,ϕ¯AnA±1} (10.151)
  • Compute the electronic coupling between |ψ¯a and |ψ¯b, which is approximated by the coupling of the orthogonalized fragment orbitals through the Kohn-Sham Fock operator (built from the reactant diabat)

    ψ¯a|H^|ψ¯b{ϕDnD|f^KS|ϕAnA,HTϕDnD+1|f^KS|ϕAnA+1,ET (10.152)

The approach described above is denoted as FODFT(2n-1)@D+A (HT) / FODFT(2n+1)@D-A (ET) 1005 Schober C., Reuter K., Oberhofer H.
J. Chem. Phys.
(2016), 144, pp. 054103.
Link
as the charged fragment is explicitly taken into account when preparing the fragment orbitals and the KS Fock matrix is built from 2n1 occupied orbitals. Besides this, there are two other variants of FODFT:

  1. 1.

    FODFT(2n)@DA: 1018 Senthilkumar K. et al.
    J. Chem. Phys.
    (2003), 119, pp. 9809.
    Link
    fragment orbitals prepared with D and A both closed-shell; KS Fock operator constructed from 2n occupied orbitals

  2. 2.

    FODFT(2n-1)@DA (HT) / FODFT(2n+1)@D-A- (ET): 828 Oberhofer H., Blumberger J.
    Phys. Chem. Chem. Phys.
    (2012), 14, pp. 13846.
    Link
    fragment orbitals prepared with the system having one excess electron (DA for HT and D-A- for ET), while one occupied orbital is removed when building the KS Fock operator

According to the benchmark results, 1005 Schober C., Reuter K., Oberhofer H.
J. Chem. Phys.
(2016), 144, pp. 054103.
Link
, 740 Mao Y., Montoya-Castillo A., Markland T. E.
J. Chem. Phys.
(2019), 151, pp. 164114.
Link
FODFT(2n-1)@D+A (HT) / FODFT(2n+1)@D-A (ET) is the best-performing method, possibly because of its explicit account for charged fragments and consistent electron count in the preparation of fragment orbitals and in the construction of Fock matrix.

One issue associated with the FODFT methods is that for asymmetric systems, the results would depend on how one chooses the initial and final states for an electron or hole transfer process (e.g. D+A vs. DA+), especially for the two variants that build the Fock matrix with 2n±1 occupied orbitals. 740 Mao Y., Montoya-Castillo A., Markland T. E.
J. Chem. Phys.
(2019), 151, pp. 164114.
Link
The Q-Chem implementation of FODFT(2n-1)@DA / FODFT(2n+1)@D-A- automatically computes Hab in both ways and then reports the average, as it only requires an extra Fock matrix build. This, however, is not automatically done for FODFT(2n-1)@D+A / FODFT(2n+1)@D-A.

10.14.3.4 Job control of fragment based diabatization methods

POD, FODFT, and ALMO(MSDFT) calculations in Q-Chem require specification of fragments in the $molecule section (see Sec. 12.2). For ALMO(MSDFT) calculations, one also needs to specify the charge and multiplicity of each fragment in each diabatic state in the $almo_coupling section, where two hyphens indicate the separation of different diabats:

$almo_coupling
   charge_frag_1     mult_frag_1        !diabat 1
   charge_frag_2     mult_frag_2
   --
   charge_frag_1     mult_frag_1        !diabat 2
   charge_frag_2     mult_frag_2
$end

The current implementation of FODFT is limited to hole transfer between the HOMOs of two fragments or electron transfer between the LUMOs, and the current simplementation of ALMO(MSDFT) is limited to ground state electron or hole transfer involving two states.

FRAG_DIABAT_METHOD

FRAG_DIABAT_METHOD
       Specify fragment based diabatization method
TYPE:
       STRING
DEFAULT:
       NONE
OPTIONS:
       ALMO_MSDFT Perform ALMO(MSDFT) diabatization POD Perform projection operator diabatization (the original method) POD2_L Perform POD2 with Löwdin orthogonalization POD2_GS Perform POD2 with Grad-Schmidt orthogonalization ESID The energy-split-in-dimer method, 1143 Valeev E. F. et al.
J. Am. Chem. Soc.
(2006), 128, pp. 9882.
Link
which is equivalent to the FMO approach
introduced in Section 10.14.2.5 FODFT Calculate electronic coupling using fragment orbital DFT

RECOMMENDATION:
       NONE

FRAG_DIABAT_DOHT

FRAG_DIABAT_DOHT
       Specify whether hole or electron transfer is considered
TYPE:
       BOOLEAN
DEFAULT:
       TRUE
OPTIONS:
       TRUE Do hole transfer FALSE Do electron transfer
RECOMMENDATION:
       Need to be specified for POD and FODFT calculations

FRAG_DIABAT_PRINT

FRAG_DIABAT_PRINT
       Specify the print level for fragment based diabatization calculations
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 No additional prints 1 Print additional details
RECOMMENDATION:
       Use the default unless debug information is needed

MSDFT_METHOD

MSDFT_METHOD
       Specify the scheme for ALMO(MSDFT)
TYPE:
       INTEGER
DEFAULT:
       2
OPTIONS:
       1 The original MSDFT scheme [Eq. (10.134)] 2 The ALMO(MSDFT2) approach [Eq. (10.137)]
RECOMMENDATION:
       Use the default method. Note that the method will be automatically reset to 1 if a meta-GGA functional is requested.

MSDFT_PINV_THRESH

MSDFT_PINV_THRESH
       Set the threshold for pseudo-inverse of the interstate overlap
TYPE:
       INTEGER
DEFAULT:
       4
OPTIONS:
       n Set the threshold to 10-n
RECOMMENDATION:
       Use the default value

POD_MULTI_PAIRS

POD_MULTI_PAIRS
       Calculate the couplings between multiple pairs of donor and acceptor orbitals in POD
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Calculate the couplings between multiple pairs of orbitals FALSE Only calculate the D(HOMO)–A(HOMO) coupling (for HT) or D(LUMO)–A(LUMO) coupling (for ET)
RECOMMENDATION:
       None

POD_WINDOW

POD_WINDOW
       Specify the number of donor and acceptor orbitals when couplings between multiple pairs are requested
TYPE:
       INTEGER
DEFAULT:
       5
OPTIONS:
       n Including n frontier occupied orbitals (from HOMO-n+1 to HOMO) and n frontier virtual orbitals (from LUMO to LUMO+n-1) for both donor and acceptor
RECOMMENDATION:
       None

FODFT_METHOD

FODFT_METHOD
       Specify the flavor of FODFT method
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       1 FODFT(2n-1)@D+A (HT) / FODFT(2n+1)@D-A (ET) 2 FODFT(2n)@DA 3 FODFT(2n-1)@DA (HT) / FODFT(2n+1)@D-A- (ET)
RECOMMENDATION:
       The default approach shows the best overall performance

FODFT_DONOR

FODFT_DONOR
       Specify the donor fragment in FODFT calculation
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       1 First fragment as donor 2 Second fragment as donor
RECOMMENDATION:
       With FODFT_METHOD = 1, the charged fragment needs to be the donor fragment

Example 10.50  ALMO(MSDFT2) calculation for hole transfer in ethylene dimer

$molecule
1 2
--
1 2
  C      0.000000    0.000000    0.000000
  C      1.332000    0.000000    0.000000
  H     -0.574301    0.000000   -0.928785
  H     -0.574301    0.000000    0.928785
  H      1.906301    0.000000    0.928785
  H      1.906301    0.000000   -0.928785
--
0 1
  C     -0.000000    4.000000    0.000000
  C      1.332000    4.000000   -0.000000
  H     -0.574301    4.000000    0.928785
  H     -0.574301    4.000000   -0.928785
  H      1.906301    4.000000   -0.928785
  H      1.906301    4.000000    0.928785
$end

$rem
   METHOD               PBE0
   BASIS                6-31+G(D)
   UNRESTRICTED         TRUE
   THRESH               14
   SCF_CONVERGENCE      8
   SYMMETRY             FALSE
   SYM_IGNORE           TRUE
   SCFMI_MODE           1
   FRGM_METHOD          STOLL
   FRAG_DIABAT_METHOD   ALMO_MSDFT
$end

$almo_coupling
  1  2
  0  1
  --
  0  1
  1  2
$end

View output

Example 10.51  POD diabatization method for hole transfer in ethylene dimer. FRAG_DIABAT_METHOD can be set to POD2_L or POD2_GS for POD2 diabatization methods.

$molecule
0 1
--
0 1
  C      0.000000    0.000000    0.000000
  C      1.332000    0.000000    0.000000
  H     -0.574301    0.000000   -0.928785
  H     -0.574301    0.000000    0.928785
  H      1.906301    0.000000    0.928785
  H      1.906301    0.000000   -0.928785
--
0 1
  C     -0.000000    4.000000    0.000000
  C      1.332000    4.000000   -0.000000
  H     -0.574301    4.000000    0.928785
  H     -0.574301    4.000000   -0.928785
  H      1.906301    4.000000   -0.928785
  H      1.906301    4.000000    0.928785
$end

$rem
   METHOD               lrc-wpbeh
   BASIS                6-31+g(d)
   FRAG_DIABAT_METHOD   pod
   SCF_CONVERGENCE      8
   THRESH               14
   SYMMETRY             false
   SYM_IGNORE           true
$end

View output

Example 10.52  FODFT(2n-1)@D+A calculation for hole transfer in ethylene dimer

$molecule
1 2
--
1 2
  C      0.000000    0.000000    0.000000
  C      1.332000    0.000000    0.000000
  H     -0.574301    0.000000   -0.928785
  H     -0.574301    0.000000    0.928785
  H      1.906301    0.000000    0.928785
  H      1.906301    0.000000   -0.928785
--
0 1
  C     -0.000000    4.000000    0.000000
  C      1.332000    4.000000   -0.000000
  H     -0.574301    4.000000    0.928785
  H     -0.574301    4.000000   -0.928785
  H      1.906301    4.000000   -0.928785
  H      1.906301    4.000000    0.928785
$end

$rem
   METHOD               wb97x-d
   BASIS                6-31+g(d)
   UNRESTRICTED         true
   SCF_CONVERGENCE      8
   THRESH               14
   SYMMETRY             false
   SYM_IGNORE           true
   FRAG_DIABAT_METHOD   fodft
   FODFT_METHOD         1
$end

View output