diff --git a/README.html b/README.html index 95de81c..edec5af 100644 --- a/README.html +++ b/README.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + TREXIO source code documentation @@ -347,7 +347,7 @@ and bug reports should be submitted at

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate

diff --git a/examples.html b/examples.html index 19e91d7..e44191a 100644 --- a/examples.html +++ b/examples.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Examples @@ -333,24 +333,24 @@ for the JavaScript code in this tag.

Table of Contents

-
-

1 Accessing sparse quantities

+
+

1 Accessing sparse quantities

-
-

1.1 Fortran

+
+

1.1 Fortran

program print_energy
@@ -385,25 +385,23 @@ This program computes the energy as:
 
 

 \[
-   E = E_{\text{NN}} + \sum_{ij} D_{ij}\, \langle i | h | j \rangle\,
-   +\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle i j | k l
+   E = E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle j | h | i \rangle\,
+   +\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle k l | i j
    \rangle\; \textrm{ with } \; 0 < i,j,k,l \le n
    \]
-

-
-

 One needs to read from the TREXIO file:
 

 
 

 
\(n\)
The number of molecular orbitals

 
\(E_{\text{NN}}\)
The nuclear repulsion energy

-
\(D_{ij}\)
The one-body reduced density matrix

-
\(\langle i |h| j \rangle\)
The one-electron Hamiltonian integrals

+
\(\gamma_{ij}\)
The one-body reduced density matrix

+
\(\langle j |h| i \rangle\)
The one-electron Hamiltonian integrals

 
\(\Gamma_{ijkl}\)
The two-body reduced density matrix

-
\(\langle i j | k l \rangle\)
The electron repulsion integrals

+
\(\langle k l  | i j \rangle\)
The electron repulsion integrals

 

 
+
 

 
integer                       :: n
 double precision              :: E, E_nn
@@ -413,8 +411,8 @@ One needs to read from the TREXIO file:
-
-

1.1.1 Declare Temporary variables

+
+

1.1.1 Declare Temporary variables

integer                       :: i, j, k, l, m
@@ -429,8 +427,8 @@ One needs to read from the TREXIO file:
-
-

1.1.2 Obtain the name of the TREXIO file from the command line, and open it for reading

+
+

1.1.2 Obtain the name of the TREXIO file from the command line, and open it for reading

call getarg(1, filename)
@@ -446,8 +444,8 @@ f = trexio_open (filename, 'r', TREXIO_HDF5
-
-

1.1.3 Read the nuclear repulsion energy

+
+

1.1.3 Read the nuclear repulsion energy

rc = trexio_read_nucleus_repulsion(f, E_nn)
@@ -461,8 +459,8 @@ f = trexio_open (filename, 'r', TREXIO_HDF5
-
-

1.1.4 Read the number of molecular orbitals

+
+

1.1.4 Read the number of molecular orbitals

rc = trexio_read_mo_num(f, n)
@@ -476,8 +474,8 @@ f = trexio_open (filename, 'r', TREXIO_HDF5
-
-

1.1.5 Allocate memory

+
+

1.1.5 Allocate memory

allocate( D(n,n), h0(n,n) )
@@ -489,8 +487,8 @@ W(:,:,:,:) = 0.d0
-
-

1.1.6 Read one-electron quantities

+
+

1.1.6 Read one-electron quantities

rc = trexio_has_mo_1e_int_core_hamiltonian(f)
@@ -522,8 +520,8 @@ rc = trexio_read_rdm_1e(f, D)
-
-

1.1.7 Read two-electron quantities

+
+

1.1.7 Read two-electron quantities

Reading is done with OpenMP. Each thread reads its own buffer, and @@ -539,8 +537,8 @@ to be protected in the critical section when modified.

-
-
1.1.7.1 Electron repulsion integrals
+
+
1.1.7.1 Electron repulsion integrals
rc = trexio_has_mo_2e_int_eri(f)
@@ -589,8 +587,8 @@ icount = BUFSIZE
-
-
1.1.7.2 Reduced density matrix
+
+
1.1.7.2 Reduced density matrix
rc = trexio_has_rdm_2e(f)
@@ -634,11 +632,23 @@ icount = bufsize
-
-

1.1.8 Compute the energy

+
+

1.1.8 Compute the energy

-As \((n,m)\) 2D arrays are stored in memory as \((\n times m)\) 1D +When the orbitals are real, we can use +

+\begin{eqnarray*} +E &=& E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle j | h | i \rangle\, ++\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle k l | i j +\rangle \\ + &=& E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle i | h | j \rangle\, ++\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle i j | k l +\rangle \\ +\end{eqnarray*} + +

+As \((n,m)\) 2D arrays are stored in memory as \((n \times m)\) 1D arrays, we could pass the matrices to the ddot BLAS function to perform the summations in a single call for the 1-electron quantities. Instead, we prefer to interleave the 1-electron (negative) and @@ -669,8 +679,8 @@ E = E + E_nn

-
-

1.1.9 Terminate

+
+

1.1.9 Terminate

  deallocate( D, h0, G, W )
@@ -685,7 +695,7 @@ E = E + E_nn

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate

diff --git a/index.html b/index.html index 95de81c..edec5af 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + TREXIO source code documentation @@ -347,7 +347,7 @@ and bug reports should be submitted at

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate

diff --git a/templator_front.html b/templator_front.html index 227fa12..665d93f 100644 --- a/templator_front.html +++ b/templator_front.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Front end API @@ -333,131 +333,131 @@ for the JavaScript code in this tag.

Table of Contents

@@ -465,8 +465,8 @@ for the JavaScript code in this tag. break;

-
-

1 Coding conventions

+
+

1 Coding conventions

  • integer types will be defined using types given in stdint.h
    • @@ -481,8 +481,8 @@ break;
-
-

1.1 Memory allocation

+
+

1.1 Memory allocation

Memory allocation of structures can be facilitated by using the @@ -517,8 +517,8 @@ The maximum string size for the filenames is 4096 characters.

-
-

2 Front end

+
+

2 Front end

All calls to TREXIO are thread-safe. @@ -526,10 +526,10 @@ TREXIO front end is modular, which simplifies implementation of new back ends.

-
-

2.1 Error handling

+
+

2.1 Error handling

- +
@@ -770,8 +770,8 @@ and the corresponding message are not propagated to the source code. -
-

2.1.1 Decoding errors

+
+

2.1.1 Decoding errors

The trexio_string_of_error converts an exit code into a string. The @@ -797,8 +797,8 @@ and the corresponding message are not propagated to the source code.

-
-
2.1.1.1 C source code
+
+
2.1.1.1 C source code
const char*
@@ -909,8 +909,8 @@ and the corresponding message are not propagated to the source code.
-
-
2.1.1.2 Fortran interface
+
+
2.1.1.2 Fortran interface
interface
@@ -926,8 +926,8 @@ and the corresponding message are not propagated to the source code.
-
-
2.1.1.3 Python interface
+
+
2.1.1.3 Python interface
class Error(Exception):
@@ -966,8 +966,8 @@ and the corresponding message are not propagated to the source code.
-
-

2.2 Back ends

+
+

2.2 Back ends

TREXIO has several back ends: @@ -991,8 +991,8 @@ lines that correspond to the TREXIO_JSON back end (not implemented

-
-

2.2.1 C

+
+

2.2.1 C

typedef int32_t back_end_t;
@@ -1035,8 +1035,8 @@ This is useful due to the fact that HDF5 back end can be disabled at configure s
-
-

2.2.2 Fortran

+
+

2.2.2 Fortran

  integer(trexio_backend), parameter :: TREXIO_HDF5 = 0
@@ -1062,8 +1062,8 @@ The function below is a Fortran interface for the aforementioned C-compatible
-
-

2.2.3 Python

+
+

2.2.3 Python

# define TREXIO back ends
@@ -1077,8 +1077,8 @@ The function below is a Fortran interface for the aforementioned C-compatible
-
-

2.3 Read/write behavior

+
+

2.3 Read/write behavior

Every time a reading function is called, the data is read from the @@ -1106,8 +1106,8 @@ concurrent programs, the behavior is not specified.

-
-

2.4 TREXIO file type

+
+

2.4 TREXIO file type

trexio_s is the the main type for TREXIO files, visible to the users @@ -1141,8 +1141,8 @@ TREXIO files will have as a first argument the TREXIO file handle.

-
-

2.4.1 TREXIOFile Python class

+
+

2.4.1 TREXIOFile Python class

class File:
@@ -1215,8 +1215,8 @@ TREXIO files will have as a first argument the TREXIO file handle.
-
-

2.5 Polymorphism of the file handle

+
+

2.5 Polymorphism of the file handle

Polymorphism of the trexio_t type is handled by ensuring that the @@ -1235,8 +1235,8 @@ corresponding types for all back ends can be safely casted to

-
-

2.6 File opening

+
+

2.6 File opening

trexio_open creates a new TREXIO file or opens existing one. @@ -1275,8 +1275,8 @@ renaming the .txt data files.

-
-

2.6.1 C

+
+

2.6.1 C

trexio_t*
@@ -1463,8 +1463,8 @@ renaming the .txt data files.
-
-

2.6.2 Fortran

+
+

2.6.2 Fortran

interface
@@ -1482,8 +1482,8 @@ renaming the .txt data files.
-
-

2.6.3 Python

+
+

2.6.3 Python

def open(file_name: str, mode: str, back_end: int):
@@ -1531,8 +1531,8 @@ renaming the .txt data files.
-
-

2.6.4 Zero-based versus one-based arrays of indices

+
+

2.6.4 Zero-based versus one-based arrays of indices

Because arrays are zero-based in Fortran, we need to set a flag to @@ -1565,8 +1565,8 @@ know if we need to shift by 1 arrays of indices.

-
-

2.7 File closing

+
+

2.7 File closing

trexio_close closes an existing trexio_t file. @@ -1583,8 +1583,8 @@ output:

-
-

2.7.1 C

+
+

2.7.1 C

trexio_exit_code
@@ -1665,8 +1665,8 @@ output:
-
-

2.7.2 Fortran

+
+

2.7.2 Fortran

interface
@@ -1680,8 +1680,8 @@ output:
-
-

2.7.3 Python

+
+

2.7.3 Python

def close(trexio_file):
@@ -1703,12 +1703,12 @@ output:
-
-

3 Templates for front end

+
+

3 Templates for front end

-
-

3.1 Description

+
+

3.1 Description

Consider the following block of trex.json: @@ -1929,12 +1929,12 @@ value will result in TREXIO_INVALID_ARG_2 exit code.

-
-

3.2 Templates for front end has/read/write a single numerical attribute

+
+

3.2 Templates for front end has/read/write a single numerical attribute

-
-

3.2.1 Introduction

+
+

3.2.1 Introduction

This section concerns API calls related to numerical attributes, @@ -2005,8 +2005,8 @@ namely single value of int/float types.

-
-

3.2.2 C templates for front end

+
+

3.2.2 C templates for front end

The C templates that correspond to each of the abovementioned @@ -2020,12 +2020,12 @@ precision (see Table above).

-
-
3.2.2.1 Function declarations
+
+
3.2.2.1 Function declarations
-
-
3.2.2.2 Source code for double precision functions
+
+
3.2.2.2 Source code for double precision functions
trexio_exit_code
@@ -2088,8 +2088,8 @@ precision (see Table above).
-
-
3.2.2.3 Source code for single precision functions
+
+
3.2.2.3 Source code for single precision functions
trexio_exit_code
@@ -2164,8 +2164,8 @@ precision (see Table above).
-
-
3.2.2.4 Source code for default functions
+
+
3.2.2.4 Source code for default functions
trexio_exit_code
@@ -2220,8 +2220,8 @@ precision (see Table above).
-
-

3.2.3 Fortran templates for front end

+
+

3.2.3 Fortran templates for front end

The Fortran templates that provide an access to the C API calls from Fortran. @@ -2306,8 +2306,8 @@ These templates are based on the use of iso_c_binding. Pointers hav

-
-

3.2.4 Python templates for front end

+
+

3.2.4 Python templates for front end

def write_$group_num$(trexio_file, num_w: $group_num_py_dtype$) -> None:
@@ -2392,12 +2392,12 @@ These templates are based on the use of iso_c_binding. Pointers hav
-
-

3.3 Templates for front end has/read/write a dataset of numerical data

+
+

3.3 Templates for front end has/read/write a dataset of numerical data

-
-

3.3.1 Introduction

+
+

3.3.1 Introduction

This section concerns API calls related to datasets. @@ -2479,8 +2479,8 @@ This section concerns API calls related to datasets.

-
-

3.3.2 C templates for front end

+
+

3.3.2 C templates for front end

The C templates that correspond to each of the abovementioned functions can be found below. @@ -2491,12 +2491,12 @@ The basic (non-suffixed) API call on datasets deals with double precision (see T

-
-
3.3.2.1 Function declarations
+
+
3.3.2.1 Function declarations
-
-
3.3.2.2 Source code for double precision functions
+
+
3.3.2.2 Source code for double precision functions
trexio_exit_code
@@ -2659,8 +2659,8 @@ The basic (non-suffixed) API call on datasets deals with double precision (see T
-
-
3.3.2.3 Source code for single precision functions
+
+
3.3.2.3 Source code for single precision functions
trexio_exit_code
@@ -2811,11 +2811,11 @@ The basic (non-suffixed) API call on datasets deals with double precision (see T
-
-
3.3.2.4 Source code for memory-safe functions
+
+
3.3.2.4 Source code for memory-safe functions
-
trexio_exit_code rc;
+
trexio_exit_code rc;
 int64_t $group_dset_dim$ = 0;
 
 /* Error handling for this call is added by the generator */
@@ -2971,8 +2971,8 @@ rc = trexio_read_$group_dset_dim$_64(file, &($group_dset_dim$));
-
-
3.3.2.5 Source code for default functions
+
+
3.3.2.5 Source code for default functions
trexio_exit_code
@@ -3047,8 +3047,8 @@ rc = trexio_read_$group_dset_dim$_64(file, &($group_dset_dim$));
-
-

3.3.3 Fortran templates for front end

+
+

3.3.3 Fortran templates for front end

The Fortran templates that provide an access to the C API calls from Fortran. @@ -3133,8 +3133,8 @@ These templates are based on the use of iso_c_binding. Pointers hav

-
-

3.3.4 Python templates for front end

+
+

3.3.4 Python templates for front end

def write_$group_dset$(trexio_file, dset_w) -> None:
@@ -3329,12 +3329,12 @@ These templates are based on the use of iso_c_binding. Pointers hav
-
-

3.4 Templates for front end has/read/write a dataset of sparse data

+
+

3.4 Templates for front end has/read/write a dataset of sparse data

-
-

3.4.1 Introduction

+
+

3.4.1 Introduction

Sparse data structures are used typically for large tensors such as @@ -3495,16 +3495,16 @@ This section concerns API calls related to sparse data structures.

-
-

3.4.2 C templates for front end

+
+

3.4.2 C templates for front end

-
-
3.4.2.1 Function declarations
+
+
3.4.2.1 Function declarations
-
-
3.4.2.2 Source code for default functions
+
+
3.4.2.2 Source code for default functions
trexio_exit_code trexio_read_safe_$group_dset$(trexio_t* const file,
@@ -3779,8 +3779,8 @@ This section concerns API calls related to sparse data structures.
-
-

3.4.3 Fortran templates for front end

+
+

3.4.3 Fortran templates for front end

The Fortran templates that provide an access to the C API calls from Fortran. @@ -3875,8 +3875,8 @@ These templates are based on the use of iso_c_binding. Pointers hav

-
-

3.4.4 Python templates for front end

+
+

3.4.4 Python templates for front end

def write_$group_dset$(trexio_file: File, offset_file: int, buffer_size: int, indices: list, values: list) -> None:
@@ -4097,12 +4097,12 @@ These templates are based on the use of iso_c_binding. Pointers hav
-
-

3.5 Templates for front end has/read/write a dataset of strings

+
+

3.5 Templates for front end has/read/write a dataset of strings

-
-

3.5.1 Introduction

+
+

3.5.1 Introduction

This section concerns API calls related to datasets of strings. @@ -4142,8 +4142,8 @@ This section concerns API calls related to datasets of strings.

-
-

3.5.2 C templates for front end

+
+

3.5.2 C templates for front end

First parameter is the TREXIO file handle. Second parameter is the variable to be written/read @@ -4151,12 +4151,12 @@ to/from the TREXIO file (except for trexio_has_ functi

-
-
3.5.2.1 Function declarations
+
+
3.5.2.1 Function declarations
-
-
3.5.2.2 Source code for default functions
+
+
3.5.2.2 Source code for default functions
trexio_exit_code
@@ -4406,8 +4406,8 @@ to/from the TREXIO file (except for trexio_has_ functi
-
-

3.5.3 Fortran templates for front end

+
+

3.5.3 Fortran templates for front end

The Fortran templates that provide an access to the C API calls from Fortran. @@ -4503,8 +4503,8 @@ These templates are based on the use of iso_c_binding. Pointers hav

-
-

3.5.4 Python templates for front end

+
+

3.5.4 Python templates for front end

def write_$group_dset$(trexio_file, dset_w: list) -> None:
@@ -4620,12 +4620,12 @@ These templates are based on the use of iso_c_binding. Pointers hav
-
-

3.6 Templates for front end has/read/write a single string attribute

+
+

3.6 Templates for front end has/read/write a single string attribute

-
-

3.6.1 Introduction

+
+

3.6.1 Introduction

This section concerns API calls related to string attributes. @@ -4665,16 +4665,16 @@ This section concerns API calls related to string attributes.

-
-

3.6.2 C templates for front end

+
+

3.6.2 C templates for front end

-
-
3.6.2.1 Function declarations
+
+
3.6.2.1 Function declarations
-
-
3.6.2.2 Source code for default functions
+
+
3.6.2.2 Source code for default functions
trexio_exit_code
@@ -4778,8 +4778,8 @@ This section concerns API calls related to string attributes.
-
-

3.6.3 Fortran templates for front end

+
+

3.6.3 Fortran templates for front end

The Fortran templates that provide an access to the C API calls from Fortran. @@ -4856,8 +4856,8 @@ These templates are based on the use of iso_c_binding. Pointers hav

-
-

3.6.4 Python templates for front end

+
+

3.6.4 Python templates for front end

def write_$group_str$(trexio_file, str_w: str) -> None:
@@ -4947,8 +4947,8 @@ These templates are based on the use of iso_c_binding. Pointers hav
-
-

4 Fortran helper/wrapper functions

+
+

4 Fortran helper/wrapper functions

The function below adapts the original C-based trexio_open for Fortran. @@ -5083,7 +5083,7 @@ two code are identical, i.e. if the assert statement pass.

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate

diff --git a/templator_hdf5.html b/templator_hdf5.html index 90c1778..62d9ed4 100644 --- a/templator_hdf5.html +++ b/templator_hdf5.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + HDF5 back end @@ -311,29 +311,29 @@ for the JavaScript code in this tag.

Table of Contents

-
-

1 HDF5 back end

+
+

1 HDF5 back end

-
-

1.1 Template for HDF5 definitions

+
+

1.1 Template for HDF5 definitions

#define $GROUP$_GROUP_NAME          "$group$"
@@ -345,8 +345,8 @@ for the JavaScript code in this tag.
-
-

1.2 Template for HDF5 structures

+
+

1.2 Template for HDF5 structures

typedef struct trexio_hdf5_s {
@@ -360,8 +360,8 @@ for the JavaScript code in this tag.
-
-

1.3 Template for HDF5 init/deinit

+
+

1.3 Template for HDF5 init/deinit

trexio_exit_code
@@ -441,8 +441,8 @@ for the JavaScript code in this tag.
-
-

1.4 Template for HDF5 has/read/write the numerical attribute

+
+

1.4 Template for HDF5 has/read/write the numerical attribute

trexio_exit_code
@@ -536,8 +536,8 @@ for the JavaScript code in this tag.
-
-

1.5 Template for HDF5 has/read/write the dataset of numerical data

+
+

1.5 Template for HDF5 has/read/write the dataset of numerical data

trexio_exit_code
@@ -659,8 +659,8 @@ for the JavaScript code in this tag.
-
-

1.6 Template for HDF5 has/read/write the dataset of sparse data

+
+

1.6 Template for HDF5 has/read/write the dataset of sparse data

Sparse data is stored using extensible datasets of HDF5. Extensibility is required @@ -861,8 +861,8 @@ due to the fact that the sparse data will be written in chunks of user-defined s

-
-

1.7 Template for HDF5 has/read/write the dataset of strings

+
+

1.7 Template for HDF5 has/read/write the dataset of strings

trexio_exit_code
@@ -1066,8 +1066,8 @@ due to the fact that the sparse data will be written in chunks of user-defined s
-
-

1.8 Template for HDF5 has/read/write the string attribute

+
+

1.8 Template for HDF5 has/read/write the string attribute

trexio_exit_code
@@ -1189,8 +1189,8 @@ due to the fact that the sparse data will be written in chunks of user-defined s
-
-

1.9 Helper functions

+
+

1.9 Helper functions

trexio_exit_code
@@ -1452,7 +1452,7 @@ due to the fact that the sparse data will be written in chunks of user-defined s

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate

diff --git a/templator_text.html b/templator_text.html index e4b13c2..5267ff0 100644 --- a/templator_text.html +++ b/templator_text.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + TEXT back end @@ -311,28 +311,28 @@ for the JavaScript code in this tag.

Table of Contents

-
-

1 TEXT back end

+
+

1 TEXT back end

The "file" produced by the text back end is a directory with one @@ -353,8 +353,8 @@ The file is written when closed, or when the flush function is called.

-
-

1.1 Template for group-related structures in text back end

+
+

1.1 Template for group-related structures in text back end

typedef struct $group$_s {
@@ -373,8 +373,8 @@ The file is written when closed, or when the flush function is called.
-
-

1.2 Template for general structure in text back end

+
+

1.2 Template for general structure in text back end

typedef struct trexio_text_s {
@@ -387,8 +387,8 @@ The file is written when closed, or when the flush function is called.
-
-

1.3 Initialize function (constant part)

+
+

1.3 Initialize function (constant part)

trexio_exit_code
@@ -519,8 +519,8 @@ The file is written when closed, or when the flush function is called.
-
-

1.4 Deinitialize function (templated part)

+
+

1.4 Deinitialize function (templated part)

trexio_exit_code
@@ -542,8 +542,8 @@ The file is written when closed, or when the flush function is called.
-
-

1.5 Template for text read struct

+
+

1.5 Template for text read struct

$group$_t*
@@ -835,8 +835,8 @@ trexio_text_read_$group$ (trexio_text_t*
-
-

1.6 Template for text flush struct

+
+

1.6 Template for text flush struct

trexio_exit_code
@@ -901,8 +901,8 @@ trexio_text_read_$group$ (trexio_text_t*
-
-

1.7 Template for text free memory

+
+

1.7 Template for text free memory

Memory is allocated when reading. The following function frees memory. @@ -947,8 +947,8 @@ Memory is allocated when reading. The following function frees memory.

-
-

1.8 Template for has/read/write the numerical attribute

+
+

1.8 Template for has/read/write the numerical attribute

trexio_exit_code
@@ -1011,8 +1011,8 @@ Memory is allocated when reading. The following function frees memory.
-
-

1.9 Template for has/read/write the dataset of numerical data

+
+

1.9 Template for has/read/write the dataset of numerical data

The group_dset array is assumed allocated with the appropriate size. @@ -1108,8 +1108,8 @@ The group_dset array is assumed allocated with the appropriate size

-
-

1.10 Template for has/read/write the dataset of strings

+
+

1.10 Template for has/read/write the dataset of strings

The group_dset array is assumed allocated with the appropriate size. @@ -1210,8 +1210,8 @@ The group_dset array is assumed allocated with the appropriate size

-
-

1.11 Template for has/read/write the string attribute

+
+

1.11 Template for has/read/write the string attribute

trexio_exit_code
@@ -1285,8 +1285,8 @@ The group_dset array is assumed allocated with the appropriate size
-
-

1.12 Template for has/read/write the dataset of sparse data

+
+

1.12 Template for has/read/write the dataset of sparse data

Each sparse array is stored in a separate .txt file due to the fact that sparse I/O has to be decoupled @@ -1563,7 +1563,7 @@ User provides indices and values of the sparse array as two separate variables.

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate

diff --git a/trex.html b/trex.html index cd6c954..6acc055 100644 --- a/trex.html +++ b/trex.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + TREX Configuration file @@ -333,33 +333,33 @@ for the JavaScript code in this tag.

Table of Contents

@@ -409,8 +409,8 @@ fetched using multiple function calls to perform I/O on buffers.

-
-

1 Metadata (metadata group)

+
+

1 Metadata (metadata group)

As we expect our files to be archived in open-data repositories, we @@ -420,7 +420,7 @@ which have participated to the creation of the file, a list of authors of the file, and a textual description.

-
+
@@ -487,15 +487,15 @@ authors of the file, and a textual description. -
-

2 Electron (electron group)

+
+

2 Electron (electron group)

We consider wave functions expressed in the spin-free formalism, where the number of ↑ and ↓ electrons is fixed.

-
+
@@ -534,15 +534,15 @@ the number of ↑ and ↓ electrons is fixed. -
-

3 Nucleus (nucleus group)

+
+

3 Nucleus (nucleus group)

The nuclei are considered as fixed point charges. Coordinates are given in Cartesian \((x,y,z)\) format.

-
+
@@ -609,8 +609,8 @@ given in Cartesian \((x,y,z)\) format. -
-

4 Effective core potentials (ecp group)

+
+

4 Effective core potentials (ecp group)

An effective core potential (ECP) \(V_A^{\text{ECP}}\) replacing the @@ -643,7 +643,7 @@ The functions \(V_{A\ell}\) are parameterized as: See http://dx.doi.org/10.1063/1.4984046 or https://doi.org/10.1063/1.5121006 for more info.

-
+
@@ -741,8 +741,8 @@ The latter causes issues when written before ang_mom in the TREXIO

-
-

4.1 Example

+
+

4.1 Example

For example, consider H2 molecule with the following @@ -805,8 +805,8 @@ power = [

-
-

5 Basis set (basis group)

+
+

5 Basis set (basis group)

We consider here basis functions centered on nuclei. Hence, we enable @@ -859,7 +859,7 @@ If the the basis function is not considered normalized, \(\mathcal{N}_s=1\). All the basis set parameters are stored in one-dimensional arrays:

-
+
@@ -953,8 +953,8 @@ All the basis set parameters are stored in one-dimensional arrays:
-
-

5.1 Example

+
+

5.1 Example

For example, consider H2 with the following basis set (in GAMESS @@ -1032,8 +1032,8 @@ prim_factor =

-
-

6 Atomic orbitals (ao group)

+
+

6 Atomic orbitals (ao group)

Going from the atomic basis set to AOs implies a systematic @@ -1085,13 +1085,13 @@ shell, as in the GAMESS convention where

In such a case, one should set the normalization of the shell (in -the Basis set section) to \(\mathcal{N}_{z^2}\), which is the +the Basis set section) to \(\mathcal{N}_{z^2}\), which is the normalization factor of the atomic orbitals in spherical coordinates. The normalization factor of the \(xy\) function which should be introduced here should be \(\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}\).

- +
@@ -1143,8 +1143,8 @@ introduced here should be \(\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}\).
-
-

6.1 One-electron integrals (ao_1e_int group)

+
+

6.1 One-electron integrals (ao_1e_int group)

  • \[ \hat{V}_{\text{ne}} = \sum_{A=1}^{N_\text{nucl}} @@ -1162,7 +1162,7 @@ The one-electron integrals for a one-electron operator \(\hat{O}\) are over atomic orbitals.

    - +
    @@ -1229,8 +1229,8 @@ over atomic orbitals. -
    -

    6.2 Two-electron integrals (ao_2e_int group)

    +
    +

    6.2 Two-electron integrals (ao_2e_int group)

    The two-electron integrals for a two-electron operator \(\hat{O}\) are @@ -1251,7 +1251,7 @@ notation. \mathbf{r}_j \vert)}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron long range potential -

    +
    @@ -1291,10 +1291,10 @@ notation. -
    -

    7 Molecular orbitals (mo group)

    +
    +

    7 Molecular orbitals (mo group)

    -
    +
    @@ -1360,8 +1360,8 @@ notation.
-
-

7.1 One-electron integrals (mo_1e_int group)

+
+

7.1 One-electron integrals (mo_1e_int group)

The operators as the same as those defined in the @@ -1369,7 +1369,7 @@ The operators as the same as those defined in the the basis of molecular orbitals.

- +
@@ -1436,8 +1436,8 @@ the basis of molecular orbitals. -
-

7.2 Two-electron integrals (mo_2e_int group)

+
+

7.2 Two-electron integrals (mo_2e_int group)

The operators as the same as those defined in the @@ -1445,7 +1445,7 @@ The operators as the same as those defined in the the basis of molecular orbitals.

-
+
@@ -1485,13 +1485,64 @@ the basis of molecular orbitals. -
-

8 TODO Slater determinants

+
+

8 TODO Slater determinants

-
-

9 Reduced density matrices (rdm group)

+
+

9 Reduced density matrices (rdm group)

-
+

+The reduced density matrices are defined in the basis of molecular +orbitals. +

+ +

+The $↑$-spin and $↓$-spin components of the one-body +density matrix are given by +

+\begin{eqnarray*} + \gamma_{ij}^{\uparrow} &=& \langle \Psi | a^{\dagger}_{j\alpha}\, a_{i\alpha} | \Psi \rangle \\ + \gamma_{ij}^{\downarrow} &=& \langle \Psi | a^{\dagger}_{j\beta} \, a_{i\beta} | \Psi \rangle +\end{eqnarray*} +

+and the spin-summed one-body density matrix is +\[ + \gamma_{ij} = \gamma^{\uparrow}_{ij} + \gamma^{\downarrow}_{ij} + \] +

+ +

+The \(\uparrow \uparrow\), \(\downarrow \downarrow\), \(\uparrow \downarrow\), \(\downarrow \uparrow\) +components of the two-body density matrix are given by +

+\begin{eqnarray*} + \Gamma_{ijkl}^{\uparrow \uparrow} &=& + \langle \Psi | a^{\dagger}_{k\alpha}\, a^{\dagger}_{l\alpha} a_{j\alpha}\, a_{i\alpha} | \Psi \rangle \\ + \Gamma_{ijkl}^{\downarrow \downarrow} &=& + \langle \Psi | a^{\dagger}_{k\beta}\, a^{\dagger}_{l\beta} a_{j\beta}\, a_{i\beta} | \Psi \rangle \\ + \Gamma_{ijkl}^{\uparrow \downarrow} &=& + +\langle \Psi | a^{\dagger}_{k\alpha}\, a^{\dagger}_{l\beta} a_{j\beta}\, a_{i\alpha} | \Psi \rangle \\ + \Gamma_{ijkl}^{\downarrow \uparrow} &=& + \langle \Psi | a^{\dagger}_{k\beta}\, a^{\dagger}_{l\alpha} a_{j\alpha}\, a_{i\beta} | \Psi \rangle \\ +\end{eqnarray*} +

+and the spin-summed one-body density matrix is +\[ + \Gamma_{ijkl} = \Gamma_{ijkl}^{\uparrow \uparrow} + + \Gamma_{ijkl}^{\downarrow \downarrow} + \Gamma_{ijkl}^{\uparrow \downarrow} + \Gamma_{ijkl}^{\downarrow \uparrow} + \] +

+ +

+The total energy can be computed as: +\[ + E = E_{\text{NN}} + \sum_{ij} \gamma_{ij} \langle j|h|i \rangle + + \frac{1}{2} \sum_{ijlk} \Gamma_{ijkl} \langle k l | i j \rangle + \] +

+ +
@@ -1560,6 +1611,13 @@ the basis of molecular orbitals. + + + + + + +
(mo.num, mo.num, mo.num, mo.num) ↑↓ component of the two-body reduced density matrix
2e_dnupfloat sparse(mo.num, mo.num, mo.num, mo.num)↓↑ component of the two-body reduced density matrix
@@ -1567,7 +1625,7 @@ the basis of molecular orbitals.

Author: TREX-CoE

-

Created: 2022-01-07 Fri 18:41

+

Created: 2022-01-10 Mon 09:28

Validate