From b09cff2ff77e10cd351e5fdbdb80a4bab9c46ef0 Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Wed, 12 Feb 2020 12:25:24 +0100
Subject: [PATCH] QP solutions
---
examples/basis.BF.cc-pvqz | 98 +++++++++++++++++++++++
examples/basis.Be.cc-pvdz | 30 +++++++
examples/basis.CO.cc-pvqz | 98 +++++++++++++++++++++++
examples/basis.F2.cc-pvqz | 98 +++++++++++++++++++++++
examples/basis.H2.cc-pvqz | 46 +++++++++++
examples/basis.HCl.cc-pvqz | 108 +++++++++++++++++++++++++
examples/basis.He.cc-pvdz | 9 +++
examples/basis.LiF.cc-pvqz | 98 +++++++++++++++++++++++
examples/basis.LiH.cc-pvqz | 72 +++++++++++++++++
examples/basis.N2.cc-pvqz | 98 +++++++++++++++++++++++
examples/molecule.BF | 2 +-
examples/molecule.CO | 2 +-
examples/molecule.F2 | 2 +-
examples/molecule.HCl | 2 +-
examples/molecule.LiF | 2 +-
examples/molecule.LiH | 2 +-
examples/molecule.N2 | 2 +-
input/basis | 98 ++++-------------------
input/methods | 4 +-
input/molecule | 4 +-
input/molecule.xyz | 2 +-
input/options | 4 +-
input/weight | 98 ++++-------------------
scan_LiF.sh | 6 +-
scan_LiH.sh | 4 +-
scan_N2.sh | 4 +-
src/QuAcK/G0W0.f90 | 6 +-
src/QuAcK/QP_roots.f90 | 156 +++++++++++++++++++++++++++++++++++++
src/QuAcK/RPA.f90 | 44 +++++------
src/QuAcK/SigmaC.f90 | 58 ++++++++++++++
src/QuAcK/dSigmaC.f90 | 58 ++++++++++++++
31 files changed, 1103 insertions(+), 212 deletions(-)
create mode 100644 examples/basis.BF.cc-pvqz
create mode 100644 examples/basis.Be.cc-pvdz
create mode 100644 examples/basis.CO.cc-pvqz
create mode 100644 examples/basis.F2.cc-pvqz
create mode 100644 examples/basis.H2.cc-pvqz
create mode 100644 examples/basis.HCl.cc-pvqz
create mode 100644 examples/basis.He.cc-pvdz
create mode 100644 examples/basis.LiF.cc-pvqz
create mode 100644 examples/basis.LiH.cc-pvqz
create mode 100644 examples/basis.N2.cc-pvqz
create mode 100644 src/QuAcK/QP_roots.f90
create mode 100644 src/QuAcK/SigmaC.f90
create mode 100644 src/QuAcK/dSigmaC.f90
diff --git a/examples/basis.BF.cc-pvqz b/examples/basis.BF.cc-pvqz
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diff --git a/examples/basis.Be.cc-pvdz b/examples/basis.Be.cc-pvdz
new file mode 100644
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diff --git a/examples/basis.CO.cc-pvqz b/examples/basis.CO.cc-pvqz
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diff --git a/examples/basis.F2.cc-pvqz b/examples/basis.F2.cc-pvqz
new file mode 100644
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--- /dev/null
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diff --git a/examples/basis.H2.cc-pvqz b/examples/basis.H2.cc-pvqz
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diff --git a/examples/basis.HCl.cc-pvqz b/examples/basis.HCl.cc-pvqz
new file mode 100644
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diff --git a/examples/basis.He.cc-pvdz b/examples/basis.He.cc-pvdz
new file mode 100644
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diff --git a/examples/basis.LiF.cc-pvqz b/examples/basis.LiF.cc-pvqz
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diff --git a/examples/basis.LiH.cc-pvqz b/examples/basis.LiH.cc-pvqz
new file mode 100644
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+ 3 2.8240000 0.0755790
+S 1
+ 1 0.7977000 1.0000000
+S 1
+ 1 0.2581000 1.0000000
+S 1
+ 1 0.0898900 1.0000000
+P 1
+ 1 2.2920000 1.0000000
+P 1
+ 1 0.8380000 1.0000000
+P 1
+ 1 0.2920000 1.0000000
+D 1
+ 1 2.0620000 1.0000000
+D 1
+ 1 0.6620000 1.0000000
+F 1
+ 1 1.3970000 1.0000000
diff --git a/examples/basis.N2.cc-pvqz b/examples/basis.N2.cc-pvqz
new file mode 100644
index 0000000..d1c44f8
--- /dev/null
+++ b/examples/basis.N2.cc-pvqz
@@ -0,0 +1,98 @@
+1 15
+S 9
+ 1 45840.0000000 0.0000920
+ 2 6868.0000000 0.0007170
+ 3 1563.0000000 0.0037490
+ 4 442.4000000 0.0155320
+ 5 144.3000000 0.0531460
+ 6 52.1800000 0.1467870
+ 7 20.3400000 0.3046630
+ 8 8.3810000 0.3976840
+ 9 3.5290000 0.2176410
+S 9
+ 1 45840.0000000 -0.0000200
+ 2 6868.0000000 -0.0001590
+ 3 1563.0000000 -0.0008240
+ 4 442.4000000 -0.0034780
+ 5 144.3000000 -0.0119660
+ 6 52.1800000 -0.0353880
+ 7 20.3400000 -0.0800770
+ 8 8.3810000 -0.1467220
+ 9 3.5290000 -0.1163600
+S 1
+ 1 1.0540000 1.0000000
+S 1
+ 1 0.4118000 1.0000000
+S 1
+ 1 0.1552000 1.0000000
+P 3
+ 1 49.3300000 0.0055330
+ 2 11.3700000 0.0379620
+ 3 3.4350000 0.1490280
+P 1
+ 1 1.1820000 1.0000000
+P 1
+ 1 0.4173000 1.0000000
+P 1
+ 1 0.1428000 1.0000000
+D 1
+ 1 2.8370000 1.0000000
+D 1
+ 1 0.9680000 1.0000000
+D 1
+ 1 0.3350000 1.0000000
+F 1
+ 1 2.0270000 1.0000000
+F 1
+ 1 0.6850000 1.0000000
+G 1
+ 1 1.4270000 1.0000000
+2 15
+S 9
+ 1 45840.0000000 0.0000920
+ 2 6868.0000000 0.0007170
+ 3 1563.0000000 0.0037490
+ 4 442.4000000 0.0155320
+ 5 144.3000000 0.0531460
+ 6 52.1800000 0.1467870
+ 7 20.3400000 0.3046630
+ 8 8.3810000 0.3976840
+ 9 3.5290000 0.2176410
+S 9
+ 1 45840.0000000 -0.0000200
+ 2 6868.0000000 -0.0001590
+ 3 1563.0000000 -0.0008240
+ 4 442.4000000 -0.0034780
+ 5 144.3000000 -0.0119660
+ 6 52.1800000 -0.0353880
+ 7 20.3400000 -0.0800770
+ 8 8.3810000 -0.1467220
+ 9 3.5290000 -0.1163600
+S 1
+ 1 1.0540000 1.0000000
+S 1
+ 1 0.4118000 1.0000000
+S 1
+ 1 0.1552000 1.0000000
+P 3
+ 1 49.3300000 0.0055330
+ 2 11.3700000 0.0379620
+ 3 3.4350000 0.1490280
+P 1
+ 1 1.1820000 1.0000000
+P 1
+ 1 0.4173000 1.0000000
+P 1
+ 1 0.1428000 1.0000000
+D 1
+ 1 2.8370000 1.0000000
+D 1
+ 1 0.9680000 1.0000000
+D 1
+ 1 0.3350000 1.0000000
+F 1
+ 1 2.0270000 1.0000000
+F 1
+ 1 0.6850000 1.0000000
+G 1
+ 1 1.4270000 1.0000000
diff --git a/examples/molecule.BF b/examples/molecule.BF
index ee103e6..0955a4d 100644
--- a/examples/molecule.BF
+++ b/examples/molecule.BF
@@ -2,4 +2,4 @@
2 7 7 0 0
# Znuc x y z
B 0. 0. 0.
- F 0. 0. 2.41
+ F 0. 0. 2.39
diff --git a/examples/molecule.CO b/examples/molecule.CO
index 1d478fc..827311b 100644
--- a/examples/molecule.CO
+++ b/examples/molecule.CO
@@ -2,4 +2,4 @@
2 7 7 0 0
# Znuc x y z
C 0. 0. 0.
- O 0. 0. 2.154
+ O 0. 0. 2.106
diff --git a/examples/molecule.F2 b/examples/molecule.F2
index 1046aea..af08593 100644
--- a/examples/molecule.F2
+++ b/examples/molecule.F2
@@ -2,4 +2,4 @@
2 9 9 0 0
# Znuc x y z
F 0. 0. 0.
- F 0. 0. 2.67
+ F 0. 0. 2.64
diff --git a/examples/molecule.HCl b/examples/molecule.HCl
index 88a5912..1d42e01 100644
--- a/examples/molecule.HCl
+++ b/examples/molecule.HCl
@@ -2,4 +2,4 @@
2 9 9 0 0
# Znuc x y z
H 0. 0. 0.
- Cl 0. 0. 2.41
+ Cl 0. 0. 2.37
diff --git a/examples/molecule.LiF b/examples/molecule.LiF
index e370518..381ba52 100644
--- a/examples/molecule.LiF
+++ b/examples/molecule.LiF
@@ -2,4 +2,4 @@
2 6 6 0 0
# Znuc x y z
Li 0. 0. 0.
- F 0. 0. 3.003
+ F 0. 0. 2.965
diff --git a/examples/molecule.LiH b/examples/molecule.LiH
index d4f626f..1d6bb3f 100644
--- a/examples/molecule.LiH
+++ b/examples/molecule.LiH
@@ -2,4 +2,4 @@
2 2 2 0 0
# Znuc x y z
Li 0. 0. 0.
- H 0. 0. 3
+ H 0. 0. 2.994
diff --git a/examples/molecule.N2 b/examples/molecule.N2
index 6e92c28..85fe0df 100644
--- a/examples/molecule.N2
+++ b/examples/molecule.N2
@@ -2,4 +2,4 @@
2 7 7 0 0
# Znuc x y z
N 0. 0. 0.
- N 0. 0. 2.07
+ N 0. 0. 2.072
diff --git a/input/basis b/input/basis
index bb77ea0..fb05e68 100644
--- a/input/basis
+++ b/input/basis
@@ -1,88 +1,18 @@
-1 6
+1 3
S 3
- 1 33.8700000 0.0060680
- 2 5.0950000 0.0453080
- 3 1.1590000 0.2028220
+ 1 13.0100000 0.0196850
+ 2 1.9620000 0.1379770
+ 3 0.4446000 0.4781480
S 1
- 1 0.3258000 1.0000000
+ 1 0.1220000 1.0000000
+P 1
+ 1 0.7270000 1.0000000
+2 3
+S 3
+ 1 13.0100000 0.0196850
+ 2 1.9620000 0.1379770
+ 3 0.4446000 0.4781480
S 1
- 1 0.1027000 1.0000000
+ 1 0.1220000 1.0000000
P 1
- 1 1.4070000 1.0000000
-P 1
- 1 0.3880000 1.0000000
-D 1
- 1 1.0570000 1.0000000
-2 12
-S 13
- 1 456100.0000000 0.492970E-04
- 2 68330.0000000 0.383029E-03
- 3 15550.0000000 0.200854E-02
- 4 4405.0000000 0.838558E-02
- 5 1439.0000000 0.294703E-01
- 6 520.4000000 0.878325E-01
- 7 203.1000000 0.211473E+00
- 8 83.9600000 0.365364E+00
- 9 36.2000000 0.340884E+00
- 10 15.8300000 0.102133E+00
- 11 6.3340000 0.311675E-02
- 12 2.6940000 0.105751E-02
- 13 0.4313000 0.156136E-03
-S 13
- 1 456100.0000000 -0.138304E-04
- 2 68330.0000000 -0.107279E-03
- 3 15550.0000000 -0.565083E-03
- 4 4405.0000000 -0.236135E-02
- 5 1439.0000000 -0.845886E-02
- 6 520.4000000 -0.259638E-01
- 7 203.1000000 -0.686362E-01
- 8 83.9600000 -0.141874E+00
- 9 36.2000000 -0.199319E+00
- 10 15.8300000 -0.195662E-01
- 11 6.3340000 0.499741E+00
- 12 2.6940000 0.563736E+00
- 13 0.4313000 -0.835091E-02
-S 13
- 1 456100.0000000 0.418546E-05
- 2 68330.0000000 0.324395E-04
- 3 15550.0000000 0.171105E-03
- 4 4405.0000000 0.714176E-03
- 5 1439.0000000 0.256705E-02
- 6 520.4000000 0.788552E-02
- 7 203.1000000 0.210867E-01
- 8 83.9600000 0.442264E-01
- 9 36.2000000 0.651670E-01
- 10 15.8300000 0.603012E-02
- 11 6.3340000 -0.206495E+00
- 12 2.6940000 -0.405871E+00
- 13 0.4313000 0.725661E+00
-S 1
- 1 0.9768000 1.0000000
-S 1
- 1 0.1625000 1.0000000
-P 7
- 1 663.3000000 0.240448E-02
- 2 156.8000000 0.192148E-01
- 3 49.9800000 0.885097E-01
- 4 18.4200000 0.256020E+00
- 5 7.2400000 0.436927E+00
- 6 2.9220000 0.350334E+00
- 7 0.3818000 -0.458423E-02
-P 7
- 1 663.3000000 -0.652145E-03
- 2 156.8000000 -0.519445E-02
- 3 49.9800000 -0.246938E-01
- 4 18.4200000 -0.728167E-01
- 5 7.2400000 -0.134030E+00
- 6 2.9220000 -0.947742E-01
- 7 0.3818000 0.564667E+00
-P 1
- 1 1.0220000 1.0000000
-P 1
- 1 0.1301000 1.0000000
-D 1
- 1 1.0460000 1.0000000
-D 1
- 1 0.3440000 1.0000000
-F 1
- 1 0.7060000 1.0000000
+ 1 0.7270000 1.0000000
diff --git a/input/methods b/input/methods
index 5b88684..2aa67c1 100644
--- a/input/methods
+++ b/input/methods
@@ -1,11 +1,11 @@
# RHF UHF MOM
T F F
# MP2 MP3 MP2-F12
- T F F
+ F F F
# CCD CCSD CCSD(T) ringCCD ladderCCD
F F F F F
# CIS RPA RPAx ppRPA ADC
- T T T F F
+ F F F F F
# GF2 GF3
F F
# G0W0 evGW qsGW
diff --git a/input/molecule b/input/molecule
index 88a5912..81c624a 100644
--- a/input/molecule
+++ b/input/molecule
@@ -1,5 +1,5 @@
# nAt nEla nElb nCore nRyd
- 2 9 9 0 0
+ 2 1 1 0 0
# Znuc x y z
H 0. 0. 0.
- Cl 0. 0. 2.41
+ H 0. 0. 1.4
diff --git a/input/molecule.xyz b/input/molecule.xyz
index 64d6254..6edc99d 100644
--- a/input/molecule.xyz
+++ b/input/molecule.xyz
@@ -1,4 +1,4 @@
2
H 0.0000000000 0.0000000000 0.0000000000
- Cl 0.0000000000 0.0000000000 1.2753171701
+ H 0.0000000000 0.0000000000 0.7408481486
diff --git a/input/options b/input/options
index 5a8d22a..c47156a 100644
--- a/input/options
+++ b/input/options
@@ -5,11 +5,11 @@
# CC: maxSCF thresh DIIS n_diis
64 0.0000001 F 1
# CIS/TDHF/BSE: singlet triplet
- T T
+ T F
# GF: maxSCF thresh DIIS n_diis renormalization
64 0.00001 T 5 3
# GW: maxSCF thresh DIIS n_diis COHSEX SOSEX BSE TDA G0W GW0 lin eta
- 256 0.00001 T 5 F F T F F F F 0.000
+ 256 0.00001 T 5 F F F F F F F 0.000
# ACFDT: AC Kx XBS
T F T
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift
diff --git a/input/weight b/input/weight
index bb77ea0..fb05e68 100644
--- a/input/weight
+++ b/input/weight
@@ -1,88 +1,18 @@
-1 6
+1 3
S 3
- 1 33.8700000 0.0060680
- 2 5.0950000 0.0453080
- 3 1.1590000 0.2028220
+ 1 13.0100000 0.0196850
+ 2 1.9620000 0.1379770
+ 3 0.4446000 0.4781480
S 1
- 1 0.3258000 1.0000000
+ 1 0.1220000 1.0000000
+P 1
+ 1 0.7270000 1.0000000
+2 3
+S 3
+ 1 13.0100000 0.0196850
+ 2 1.9620000 0.1379770
+ 3 0.4446000 0.4781480
S 1
- 1 0.1027000 1.0000000
+ 1 0.1220000 1.0000000
P 1
- 1 1.4070000 1.0000000
-P 1
- 1 0.3880000 1.0000000
-D 1
- 1 1.0570000 1.0000000
-2 12
-S 13
- 1 456100.0000000 0.492970E-04
- 2 68330.0000000 0.383029E-03
- 3 15550.0000000 0.200854E-02
- 4 4405.0000000 0.838558E-02
- 5 1439.0000000 0.294703E-01
- 6 520.4000000 0.878325E-01
- 7 203.1000000 0.211473E+00
- 8 83.9600000 0.365364E+00
- 9 36.2000000 0.340884E+00
- 10 15.8300000 0.102133E+00
- 11 6.3340000 0.311675E-02
- 12 2.6940000 0.105751E-02
- 13 0.4313000 0.156136E-03
-S 13
- 1 456100.0000000 -0.138304E-04
- 2 68330.0000000 -0.107279E-03
- 3 15550.0000000 -0.565083E-03
- 4 4405.0000000 -0.236135E-02
- 5 1439.0000000 -0.845886E-02
- 6 520.4000000 -0.259638E-01
- 7 203.1000000 -0.686362E-01
- 8 83.9600000 -0.141874E+00
- 9 36.2000000 -0.199319E+00
- 10 15.8300000 -0.195662E-01
- 11 6.3340000 0.499741E+00
- 12 2.6940000 0.563736E+00
- 13 0.4313000 -0.835091E-02
-S 13
- 1 456100.0000000 0.418546E-05
- 2 68330.0000000 0.324395E-04
- 3 15550.0000000 0.171105E-03
- 4 4405.0000000 0.714176E-03
- 5 1439.0000000 0.256705E-02
- 6 520.4000000 0.788552E-02
- 7 203.1000000 0.210867E-01
- 8 83.9600000 0.442264E-01
- 9 36.2000000 0.651670E-01
- 10 15.8300000 0.603012E-02
- 11 6.3340000 -0.206495E+00
- 12 2.6940000 -0.405871E+00
- 13 0.4313000 0.725661E+00
-S 1
- 1 0.9768000 1.0000000
-S 1
- 1 0.1625000 1.0000000
-P 7
- 1 663.3000000 0.240448E-02
- 2 156.8000000 0.192148E-01
- 3 49.9800000 0.885097E-01
- 4 18.4200000 0.256020E+00
- 5 7.2400000 0.436927E+00
- 6 2.9220000 0.350334E+00
- 7 0.3818000 -0.458423E-02
-P 7
- 1 663.3000000 -0.652145E-03
- 2 156.8000000 -0.519445E-02
- 3 49.9800000 -0.246938E-01
- 4 18.4200000 -0.728167E-01
- 5 7.2400000 -0.134030E+00
- 6 2.9220000 -0.947742E-01
- 7 0.3818000 0.564667E+00
-P 1
- 1 1.0220000 1.0000000
-P 1
- 1 0.1301000 1.0000000
-D 1
- 1 1.0460000 1.0000000
-D 1
- 1 0.3440000 1.0000000
-F 1
- 1 0.7060000 1.0000000
+ 1 0.7270000 1.0000000
diff --git a/scan_LiF.sh b/scan_LiF.sh
index 13226bc..c3f11d7 100755
--- a/scan_LiF.sh
+++ b/scan_LiF.sh
@@ -1,9 +1,9 @@
#! /bin/bash
MOL="LiF"
-BASIS="cc-pvtz"
-R_START=3.980
-R_END=2.990
+BASIS="cc-pvqz"
+R_START=2.965
+R_END=2.965
DR=0.001
for R in $(seq $R_START $DR $R_END)
diff --git a/scan_LiH.sh b/scan_LiH.sh
index 4eed6e1..5061aae 100755
--- a/scan_LiH.sh
+++ b/scan_LiH.sh
@@ -2,8 +2,8 @@
MOL="LiH"
BASIS="cc-pvqz"
-R_START=2.990
-R_END=3.000
+R_START=3.013
+R_END=3.013
DR=0.001
for R in $(seq $R_START $DR $R_END)
diff --git a/scan_N2.sh b/scan_N2.sh
index c62b21e..05e6af6 100755
--- a/scan_N2.sh
+++ b/scan_N2.sh
@@ -1,8 +1,8 @@
#! /bin/bash
MOL="N2"
-BASIS="cc-pvtz"
-R_START=2.066
+BASIS="cc-pvqz"
+R_START=2.071
R_END=2.080
DR=0.001
diff --git a/src/QuAcK/G0W0.f90 b/src/QuAcK/G0W0.f90
index 67a517d..cd20734 100644
--- a/src/QuAcK/G0W0.f90
+++ b/src/QuAcK/G0W0.f90
@@ -95,10 +95,14 @@ subroutine G0W0(doACFDT,exchange_kernel,doXBS,COHSEX,SOSEX,BSE,TDA,singlet_manif
call renormalization_factor(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, &
Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),Z(:))
+! Find all the roots of the QP equation if necessary
+
+ call QP_roots(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho)
+
! Solve the quasi-particle equation
eGW(:) = eHF(:) + Z(:)*SigC(:)
-
+
! Dump results
! call print_excitation('RPA ',ispin,nS,Omega(:,ispin))
diff --git a/src/QuAcK/QP_roots.f90 b/src/QuAcK/QP_roots.f90
new file mode 100644
index 0000000..2dca6fe
--- /dev/null
+++ b/src/QuAcK/QP_roots.f90
@@ -0,0 +1,156 @@
+subroutine QP_roots(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho)
+
+! Compute all the roots of the QP equation for each orbital
+
+ implicit none
+ include 'parameters.h'
+
+! Input variables
+
+ integer,intent(in) :: nBas
+ integer,intent(in) :: nC
+ integer,intent(in) :: nO
+ integer,intent(in) :: nV
+ integer,intent(in) :: nR
+ integer,intent(in) :: nS
+ double precision,intent(in) :: eta
+ double precision,intent(in) :: eHF(nBas)
+ double precision,intent(in) :: Omega(nS)
+ double precision,intent(in) :: rho(nBas,nBas,nS)
+
+! Local variables
+
+ integer :: i,j,a,b,x,jb,g
+ integer :: nRoot
+ integer,parameter :: nGrid = 10000
+ double precision,parameter :: wmin = -10d0
+ double precision,parameter :: wmax = +10d0
+ double precision :: dw
+ double precision :: eps
+ double precision :: left_sign,right_sign
+ double precision :: left_QP,right_QP
+ double precision,allocatable :: w(:)
+ double precision,allocatable :: SigC(:)
+ double precision,allocatable :: dSigC(:)
+
+ integer :: nIt
+ integer,parameter :: maxIt = 64
+ double precision,parameter :: thresh = 1d-6
+ double precision,external :: SigmaC,dSigmaC
+ double precision :: f,df
+ double precision :: s,ds
+ double precision :: om
+
+! Construct grid
+
+ allocate(w(nGrid),SigC(nGrid),dSigC(nGrid))
+
+! Minimum and maximum frequency values
+
+ dw = (wmax - wmin)/dble(nGrid)
+
+ do g=1,nGrid
+ w(g) = wmin + dble(g)*dw
+ enddo
+
+! Main loop over the orbitals
+
+ do x=nC+1,nBas-nR
+
+ SigC(:) = 0d0
+ dSigC(:) = 0d0
+
+ ! Loop over grid points
+
+ do g=1,nGrid
+
+ ! Occupied part of the self-energy and spectral weight
+
+ do i=nC+1,nO
+ jb = 0
+ do j=nC+1,nO
+ do b=nO+1,nBas-nR
+
+ jb = jb + 1
+ eps = w(g) - eHF(i) + Omega(jb)
+ SigC(g) = SigC(g) + 2d0*rho(x,i,jb)**2*eps/(eps**2 + eta**2)
+ dSigC(g) = dSigC(g) - 2d0*rho(x,i,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
+
+ enddo
+ enddo
+ enddo
+
+ ! Virtual part of the self-energy and spectral weight
+
+ do a=nO+1,nBas-nR
+ jb = 0
+ do j=nC+1,nO
+ do b=nO+1,nBas-nR
+
+ jb = jb + 1
+ eps = w(g) - eHF(a) - Omega(jb)
+ SigC(g) = SigC(g) + 2d0*rho(x,a,jb)**2*eps/(eps**2 + eta**2)
+ dSigC(g) = dSigC(g) - 2d0*rho(x,a,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
+
+ enddo
+ enddo
+ enddo
+
+ enddo
+
+! Find the zeros of the QP equation
+
+ nRoot = 0
+
+ write(*,*) '-----------------'
+ write(*,'(A10,I3)') 'Orbital ',x
+ write(*,*) '-----------------'
+ write(*,*)
+ left_QP = w(1) - eHF(x) - SigC(1)
+ left_sign = sign(1d0,left_QP)
+
+ do g=2,nGrid
+
+ right_QP = w(g) - eHF(x) - SigC(g)
+ right_sign = sign(1d0,right_QP)
+
+ if(left_sign /= right_sign .and. left_sign == sign(1d0,-1d0)) then
+
+ nRoot = nRoot + 1
+ write(*,'(A20,I6,F10.6,F10.6,I6,F10.6,F10.6,F10.6)') &
+ 'root right here!',g-1,w(g-1),left_QP,g,w(g),right_QP,1d0/(1d0-dSigC(g))
+
+ ! Run Newton's algorithm to find the root
+
+ om = w(g-1)
+ nIt = 0
+ f = 1d0
+
+ do while (abs(f) > thresh .and. nIt < maxIt)
+
+ nIt = nIt + 1
+
+ s = SigmaC(x,om,eta,nBas,nC,nO,nV,nR,nS,eHF,Omega,rho)
+ ds = dSigmaC(x,om,eta,nBas,nC,nO,nV,nR,nS,eHF,Omega,rho)
+ f = om - eHF(x) - s
+ df = 1d0 - ds
+
+ write(*,'(A3,I3,A1,1X,4F15.9)') 'It.',nIt,':',om,f,s,1d0/(1d0-ds)
+
+ om = om - f/df
+
+ end do
+
+ end if
+
+ left_sign = right_sign
+ left_QP = right_QP
+
+ end do
+ write(*,*)
+ write(*,'(A32,I3,A1,I3)') 'Number of roots for orbital ',x,':',nRoot
+ write(*,*)
+
+ end do
+
+end subroutine QP_roots
diff --git a/src/QuAcK/RPA.f90 b/src/QuAcK/RPA.f90
index 767f80f..d4046de 100644
--- a/src/QuAcK/RPA.f90
+++ b/src/QuAcK/RPA.f90
@@ -96,33 +96,33 @@ subroutine RPA(doACFDT,exchange_kernel,singlet_manifold,triplet_manifold,eta, &
! Compute the correlation energy via the adiabatic connection
! Switch off ACFDT for RPA as the trace formula is equivalent
- if(doACFDT) then
+! if(doACFDT) then
- write(*,*) '------------------------------------------------------'
- write(*,*) 'Adiabatic connection version of RPA correlation energy'
- write(*,*) '------------------------------------------------------'
- write(*,*)
+! write(*,*) '------------------------------------------------------'
+! write(*,*) 'Adiabatic connection version of RPA correlation energy'
+! write(*,*) '------------------------------------------------------'
+! write(*,*)
- call ACFDT(exchange_kernel,.false.,.true.,.false.,.false.,singlet_manifold,triplet_manifold,eta, &
- nBas,nC,nO,nV,nR,nS,ERI,e,Omega,XpY,XmY,rho,EcAC)
+! call ACFDT(exchange_kernel,.false.,.true.,.false.,.false.,singlet_manifold,triplet_manifold,eta, &
+! nBas,nC,nO,nV,nR,nS,ERI,e,Omega,XpY,XmY,rho,EcAC)
- if(exchange_kernel) then
-
- EcAC(1) = 0.5d0*EcAC(1)
- EcAC(2) = 1.5d0*EcAC(1)
-
- end if
+! if(exchange_kernel) then
+!
+! EcAC(1) = 0.5d0*EcAC(1)
+! EcAC(2) = 1.5d0*EcAC(1)
+!
+! end if
- write(*,*)
- write(*,*)'-------------------------------------------------------------------------------'
- write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (singlet) =',EcAC(1)
- write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (triplet) =',EcAC(2)
- write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy =',EcAC(1) + EcAC(2)
- write(*,'(2X,A50,F20.10)') 'AC@RPA total energy =',ENuc + ERHF + EcAC(1) + EcAC(2)
- write(*,*)'-------------------------------------------------------------------------------'
- write(*,*)
+! write(*,*)
+! write(*,*)'-------------------------------------------------------------------------------'
+! write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (singlet) =',EcAC(1)
+! write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (triplet) =',EcAC(2)
+! write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy =',EcAC(1) + EcAC(2)
+! write(*,'(2X,A50,F20.10)') 'AC@RPA total energy =',ENuc + ERHF + EcAC(1) + EcAC(2)
+! write(*,*)'-------------------------------------------------------------------------------'
+! write(*,*)
- end if
+! end if
end subroutine RPA
diff --git a/src/QuAcK/SigmaC.f90 b/src/QuAcK/SigmaC.f90
new file mode 100644
index 0000000..32a07ca
--- /dev/null
+++ b/src/QuAcK/SigmaC.f90
@@ -0,0 +1,58 @@
+double precision function SigmaC(x,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
+
+! Compute diagonal of the correlation part of the self-energy
+
+ implicit none
+ include 'parameters.h'
+
+! Input variables
+
+ integer,intent(in) :: x
+ double precision,intent(in) :: w
+ double precision,intent(in) :: eta
+ integer,intent(in) :: nBas
+ integer,intent(in) :: nC
+ integer,intent(in) :: nO
+ integer,intent(in) :: nV
+ integer,intent(in) :: nR
+ integer,intent(in) :: nS
+ double precision,intent(in) :: e(nBas)
+ double precision,intent(in) :: Omega(nS)
+ double precision,intent(in) :: rho(nBas,nBas,nS)
+
+! Local variables
+
+ integer :: i,j,a,b,p,jb
+ double precision :: eps
+
+! Initialize
+
+ SigmaC = 0d0
+
+! Occupied part of the correlation self-energy
+
+ do i=nC+1,nO
+ jb = 0
+ do j=nC+1,nO
+ do b=nO+1,nBas-nR
+ jb = jb + 1
+ eps = w - e(i) + Omega(jb)
+ SigmaC = SigmaC + 2d0*rho(x,i,jb)**2*eps/(eps**2 + eta**2)
+ enddo
+ enddo
+ enddo
+
+! Virtual part of the correlation self-energy
+
+ do a=nO+1,nBas-nR
+ jb = 0
+ do j=nC+1,nO
+ do b=nO+1,nBas-nR
+ jb = jb + 1
+ eps = w - e(a) - Omega(jb)
+ SigmaC = SigmaC + 2d0*rho(x,a,jb)**2*eps/(eps**2 + eta**2)
+ enddo
+ enddo
+ enddo
+
+end function SigmaC
diff --git a/src/QuAcK/dSigmaC.f90 b/src/QuAcK/dSigmaC.f90
new file mode 100644
index 0000000..6323de9
--- /dev/null
+++ b/src/QuAcK/dSigmaC.f90
@@ -0,0 +1,58 @@
+double precision function dSigmaC(x,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
+
+! Compute the derivative of the correlation part of the self-energy
+
+ implicit none
+ include 'parameters.h'
+
+! Input variables
+
+ integer,intent(in) :: x
+ double precision,intent(in) :: w
+ double precision,intent(in) :: eta
+ integer,intent(in) :: nBas
+ integer,intent(in) :: nC
+ integer,intent(in) :: nO
+ integer,intent(in) :: nV
+ integer,intent(in) :: nR
+ integer,intent(in) :: nS
+ double precision,intent(in) :: e(nBas)
+ double precision,intent(in) :: Omega(nS)
+ double precision,intent(in) :: rho(nBas,nBas,nS)
+
+! Local variables
+
+ integer :: i,j,a,b,p,jb
+ double precision :: eps
+
+! Initialize
+
+ dSigmaC = 0d0
+
+! Occupied part of the correlation self-energy
+
+ do i=nC+1,nO
+ jb = 0
+ do j=nC+1,nO
+ do b=nO+1,nBas-nR
+ jb = jb + 1
+ eps = w - e(i) + Omega(jb)
+ dSigmaC = dSigmaC - 2d0*rho(x,i,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
+ enddo
+ enddo
+ enddo
+
+! Virtual part of the correlation self-energy
+
+ do a=nO+1,nBas-nR
+ jb = 0
+ do j=nC+1,nO
+ do b=nO+1,nBas-nR
+ jb = jb + 1
+ eps = w - e(a) - Omega(jb)
+ dSigmaC = dSigmaC - 2d0*rho(x,a,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
+ enddo
+ enddo
+ enddo
+
+end function dSigmaC