Simple theorems, proofs, and derivations in quantum chemistry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Kluwer Academic/Plenum
2003
|
| Series: | Mathematical and computational chemistry
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 337 p. ill. : 26 cm |
| ISBN: | 9781441933898 0306474093 |
Staff View
MARC
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| 100 | 1 | |a Mayer, István |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Simple theorems, proofs, and derivations in quantum chemistry |c István Mayer |
| 264 | 1 | |a New York [u.a.] |b Kluwer Academic/Plenum |c 2003 | |
| 300 | |a xiii, 337 p. |b ill. : 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematical and computational chemistry | |
| 650 | 4 | |a Quantum chemistry | |
| 650 | 0 | 7 | |a Quantenchemie |0 (DE-588)4047979-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenchemie |0 (DE-588)4047979-1 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009945294 | ||
Record in the Search Index
| _version_ | 1804129409253244928 |
|---|---|
| adam_text | ********** *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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* * * * * **** ****** * * * * **** * * * * * * * * * * * * * * * * * * *
* * * * * * * * *** * * * * * * * * * * **** ****** A P P R O X I M A T
E D E C O U P L I N G . . . . . . . . . . . 15* 2.5. A N O T E
O N T H E B O M - O P P E N H E I M E R S E P A R A T I O N
16* N O T E S 17* 2. G E N E R A L T H E O R E M S A N D
P R I N C I P L E S * 19* I . T H E V A R I A T I O N P R I N C I
P L E . . . . . . . . . . . . . . . 19* I. I . * T H E R
A Y L E I G H Q U O T I E N T . 19* 1.2.* T H E V A R I A T
I O N P R I N C I P L E F O R THE G R O U N D S T A T E
19* 1.3.* T H E V A R I A T I O N P R I N C I P L E AS AN E Q U
I V A L E N T O F T H E S C H R OE D I N G E R * E Q U A T I O N
: A U S E F U L F O N N U L A T I O N O F THE V A R I A T
I O N P R I N C I P L E 21* 104.* E C K A R T S I N E Q U A L
I T Y . . . . 23* 1.5.* E X C I T E D S T A T E S . . . . . .
. . . . . 2 4 * 2. T H E H E L L M A N N - F E Y N M A N T H
E O R E M * 2 6 * 2.1.* T H E D I F F E R E N T I A L H E L
L M A N N - F E Y N M A N T H E O R E M 2 6 * 2.2.* T H E I
N T E G R A L H E J L M A N N - F E Y N M A N T H E O R E M 3
I * 3. THE V I R I A L T H E O R E M IN Q U A N T U M M E
C H A N I C S . . . * 3 2 * 3 . 1 . * T I M E D E P E N D
E N C E O F A P H Y S I C A I Q U A N T I T Y . 3 2 *
3.2.* T H E V I R I A L T H E O R E M !~ 3 3 * 3 . 3 .
* S C A L I N G - A C O N N E C T I O N WITH THE V A R I A T I
O N P R I N C I P L E 3 5 * 304.* T H E V I R I A L T H E
O R E M IN THE B O M - O P P E N H E I M E R * A P P R O X I M A T
I O N . . 3 6 * 3 . 5 . T H E V I R I A L T H E O R E
M A N D C H E M I C A L BOFLDING 41* N O T E S 4 2 * IX X
THEOREMS, PROOFS, AND DERIVATIONS IN QUANTUM CHEMISTRY 3.* THE LINEAR
VARIATIONAL METHOD AND LOEWDIN S ORTHOGONALIZATION SCHEMES 45 1.* THE
LINEAR VARIATIONAL METHOD (RITZ METHOD) 45 2.* LOEWEJIN S SYMMETRIE
ORTHOGONALIZATION 52 M . 8 - 1/ 2 2 . . I ATNX . 52 2 2.2.* THE 8-
1 / TRANSFORMATION . . . 53 2.3.* THE LOEWDIN BASIS . 54 2.1.* THE
STATIONARY PROPERTY OF LOEWDIN S SYMMETRIE ORTHOGONAIIZATION SEHEME 55
2.5.* LOEWDIN ORTHOGONALIZATION: A TWO-DIMENSIONAL EXAMPLE 59 3.* LINEAR
INDEPENDENEE OF THE BASIS AND LOEWDIN S EANONIE ORTHOGONALIZATION . . .
. . . . . . . . . . . . . . . . . . . . . 62 3.1.* EIGENVALUES OF THE
OVEDAP MATRIX: A MEASURE FOR THE LINEAR INDEPENDENEE OF THE BASIS .. 62
3.2. LOEWDIN S EANONIE ORTHOGONALIZATION 64 NOTES* 67 4.* PERTURBATIONAL
METHODS 69 I.* NONDEGENERATE RAYLEIGH-SEHROEDINGER PERTURBATION THEORY 69
1.1.* THE PROBLEM 69 1.2.* ALGEBRAIE EXPANSION . . . . . . . . . . .
72 1.3.* THE USE OF THE REDUEED RESOLVENT IN THE RAYLEIGH~SEHROEDINGER
PERTURBATION THEORY 76 1.4.* WIGNER S 2N + 1 THEOREM 81 1.4.1* THE
AEEURAEY OFTHE ENERGY EXPEETATION VALUE EALCULATED BY THE NTH ORDER
PERTURBATIONAL WAVE FUNETION . . . .. 81 1.4.2* COMPUTING THE EXAET
ENERGY EORREETIONS UP TO ORDER 2N + 1 BY USING THE FIRST N WAVE
FUNCTION EORRECTIONS 82 2.* VARIATIONAL-PERTURBATIONAL METHOD: THE
HYLLERAAS FUNCTIONAL 88 3. DEGENERATE RAYLEIGH-SEHROEDINGER PERTURBATION
THEORY 93 4. BRILLOUIN-WIGNER PERTURBATION THEORY .... 95 4.1.* THE
SIZE-EONSISTENEY PROBLEM . . . . 98 5.* SIZE EONSISTENCY OF THE
RAYLEIGH-SCHROEDIGER PERTURBATION THEORY . . . . . . . . . . . . . . 100
5.1.* FORMAL EONSIDERATIONS BASED ON THE PROPERTIES OF POWER SERIES* . .
. . . . . . . . . . . . . . . . . . . . . 100* 5.2.* SIZE CONSISTENEY OF
THE PERTURBATIONAL EXPANSIONS 102 6. LOEWDIN S PARTITIONING METHOD .. 115
NOTES 118 5. DETERMINANT WAVE FUNCTIONS 121 1. SPIN ORBITALS 121 2.
MANY-ELEETRON SPIN STATES 124 3. SLATER DETERMINANTS . . . . 126
CONTENTS* X L 3 . 1 . * T W O - E L E C T R O N E X A M P L E S
127* 4.* T H E A N T I S Y M M E T R I Z I N G O P E R A T O R
129* 4 . 1 . * T H E P R O J E C T I O N C H A R A C T E R
O F T H E A N T I S Y M M E T R I Z I N G * O P E R A T O R
130* 4 . 2 . * C O M M U T A T I O N P R O P E R T I E S O F
T H E A N T I S Y M M E T R I Z I N G * O P E R A T O R 134*
4 . 3 . * A N T I S Y M M E T R I Z A T I O N B E T W E E N D I
S T A N T S U B S Y S T E M S 135* 5.* I N V A R I A N C E O F
T H E D E T E R M I N A N T W A V E F U N C T I O N W I T
H R E S P E C T TO* M I X I N G THE O C C U P I E D O R B I T
A L S . . . . . . . . . . . . . . . . . 137* 6.* M A T R I X
E L E M E N T S B E T W E E N D E T E R M I N A N T W A V E
F U N C T I O N S : L OE W D I N S * G E N E R A L F O N N U L
A E F O R N O N O R T H O G O N A L O R B I T A L S 140* 6 .
1 . * O V E R L A P . . . 1 4 ) 6 . 1 . 1 . * G E N E R A L
C A S E 141* 6 . 1 . 2 . * F A C T O R I Z A T I O N . . . .
. . . . . . . . 142* 6 . 1 . 3 . * S P E C I A L C A S E S F
O R O R T H O N O R M A L I Z E D O R B I T A L S ( S L A T E R
R U L E S ) 144* 6 . 2 . * O N E - E L E C T R O N O P E R A T
O R S . . . . . . . . . . . . . . . . . 145* 6 . 2 . 1 . * G E
N E R A L C A S E . . . . . . . . . . . . . . 145* 6 . 2 . 2 . *
S P E C I A L C A S E S F O R O R T H O N O R M A L I Z E D
O R B I T A L S ( S L A T E R R U L E S ) 4 7 6 . 3 . *
T W O - E L E C T R O N O P E R A T O R S . . . . . . . . . . . .
. . . . . 149* 6 . 3 . 1 . * G E N E R A L C A S E 149* 6
. 3 . 2 . * S P E C I A L C A S E S FOR O R T H O N O R M A L I
Z E D O R B I T A L S ( S L A T E R R U L E S ) 151* 7.* L OE
W D I N S P A I R I N G T H E O R E M A N D I T S G E N
E R A L I Z A T I O N 153* 7.1.* L OE W D I N S P A I R I N G
T H E O R E M 154* 7 . 2 . * K A R A D A K O V S E X T E N
D E D P A I R I N G T H E O R E M 157* 8.* T H E O R E M A B
O U T T H E E X I S T E N C E O F O R B I T A L S O F
S P E C I A L S T R U C T U R E 160* 8.1.* E X I S T E N C E T
H E O R E M . . . . 161* 8.2. A POSLERIOJ-I D E T E R M I N A T I
O N 162* N O T E S 163* 5. T H E H A R T R E E - F O C K M E
T H O D * 165* I.* T H E V A R I A T I O N P R I N C I P L E
FOR S I N G L E D E T E R M I N A N T W A V E F U N C T I O N S
: * T H E B R I L L O U I N T H E O R E M 166* 1.1.* T H E
B R I L L O U I N T H E O R E M FOR T H E D E T E R M I N A
N T W I T H THE* A B S O L U T E M I N I M U M O F T H E
E N E R G Y . . . . . . . . 166* 1.2.* T H E B R I L L O U I
N T H E O R E M F O R A D E T E R M I N A N T WITH A *
S T A T I O N A R Y E N E R G Y . . . . . . . . . . . . . . . .
167* 1.3.* A L G O R I T H M O F C A I C U L A T I O N S B A
S E D ON T H E B R I L L O U I N * T H E O R E M . . . . . . .
. . . . . . . . . 169* 2.* T H E H A R T R E E - F O C K E Q U A T I
O N S . . . . . . . . . . . . . . , .; 170* 2 . 1 . * U N R
E S T R I C T E D H A R T R E E - F O C K E Q U A T I O N S
171* 2 . 2 . * A L T E R N A T E D E R I V A T I O N BY U S I N
G L A G R A N G I A N MULTIPLIERS 177* 2 . 3 . * A L T E R N A
T E D E R I V A T I O N BY U S I N G S P E C I F I E D V A R
I A T I O N S 180* 3.* K O O P M A N S T H E O R E M . . . . . . .
. . . . . . . . 182* 3 . 1 . * T H E O R B I T A L E N E R
G I E S A N D T H E T O T A L E N E R G Y 184* X I I
THEOREMS, PROOFS, AND DERIVAT/ONS IN QUANTUM CHEMISTRY 4.* T H E R H F M
E T H O D . . . . . . . . . . . . 187* 4. 1.* T H E R H F
AND U H F S C H E M E S . . 187* 4 . 2 . * S Y M M E T R Y
AND T H E R H F M E T H O D 189* 4 . 3 . * T H E D I
S S O C I A T I O N C A T A S T R O P H E ; D I F F E R E N T
H A R T R E E - F O C K * / M E T H O D S 190* 4 . 4 . * S I
N G L E T AND T R I P L E T E X C I T A T I O N S . . . 195*
5.* F I N I T E B A S I S H A R T R E E - F O C K T H E O R Y
. . . . . . 198* 5 . 1 . H A R T R E E - F O C K - R O O T H A
A N E Q U A T I O N S 198* 5.2 : T H E P - M A T R I X . . . .
. . . . . . . . 2 0 2 * 5 . 3 . * E X A M P L E O F U S I
N G P R O J E C T O R S IN T H E L C A O F R A M E W O R K :
* T H E U H F E Q U A T I O N S F O R S U C C E S S I V E
O P T I M I Z A T I O N O F T H E * O R B I T A L S . . .
. . . . . . . . . . . . 2 0 4 * 5 . 4 . * T H E F O C K M
A T R I X A N D THE E N E R G Y . . 2 0 6 * 6.* R E S T R
I C T E D O P E N - S H E L L H A R T R E E - F O C K M E T H O
D 2 0 9 * 6 . 1 . * T H E R O H F E Q U A T I O N S . . . .
. . . . 211* 6 . 2 . * T H E C O U P L I N G C O E F F I C I
E N T S F O R S O M E O P E N - S H E L L S Y S T E M S
215* 7.* T H E G R A D I E N T O F THE E N E R G Y . . . . . . . 2
1 6 * N O T E S 223* 7. P O P U L A T I O N A N A L Y S I S ,
B O N D O R D E R S , A N D V A L E N C E S 2 2 7 *
1.* M U L L I K E N S P O P U L A T I O N A N A L Y S I S
228* 1.1.* E L E C T R O N D E N S I T Y . . 228* 1.2.* P O P U
L A T I O N A N A L Y S I S 2 3 0 * 2.* B O N D O R D E R S
AND V A L E N C E S 235* 2 . 1 . * B O N D O R D E R I N
D E X . . 235* 2 . 2 . * V A L E N C E I N D I C E S . .
. 238* 2 . 3 . * E X C H A N G E D E N S I T Y A N D B O
N D O R D E R 241* 2 . 4 . B O N D O R D E R S IN T H R E
E - C E N T E R B O N D S 245* N O T E S 247* 8. T H E E L E
C T R O N C O R R E L A T I O N * 251* 1. * T H E C I E X P A N
S I O N . . . . . . . . . . . . . . . 251* 2.* T H E C O R R E
L A T I O N E N E R G Y A N D N E S B E T S T H E O R E M
253* 3 . M E T H O D S O F E L E C T R O N C O R R E L A
T I O N C A L C U L A T I O N S * 2 6 0 * 3 . 1 . * T H E CI
M E T H O D . . . . . . . . . . . . 2 6 0 * 3 . 2 . * M C -
S C F M E T H O D S . . . . . . . . . . 2 6 2 * 3 . 3 . * T
H E M B P T O R M011ER-PLESSET M E T H O D 2 6 4 * 3 . 4
. T H E C O U P L E D C L U S T E R A P P R O A C H 269*
N O T E S . . . . . . . . . . . . . . . . 278* 9. M I S C E L L A
N E O U S * 281* 1.* T H E LRZ E X P A N S I O N 281* 2.* T H E
C U S P C O N D I T I O N 283* 2.1 . * T H E N U C L E A
R C U S P 2 8 3 * 2 . 2 . * T H E E L E C T R O N I C
C U S P 2 8 6 * C O N T E N T S * X I I I 3.* T H E A S Y
M P T O T I C A J B E H A V I O R O F T H E W A V E F U N
C T I O N AT V E R Y L A R G E D I S T A N C E S 2 8 6 4
. * B A S I S F U N C T I O N S : T H E G A U S S I A N P
R O D U C T T H E O R E M 2 8 7 5 . * T H E I N T E G R A
L T R A N S F O R M A T I O N P R O B L E M 2 9 0 N O T E S
291 A P P E N D I C E S * 2 9 3 I.* S E P A R A T I N G T H
E M O T I O N O F T H E C E N T E R O F M A S S IN C L A
S S I C A L M E C H A N I C S 2 9 5 11.* R E D U C I N G T H
E T W O - B O D Y P R O B L E M TO T W O O N E - B O D Y
ON E S IN C 1 A S S I C A L M E C H A N I C S 2 9 9 I I I .
* A N A L O G Y B E T W E E N D I F F E R E N T I A L S A N
D V A R I A T I O N S 3 0 3 IV.* E U L E R S T H E O R E M
F O R H O M O G E N O U S F U N C T I O N S 3 0 5 V.* T H
E V I R I A L T H E O R E M IN C 1 A S S I C A L M E C H A N
I C S 3 0 7 V I . * T H E E L E C T R O N I C S C H
R OE D I N G E R E Q U A T I O N IN A T O M I C U N I T S 3 0 9
V I I . * T H E B R A - K E T F O R M A L I S M 311 I
. * D I R A C S B R A A N D K E T V E C T O R S
311 2.* A N A L O G Y W I T H T H E M A T R I X F O R M A
L I S M 313 3 . * T H E U S E O F A N O V E R L A P P
I N G B A S I S . . 3 1 4 4 . * E X A M P L E O F U S
I N G T H E B R A - K E T F O R M A L I S M : T H E H Y P
E R V I R I A L T H E O R E M . . . . . . . . 3 1 5 5.* P R
O J E C T I O N O P E R A T O R S 3 1 6 6 . * R E S O L U T
I O N O F I D E N T I T Y 3 1 7 7.* S P E C T R A L R E S
O L U T I O N O F H E R M I T I A N O P E R A T O R S 3 1 8
8.* T H E C A S E O F N O N - H E R M I T I A N O P E R A
T O R S - B I O R T H O G O N A L S E T S O F F U N C T I O N S
3 1 9 9.* T H E T R A C E O F T H E P R O J E C T O R
321 V I I I . C O L L E C T I O N O F F O R M U L A S F O R
R A Y L E I G H - S C H R OE D I N G E R P E R T U R B A T I O N
T H E O R Y ( N O N D E G E N E R A T E C A S E ) 3 2 3 I X
. * D I R E C T P R O D U C T S O F M A T R I C E S . . .
3 2 5 X . * P E R M U T A T I O N S 3 2 9 X I . * A N
O R T H O G O N A L I Z A T I O N A L G O R I T H M 331 L N D E
X 3 3 3 , /
|
| any_adam_object | 1 |
| author | Mayer, István |
| author_facet | Mayer, István |
| author_role | aut |
| author_sort | Mayer, István |
| author_variant | i m im |
| building | Verbundindex |
| bvnumber | BV014651096 |
| callnumber-first | Q - Science |
| callnumber-label | QD462 |
| callnumber-raw | QD462 |
| callnumber-search | QD462 |
| callnumber-sort | QD 3462 |
| callnumber-subject | QD - Chemistry |
| classification_tum | CHE 150f |
| ctrlnum | (OCoLC)50403687 (DE-599)BVBBV014651096 |
| dewey-full | 541.2/8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 541 - Physical chemistry |
| dewey-raw | 541.2/8 |
| dewey-search | 541.2/8 |
| dewey-sort | 3541.2 18 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Chemie |
| format | Book |
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| id | DE-604.BV014651096 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:41Z |
| institution | BVB |
| isbn | 9781441933898 0306474093 |
| language | English |
| lccn | 2002027573 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009945294 |
| oclc_num | 50403687 |
| open_access_boolean | |
| owner | DE-29T DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-91G DE-BY-TUM |
| physical | xiii, 337 p. ill. : 26 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer Academic/Plenum |
| record_format | marc |
| series2 | Mathematical and computational chemistry |
| spelling | Mayer, István Verfasser aut Simple theorems, proofs, and derivations in quantum chemistry István Mayer New York [u.a.] Kluwer Academic/Plenum 2003 xiii, 337 p. ill. : 26 cm txt rdacontent n rdamedia nc rdacarrier Mathematical and computational chemistry Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantenchemie (DE-588)4047979-1 s DE-604 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009945294&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mayer, István Simple theorems, proofs, and derivations in quantum chemistry Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd |
| subject_GND | (DE-588)4047979-1 |
| title | Simple theorems, proofs, and derivations in quantum chemistry |
| title_auth | Simple theorems, proofs, and derivations in quantum chemistry |
| title_exact_search | Simple theorems, proofs, and derivations in quantum chemistry |
| title_full | Simple theorems, proofs, and derivations in quantum chemistry István Mayer |
| title_fullStr | Simple theorems, proofs, and derivations in quantum chemistry István Mayer |
| title_full_unstemmed | Simple theorems, proofs, and derivations in quantum chemistry István Mayer |
| title_short | Simple theorems, proofs, and derivations in quantum chemistry |
| title_sort | simple theorems proofs and derivations in quantum chemistry |
| topic | Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd |
| topic_facet | Quantum chemistry Quantenchemie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009945294&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mayeristvan simpletheoremsproofsandderivationsinquantumchemistry |