START 2022 Scholarship of the Foundation for Polish Science

Winner: Sylwia Zięba, M.Sc.

Duration: 01.07.2022 - 30.06.2023

Aix-Mareseille University Scholarship in France

Winner: Arkadiusz Frąckowiak, PhD

Duration: 16.03.2022–13.04.2022

Chirality and electrical conductivity in new multifunctional materials for electronic applications

NAWA PHC Polonium between the Republic of Poland and the French Republic

BPN/BFR/2021/1/00001/U/00001

Coordinator: Iwona Olejniczak, PhD, DSc

Duration: 01.01.2022-31.12.2023

French Government BGF Scholarship

Winner: Arkadiusz Frąckowiak, PhD

Duration: 06.12.2021-15.03.2022

MINIATURA 3 - funded by the National Science Center

Head:  Arkadiusz Frąckowiak, PhD

Duration: 01.07.2021-30.11.2021

Influence of temperature and pressure on helical hydrogen bonding network of new solid electrolytes

PRELUDIUM 18 - funded by the National Science Center

2019/35/N/ST5/03324

Head: Sylwia Zięba, M.Sc.

Duration: 01.07.2020-31.07.2023

Scholarship of the Deutscher Akademischer Austauschdienst (DAAD)

Winner: Arkadiusz Frąckowiak, PhD

Duration: 01.09.2018–30.11.2018

Analysis of physicochemical properties of novel proton conductors derived from dicarboxylic acids

Diamentowy Grant, 6th edition - funded by the Ministry of Science and Higher Education

DI2016 015846

Head:  Sylwia Zięba, M.Sc.

Duration: 30.08.2017–29.08.2020

Production and optoelectronic properties of composites based on graphene oxide

the leader of the project was the AGH University of Science and Technology in Cracow

OPUS 9 - funded by the National Science Center

2015/17/ST8/01783

Coordinator: Kornelia Lewandowska, PhD

Duration: 13.03.2016–12.04.2020

Synthesis and photoelectrochemical properties of novel hybrid systems of graphene oxide with organic modifiers for application in molecular optoelectronics

Iuventus Plus Project, 4th edition - funded by the Ministry of Science and Higher Education

IP2014 025673

Head: Kornelia Lewandowska, PhD

Duration:19.03.2015–18.03.2017

Scholarship of the Deutscher Akademischer Austauschdienst (DAAD)

Winner: Andrzej Łapiński, PhD

Duration: 01.01.2015–28.02.2015

Multifunctional molecular materials: electronic and magnetic properties of molecular crystals

DAAD PPP-PL Program, Proj-ID 57154349

Coordinator: prof. dr hab. Roman Świetlik

Duration: 2015-2016

Investigations by IR and Raman spectroscopy of the role of hydrogen and halogen bonding in the formation of Mott insulator state in low dimensional organic conductors formed by tetrathiafulvalene (TTF) derivatives

HARMONIA - funded by the National Center for Science

Head: Prof. Roman Świetlik, PhD, DSc

Duration: 2012-2015

Photoelectrochemical characterization of thin films of organic semiconductors

FUGA - funded by the National Science Center

Head: Kornelia Lewandowska, PhD

Duration: 2012-2014

Functionalization of "small" carbon nano-onions with polyphenolic compounds and their potential application in elastin/collagen biosensors

The project leader was the University of Bialystok

UMO-2011/01/B/ST5/06051 - funded by the National Science Center

Coordinator: Andrzej Łapiński. PhD

Duration: 21.12.2011–20.12.2014

The effect of chemical bonding in selected fullerene-chromophore organic systems Promoter project - funded by the Ministry of Science and Higher Education.

(Promoter's grant - mgr. B. Laskowska, PhD student)

Head: prof. Andrzej Graja, PhD, DSc

Duration: 2010-2011

Infrared and Raman spectra of new magnetic and/or conductive organic charge-transfer salts

POLONIUM - funded by the Ministry of Science and Higher Education

(DPN/N9/POLONIUM/2009), executive protocol: 7818/R09/R10

Head: prof. Roman Swietlik, PhD, DSc

Duration: 2009-2011

Novel organic photoactive systems - molecular and electron structure, optical excitations, dynamics

N N202 260234 - funded by the Ministry of Science and Higher Education.

Head: prof. Andrzej Graja, PhD, DSc

Duration: 2008-2011

Magnetic charge-transfer salts formed by organometallic dithiolene complexes - studies of spectroscopic properties

N N202 207734 - funded by the Ministry of Science and Higher Education

Head: prof. Andrzej Graja, PhD, DSc

Duration: 11.09.2008 -10.10.2010

Characterization of novel supermolecular organic dye-fullerene systems in solution and Langmuir monolayers and Langmuir-Blodgett nanolayers, for applications in microtechnology

(Promoter grant - doctoral student K. Lewandowska, M.Sc.)

N N507 402035 - funded by the Ministry of Science and Higher Education.

Head: prof. Danuta Wróbel, PhD, DSc

Duration: 2008-2010

Magnetic charge-transfer salts formed by organometallic dithiolene complexes - studies of spectroscopic properties

N N202 207734 - funded by the Ministry of Science and Higher Education

Head: prof. Roman Świetlik, PhD, DSc

Duration: 11.04.2008–10.10.2010

Spectral properties of new asymmetric organic molecules and their ion-radical salts

(Promoter grant - doctoral student B. Barszcz, M.Sc.)

N N202 1209 33 - funded by the Ministry of Science and Higher Education.

Head: prof. Andrzej Graja, PhD, DSc

Duration: 02.11.2007-01.11.2008

Study of the vibrational and electron structures of a new class of conductors formed by electro-donor organic molecules

N N202 1330 33 - funded by the Ministry of Science and Higher Education

Head: Andrzej Łapiński, PhD

Duration: 28.08.2007-1.10.2009

Application of advanced spectral methods in the study of peramine as an alternative plant protection agent

N310 063 31/2813 - funded by the Ministry of Science and Higher Education

Head: Andrzej Łapiński, PhD

Duration: 26.09.2006–25.09.2008

Scholarship of the Deutscher Akademischer Austauschdienst (DAAD)

Winner: Iwona Olejniczak, PhD

Duration: February 2004

Magnetic ordering and electron pairing mechanisms in molecular hybrid materials

1 P03B 103 27- funded by the Ministry of Science and Higher Education.

Head: prof. Dr. Andrzej Graja, PhD, DSc

Duration: 23.08.2004–22.08.2007

Spectroscopic studies of charge ordering in organic conductors formed by BEDT-TTF and related molecules

2 P03B 087 22 - funded by the Ministry of Science and Higher Education.

Head: prof. Roman Świetlik, PhD, DSc

Duration: 1.04.2002-31.08.2004

Electrodynamics of organic molecular systems: a PAN/NSF collaboration study

NSF: INT-0086475

Head: Iwona Olejniczak, PhD

Duration: 2001-2004

NSF/NATO Postdoctoral Fellowship.

Postdoctoral Fellowship in Science and Engineering for Visiting Scientists from Cooperation Partner Countries

DGE 9804462

Winner: Iwona Olejniczak, PhD

Duration: 1998–1999

START 1998 Scholarship from the Foundation for Polish Science

Winner: Andrzej Łapiński, M.Sc.

Duration: 1998

Electron structure and electron-phonon interaction in charge-transfer salts of Pd(dddt)₂ and Ni(dddt)₂

(promoter grant - doctoral student A. Lapinski, M.Sc.)

2 P03B 113 15 - funded by the Ministry of Science and Higher Education

Head: Prof. Roman Swietlik, PhD, DSc

Duration: 1.07.1998-30.09.1999

IR spectroscopy of new metals and organic semiconductors: electron structure, electron-electron and electron-phonon interactions

2 P03B 112 12 - funded by the Ministry of Science and Higher Education.

Head: prof. Roman Świetlik, PhD, DSc

Duration: 1.04.1997 -31.03.2000

Investigation of fullerene complexes with organic molecules by vibrational spectroscopy methods

2 P302 255 06 - funded by the Ministry of Science and Higher Education.

Head: prof. Andrzej Graja, PhD, DSc

Duration: 1.05.1994-31.03.1996

• Univ Angers, CNRS, MOLTECH-Anjou, Angers, France
• Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS, Université Paris-Sud, Orsay, France.
• Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes), Rennes, France
• Aix-Marseille Université, Univ. de Toulon, CNRS, Institut Matériaux Microélectronique Nanosciences de Provence, Marseille, France
• Physikalisches Institut, Universität Stuttgart, Stuttgart, Germany
• Materials Science Divisions, Argonne National Laboratory, Argonne, USA
• Litvinenko Institute of Physical-Organic Chemistry and Coal Chemistry The National Academy of Science of Ukraine, Kiyv, Ukraine
• Faculty of Chemistry, University of the Basque Country UPV/EHU, Donostia International Physics Center (DIPC), Donostia, Euskadi, Spain
• Department of Pharmacognosy, Poznan University of Medical Sciences, Poznań
• Faculty of Chemistry, University of Bialystok, Białystok
• Faculty of Chemistry, Adam Mickiewicz University, Poznań
• Faculty of Mathematics and Natural Sciences; Institute of Chemistry, Jan Kochanowski University, Kielce
• Institute of Organic Chemistry Polish Academy of Sciences, Warszawa
• Institute of Low Temperature and Structure Research Polish Academy of Sciences, Wrocław
• The Faculty of Materials Engineering and Technical Physics, Poznan University of Technology, Poznań
• Academic Centre for Materials and Nanotechnology, AGH University of Science and Technology

Promoted doctorates

Malgorzata Widelicka

Defense Date: 2020-07-06 / Date of degree conferral: 2020-07-13

Subject: Optical, thermal, and transport properties of proton conductors of salts of dicarboxylic acids with different dimensionality of the hydrogen bonding network

Promoter: assoc. prof. Andrzej Łapiński, PhD, DSc

Reviewers: prof. Jan Baran, Ph.D., DSc, prof. Grażyna Bator, PhD, DSc

Aneta Pindela (née Suseł)

Defense date: 2020-07-02/ Date of degree conferral: 2020-08-26

Subject: Studies of the phenomenon of proton amine-imine tautomerism and stereoisomerism in 4-amino-1,3-thiazol-2(5H)-one derivatives

(interdisciplinary doctoral dissertation)

Promoters: prof. Andrzej Gzella, PhD, DSc,  assoc. prof. Andrzej Łapiński, PhD, DSc

Reviewers: prof. Michał Marszał, PhD, DSc, prof. Maciej Kozak, PhD, DSc

Arkadiusz Frąckowiak

Defense Date: 2015-12-02 / Date of degree conferral: 2016-02-16

Subject: Charge localization in organic conductors with hydrogen and halogen bonds - studies by optical spectroscopy methods

Promoter: prof. Roman Świetlik, PhD, DSc

Reviewers: prof. Bolesław Kozankiewicz, , PhD, DSc, prof. Jacek Ulański, PhD, DSc

Damian Jankowski

Defense Date: 2013-06-10 / Date of degree conferral: 2013-06-25

Subject: Spectroscopic studies of charge localization in one-dimensional organic conductors formed by TTF derivatives

Promoter: prof. Roman Świetlik, PhD, DSc

Reviewers: prof. Juliusz Sworakowski, PhD, DSc, prof. Jacek Ulański, PhD, DSc

Bolesław Barszcz

Date of defense: 2008-09-30 / Date of degree conferral: 2008-10-28

Subject: Normal vibrations and intramolecular excitations in selected organic conductors of TTF derivatives

Promoter: prof. Andrzej Graja, PhD, DSc

Reviewers: prof. Bolesław Kozankiewicz, PhD, DSc, prof. Juliusz Sworakowski, PhD, DSc

Master's degrees promoted

• Sc. Agata Piotrowska (2021)

• Sc. Adam Mizera (2017)

• Sc. Jacek Matysiak (2017)

• Sc. Natalia Rosiak (2017)

• Sc. Natalia Zborowska (2017)

• Sc. Sylwia Zięba (2017)

• Sc. Bartłomiej Gromadziński (2005)

• Sc. Alicja Gąsecka (2005)

• Sc. Krystian Klemt (2004)

• Sc. Bolesław Barszcz (2003)

• Sc. Roman Wesołowski (2002)

• Sc. Anna Szutarska (2001)

Promoted engineers

• Agata Piotrowska (2020)

• Michał Walczak (2017)

• Anna Wójcik (2017)

• Natalia Zborowska (2017)

• Adam Mizera (2016)

• Jacek Matysiak (2016)

• Natalia Rosiak (2016)

• Sylwia Zięba (2016)

• Michał Soja (2015)

Educational and popularization activities

• Lectures for doctoral students of the International Doctoral Program at IMP PAS entitled "Molecular Spectroscopy" delivered by Prof. Roman Swietlik (winter semester 2000/2001, summer semester 2001/2002 ).

• A series of lectures for doctoral students of the International Doctoral Program at IMP PAS entitled "Interactions of light with matter" delivered by Assoc. Prof. Andrzej Łapiński, (winter semester 2018, winter semester 2013).

• Laboratory classes entitled. "The phenomenon of light absorption in everyday life" was organized in 2018 for high school students at IMP PAS in Poznań - Sylwia Zięba, M.Sc. Adam Mizera, M.Sc.

• Popular science seminar entitled. "Photovoltaic boom" delivered as part of the European Funds Open Days on 10-05-2019 at IMP PAS - Bolesław Barszcz, Ph.D.

• Participation in the organization of demonstrations for young people as part of the Night of Scientists organized at the IMP PAS in Poznan in 2019: "Lights in the Dark" - Sylwia Zięba, M.Sc., Boleslaw Barszcz, Ph.D., and "Nitrogen madness" - Iwona Olejniczak, Ph.D., Arkadiusz Frąckowiak, Ph.D.

• Popular science lecture entitled. "Journey to the interior of the Earth - high pressures" delivered as part of the series "Fizyka Warta Poznania" 2019 at IMP PAS in Poznań - Sylwia Zięba, M.Sc.

• Preparation and conduct of interactive demonstrations as part of the XXII Poznań Festival of Science and Arts, April 9, 2019 - Iwona Olejniczak, Ph.D.

• Participation in the organization of demonstrations for young people as part of the Researchers' Night organized at the IMP PAS in Poznań in 2020: entitled. "Nitrogen madness" - Iwona Olejniczak, PhD, DSc, Boleslaw Barszcz, PhD, Arkadiusz Frąckowiak, PhD and "On the trail of greenhouse gases" - Iwona Olejniczak, PhD, DSc, Boleslaw Barszcz, PhD, Arkadiusz Frąckowiak, PhD

• Participation in the organization of demonstrations for young people as part of the Night of Scientists organized at IMP PAS in Poznan in 2021: "Planet Earth - Warm, getting warmer" - Iwona Olejniczak, Ph.D., DSc, Boleslaw Barszcz, Ph.D. and "Meeting with light" - Boleslaw Barszcz, Ph.D., Sylwia Zięba, M.Sc., Adam Mizera, M.Sc.

• Popular science lecture entitled. "Solar energy" delivered as part of the series "Fizyka Warta Poznania" in 2021 at the IFM PAN in Poznan - Boleslaw Barszcz, PhD

  Popular science lecture entitled. "Changing the world for the better - how to take care of the climate and the environment" delivered as part of the series "Fizyka Warta Poznania" in 2022 at the IMP PAS in Poznań - Iwona Olejniczak, Ph.D., DSc.

• Participation in the organization of the finals of the "Physics in Motion" competition in 2022 at the IMP PAS - Iwona Olejniczak, Ph.D., DSc, Boleslaw Barszcz, Ph.D., Adam Mizera, M.Sc.

FT-IR spectrometer Bruker Equinox 55 combined with FT-IR microscope Bruker Hyperion 2000 and accessories

The measuring system allows for recording spectra in polarized light from 30 to 18 000 cm^-1. The radiation sources in the spectrometer are a tungsten halogen lamp (1800-18000 cm^-1) and a silicon carbide ceramic rod (30-7000 cm^-1). The system is equipped with the following detectors: Si (operating in the range 10000-20000 cm^-1), InSb (3000-12500 cm^-1), MCT (400-7500 cm^-1), DLaTGS (180-12000 cm^-1) and DTGS (10-700 cm^-1). The instrument is equipped with the following beam splitters: quartz (3300-18000 cm^-1), KBr (370-7500 cm^-1), and Mylar (30-700 cm^-1). The spectrometer operates with a maximum spectral resolution of 0.5 cm^-1. FT-IR microscope Hyperion 2000 from Bruker attached to the spectrometer allows measuring reflection and transmission spectra in polarized light of micro samples with dimensions of fractions of a millimeter in the spectral range from 600 to 18000 cm^-1 as a function of temperature from 10 to 870 K. The microscope is equipped with an objective for recording reflection-absorption spectra from thin films applied to metallic substrates (600-6500 cm^-1). The microscope table (controlled by stepper motors) enables to study of the spatial distribution of substances in the material (spatial resolution of 1 mm). The diamond anvils allow for recording mid-infrared transmission spectra as a function of pressure (up to 20 GPa) at room temperature.

The spectrometer equipment includes the following components:

• Parker dry air purge system (the system is connected to the spectrometer and microscope)
• Bruker variable-angle reflectance accessory (enables recording of reflectance spectra in polarized light in the range from 400 to 7000 cm^-1 for angles of incidence and reflection from 10° to 80°)
• Gateway™ Attenuated Total Internal Reflection (ATR) accessory (six reflections horizontal ATR sampling system) to record ATR spectra as a function of temperature from room temperature to 200 °C in the spectral range from 600 to 7000 cm^-1)
• Beckman reflectance spectra accessory (enables the registration of reflectance spectra in a spectrometer chamber in the spectral range from 400 to 7000 cm^-1)
• Perkin-Elmer Diffuse Reflection (DRIFT) accessory (allows registration of reflectance-absorption spectra in the range of 400 to 7000 cm^-1)
• mirrors, cuvettes, and polarizers

Raman spectrometer LabRAM HR 800 Jobin Yvon and accessories

The spectrometer contains two diffraction gratings (600 and 1800 lines/mm), input and filter optics, and a multi-channel detector (CCD 1024´256) operating at liquid nitrogen temperature. It is equipped with a He–Ne laser (λ_ext = 632.8 nm), a tunable Stabilite 2017 argon laser with a power supply (λ_ext=454.5, 457.9, 465.8, 472.7, 476.5, 488.0, 496.5, 501.7, 514.5 nm) and a NIR laser with power supply (λ_ext=785 nm). The spectrometer is equipped with "Notch" type VLFIE filter sets: for 457 mm line (allowing approach to Rayleigh line at 150 cm^-1), for 488 mm line (allowing approach to Rayleigh line at 50 cm^-1), for 514 mm line (allowing approach to Rayleigh line at 50 cm^-1), for 633 mm line (allowing approach to Rayleigh line at 50 cm^-1), and for 785 mm line (allowing approach to Rayleigh line at 100 cm^-1). The spectrometer is equipped with an L-BXFM confocal microscope containing the following objectives: plan-achromatic objective ´10, NA=0.25, WD=10.6 mm, plan-achromatic objective ´50, NA=0.75, WD=0.37 mm, plan-achromatic lens ´100, NA=0.90, WD=0.21 mm, long-focus lens ´10, NA=0.25, WD=21 mm, long-focus lens ´20, NA=0.25, WD=12 mm, and macro-sample lens WD=40 mm. The LabRAM HR 800 Jobin Yvon Raman spectrometer is used to study Raman scattering spectra as a function of temperature and pressure.

Hitachi U-2900 NIR/Vis/UV Spectrometer

It enables the registration of absorption spectra in polarized light in the spectral range from 190 to 1100 nm of solid and liquid phase samples. Transmission and reflection spectra can be recorded at scan rates of: 10, 100, 200, 400, 800, 1200, 2400, and 3600 nm/min. The instrument has two radiation sources: a tungsten lamp (measurements in the visible light range) and a deuterium lamp (measurements in the ultraviolet light range). A silicon photodiode is used as a radiation detector. The spectrum measurement accuracy changes with the absorbance range change and is as follows: in the range from 0 to 0.5 ±0.002, from 0.5 to 1.0 ±0.004, and 1.0 to 2.0 ±0.008. The measurement error of transmittance value is equal to ±0.3%.

Hitachi F-7000 Spectrofluorimeter

Enables measurements of fluorescence, luminescence, and phosphorescence of solutions and solid samples as a function of temperature (Optistat CF cryostat by Oxford Inst). It is possible to perform measurements of fluorescence lifetime up to 1 ms. It is equipped with two monochromators allowing continuous selection of excitation and fluorescence emission wavelengths. The spectrofluorimeter is fitted with a set of edge filters and polarizers, allowing emission and excitation spectra to be measured in the range from 900 to 200 nm.

Conductivity measuring station

Specific electrical conductivity measurements are made using the four-electrode method. A Keithley 220 programmable current source allows current variations in the range of 1 nA - 100 mA, and a Keithley 182 digital voltmeter will enable measurements in the range of 3 mV - 30 V with a resolution of 1 nV - 10 μV. Temperature measurements are made in the range of 1.8 - 370 K. A 40 μm silver wire is used to attach the sample to the copper paths using a silver paste, which is also used for the electrodes. We can use gold or carbon paste (and other wire than silver) depending on our needs. The system allows the measurement of samples smaller than 1 mm (maximum about 1 cm).

Thermo-optical Analysis (TOA) Workstation

The thermo-optical analysis is a visual aid to observe physical effects during thermal analysis measurements. It allows for the determination of the temperature of the phase transition in the condensed phase under the occurrence of apparent texture changes in the tested material. This method is complementary to DSC, TG, or infrared measurements as a function of temperature. The measurement system consists of the following elements: stereo microscope Delta Optical IPOS 810 WS (objective plan achromat ´2 - maximum magnification ´400 together with coaxial illuminator, dark field module, photographic adapter with microscope camera), cryostat Linkam TC92 with accessories, multimeter - HP 34401a (ranges: 10 mA, 100 mA, 1A, 3A; maximum resolution: 10 nA), diode - OSRAM BPW 21 (dark current: 2 nA; wavelength 350-820 nm) and computer.

Temperature testing systems

• System for testing as a function of temperature from 1.8 to 370 K
  (Optistat CF optical cryostat by Oxford Inst. (sets of windows - KBr, KRS-5, quartz), Oxford Inst. ITC 503 thermoregulator, transfer line GFS 650, flowmeter PKR 251/26001, helium dewar 50 l, pump system: turbomolecular pump TSH 071E, membrane pump MVP 015, circulating pump, pressure gauge PKR 251 / 26001)
  Enables recording of fluorescence spectra as a function of temperature and is used in conductivity measurements.

• System for testing as a function of temperature from 4.2 to 300 K
  (Optical cryostat CF 2102 by Oxford Inst., thermoregulator Oxford Inst. ITC 503, transfer line GFS 650, flowmeter PKR 251/26001, helium dewar 50 l, pump system: turbomolecular pump TSH 071E, membrane pump MVP 015, circulation pump, pressure gauge PKR 251 / 26001).
  Enables absorption and reflection spectra recording in polarized light (600 -18000 cm^-1) and Raman scattering spectra.

• System for testing as a function of temperature from 77 K to 870 K
  (cryostat from Linkam Corp. TC92, Linkam Inst. thermoregulator, nitrogen dewar with desiccants for blowing the cryostat, heating line for cryostat housing)
  It enables the recording of absorption and reflection spectra in polarized light (600 -18000 cm^-1) and Raman scattering spectra and is used in the thermo-optical analysis (TOA).
• System for testing optical properties simultaneously as a function of temperature (4.2-300 K) and pressure (from atmospheric pressure to 20 GPa)
  (Optical cryostat CF 2102 by Oxford Inst. with equipment, diamond anvil Diacell D-07 placed on a cold finger of the cryostat - max. pressure 100 GPa)
  It allows the recording of Raman scattering spectra as a function of temperature and pressure.

Equipment for sample preparation

• chemistry lab
• Laurell W5-650MZ-23NPPB Rotary thin-film coater
• mechanosynthesis ball mill
• laboratory dryer
• KBr Pellet Making Die Set
• hydraulic press,
• laboratory balance
• cuvettes for gases (l=10 cm) and liquids (l = 0.1 mm - 50 mm) made of glass, quartz, NaCl, KRS-5, BaF2, KBr, CsJ
• diamond anvils,
• ED wire cutting machine for making holes in gaskets,
• device for assembling gaskets,
• ultrasonic cleaner,
• stereo microscope (max. 20),
• soldering station
• stereo microscope Delta Optical IPOS 810 WS (objective plan achromat 2 - maximum magnification 400 with coaxial illuminator, dark field module, and camera adapter

Computing stations

The software we use (Gaussian and Crystal programs) enables us to perform lattice vibration (phonon), vibrational, and electron transition calculations.